Abstract:
A machine for rotating a part includes a rotatable shaft having at least one first surface configured to form a first hydrostatic bearing between the first surface and a substantially cylindrical surface of a part rotationally mountable thereat such that the part rotates coaxially about the substantially cylindrical surface. The machine further includes a stationary fixture having at least one stationary surface having substantially a non-cylindrical shape that is positioned and configured to form a second hydrostatic bearing between the at least one stationary surface and a complementary surface on the part.

Description:
CROSS REFERENCE TO RELATED APPLICATION 
       [0001]    This application is a nonprovisional application of U.S. Provisional Patent Application No. 61/410,639, filed Nov. 5, 2010, the entire contents of which are incorporated herein by reference. 
     
    
     BACKGROUND 
       [0002]    A common problem in metrology and machining applications is how to rotate a part precisely coaxially to one of its cylindrical surfaces. The problem becomes significantly more difficult when sub-micron accuracy is required. Additional difficulties arise when fast throughput is required such as during mass production applications. One simple example is illustrated by part  1  in  FIG. 1  that has two precision openings, a first opening  2  and a second opening  3 . The run-out of surface  4  of the second opening  3  needs to be measured relative to an axis  5  of the first opening  2 . Typical systems to measure the run-out is to use high precision and very expensive equipment as with a Round Test Machine, for example (see  FIG. 2 ). The part  1  needs to be centered on a surface  14  of precisely rotating table  8  that is fixed by means of chuck  9 . The table  8  rotates around its rotational axis  10 . A high sensitivity pick-up sensor  11  with end ball  12  (usually made of a ruby) measures roundness of the first opening  2  at two different locations of cross-sections  6  and  7  (on  FIG. 1 ) and calculates the positions of geometrical centers for the cross-sections  6  and  7 . A straight line connecting centers of these cross-sections is considered a geometrical axis  15  of the first opening  2 . After the axis  15  is built and saved in memory of the measuring device computer, a roundness of the second opening  3  is measured and a geometrical center of its cross-section is found. A doubled distance between a center of the second opening  3  and an axis of the first opening  2  will be a number describing the surface&#39;s  4  run-out relative to the axis  5  of the first opening  2 . 
         [0003]    For this measurement to be made correctly, the foregoing procedure requires very expensive equipment and highly skilled operators. If an external surface  13  of the part  1  is not finished precisely or if it is not round, the operation to center the part  1  on the table  8  will be time consuming. The distance between the rotational axis  10  of the table  8  and the to be determined geometrical axis  15  of the first opening  2  has to be minimal and less than the measuring range of the sensor  11 . Additionally, the likely out of roundness condition as measured at the cross-sections  6  and  7  in the first opening  2  will affect the calculated position of the axis  15  of the first opening  2 . The magnitudes of the foregoing difficulties are amplified as precision of machining operations increases. Lets assume, for example, that the precision first opening  2  in the part  1  is finished and that the second opening  3  needs to be ground precisely concentric to the previously finished first opening  2 . Current methods and systems are not available to quickly and precisely align the axis of first opening  2  to make it coaxial to the rotational axis of a grinding machine&#39;s spindle. The most precise and advanced Round Test Device grinding machines currently available are not capable of making the powerful measurements described above. 
         [0004]    Machines and methods to precisely rotate a part about an average geometrical axis of a cylindrical surface on the part are always of interest to those in the art. 
       BRIEF DESCRIPTION 
       [0005]    Disclosed herein is a machine for rotating a part. The machine includes a rotatable shaft having at least one first surface configured to form a first hydrostatic bearing between the first surface and a substantially cylindrical surface of a part rotationally mountable thereat such that the part rotates coaxially about the substantially cylindrical surface. The machine further includes a stationary fixture having at least one stationary surface having substantially a non-cylindrical shape that is positioned and configured to form a second hydrostatic bearing between the at least one stationary surface and a complementary surface on the part. 
         [0006]    Further disclosed herein is a machine for rotating a part. The machine includes, a rotatable shaft having at least one first surface configured to form a hydrostatic bearing with a substantially cylindrical surface of the part and at least one second surface oriented substantially perpendicular to a rotational axis of the rotatable shaft configured to form a second hydrostatic bearing with a second surface of the part, and a stationary fixture having a third surface oriented substantially parallel to the second surface configured to form a third hydrostatic bearing with a third surface of the part. 
         [0007]    Further disclosed herein is a method of rotating a part about a geometrical axis of a cylindrical surface thereon with a machine. The method includes, radially hydrostatically supporting the part with a hydrostatic bearing formed between the cylindrical surface of the part and a first surface of a shaft of the machine, longitudinally positioning the part with two hydrostatic bearings urging the part in longitudinally opposing directions, each of the two hydrostatic bearings having one surface of the bearing on the part and an opposing surface of the bearing on the machine, rotating the shaft, and rotating one of two surfaces of the machine defining one of the two hydrostatic bearings while maintaining the other of the two surfaces of the machine stationary. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0008]    The following descriptions should not be considered limiting in any way. With reference to the accompanying drawings, like elements are numbered alike: 
           [0009]      FIG. 1  depicts an example of a part with a surface of a second opening that is to be aligned (as if for machining) precisely coaxially to a first opening; 
           [0010]      FIG. 2  depicts a set up configured to measure non-coaxiality between a second opening and a first opening using a Round Test Device; 
           [0011]      FIG. 3  depicts a machine disclosed herein that is configured to rotate the part of  FIG. 1  coaxial to the first opening; 
           [0012]      FIG. 4   a  depicts a part rotationally supported by stepped journal bearings having inclined surfaces; and 
           [0013]      FIG. 4   b  depicts a cross-sectional view of  FIG. 4   a  taken at arrows A-A illustrating portions of journal bearings defined in part by the inclined surfaces. 
       
    
    
     DETAILED DESCRIPTION 
       [0014]    A detailed description of one or more embodiments of the disclosed apparatus and method are presented herein by way of exemplification and not limitation with reference to the Figures. 
         [0015]    The part  1  shown on the  FIG. 1  is used as an example only to describe a machine  16  disclosed herein in detail. Alternate parts having internal or external cylindrical surfaces could just as well be employed to aid in describing the machine  16  disclosed herein. 
         [0016]    Referring to  FIG. 2 , a spindle housing  20  is mounted on the base  21 . Technological shaft  23  is clamped to the rotating spindle&#39;s shaft  22  by means of the technological shaft&#39;s flange  24 . The technological shaft  23  has two independent rows of hydrostatic journal bearings  29  and  30  shown schematically as cylindrical surfaces. An annular groove  27  in the flange  24  functions as an axial thrust hydrostatic bearing  27 . A non-rotating fixture  25  is mounted to the non-rotating spindle housing  20  and supports a cover  26  that includes an annular groove  28  configured to preload the axial thrust hydrostatic bearing  27 . 
         [0017]    A part  31  to be rotated is mounted onto the shaft  23  and is radially separated from the shaft by journal hydrostatic bearings  29  and  30 . Axial separation between the part  31  and the flange  24  is maintained by the axial thrust hydrostatic bearing  27 . The bearing  27  is preloaded with via pressurized fluid such as oil, for example, supplied to the annular groove  28  through channel  35 . 
         [0018]    Similarly, oil is supplied to recesses  33  of the journal bearings  29  and  30  through a channel  44  and inlet restrictors  43 . Oil is also supplied to the thrust bearing groove  27  through channel  36  and inlet restrictor  37 . 
         [0019]    As the spindle shaft  22  and the technological shaft  23  attached thereto start to rotate, the part  31  will also start to rotate because of viscous friction in oil in the grooves  27 ,  28  and the recesses  33 , as well as the gaps  34  that straddle each of the grooves  27 ,  28  and each of the recesses  33 . The viscous friction between the shaft  23  and part  31  will transfer torque to the part  31  in the direction of rotation, while the viscous friction between the part  31  and the non-rotating cover  26  will transfer torque to the rotating spindle shaft  22  against the direction of rotation. As a result of these frictional forces, the rotational speed of the part  31  will be lower than the rotational speed of the shaft  23 . The ratio between the rotational speed of the part  31  and the rotational speed of the shaft  23  will be defined by a ratio between frictional torque urging the part  31  to rotate and frictional torque urging the part  31  not to rotate. 
         [0020]    The foregoing structure of the machine  16  will cause the part  31  to rotate exactly around its geometrical axis  15 . The machine  16  causes an internal surface  41  of the first opening  2  of the part  31  to generate rotation about itself. This is helpful because it is the internal surface  41  that needs to be aligned coaxial to the geometrical axis  15 . Additionally, since hydrostatic support will average the geometrical errors in the first opening  2  of the part  31 , the described method can be even more accurate than the most precise Round Test Devices. 
         [0021]    Oil that makes its way from the grooves  27 ,  28  and the recesses  33  through the gaps  34  and into annular chambers  38 ,  39  and  42  is ported back to a hydraulic power unit through lines that are not shown. Oil that makes its way from the annular preloading groove  28  and the recess  33  of the journal bearing  30  through the gaps  34  and into the chamber  40  can be directed to the surface  4  of the opening  3 , wherein it can be either ported back to the hydraulic power unit or it can be used as a grinding coolant in the case where the surface  4  is to be machined. 
         [0022]    Equations to quantify rotational speeds based upon frictional forces include the following: Frictional torque that urges the part  31  to rotate is designated M 1 , and frictional torque that urges the part  31  to stop rotating is designated M 2 . Because the frictional torques caused by the oil viscosity are proportional to the relative speed between matched surfaces, the torques M 1  and M 2  can be expressed as follows: 
         [0000]        M   1   =K   1 (ω 1 −ω)  (1)
 
         [0000]        M   2   =K   2 ω  (2)
 
         [0000]    where ω 1  is the rotational speed of shafts  22  and  23 , ω is the speed of the part  31 , K 1  and K 2  are proportionality coefficients depending on oil viscosity, the gaps  34  (both radial and axial) and sizes of the matched surfaces. 
         [0023]    The dynamic equation of rotational speed ω for the part  31  can be written as follows: 
         [0000]    
       
         
           
             
               
                 
                   
                     J 
                      
                     
                       
                          
                         ω 
                       
                       
                          
                         t 
                       
                     
                   
                   = 
                   
                     
                       
                         M 
                         1 
                       
                       - 
                       
                         M 
                         2 
                       
                     
                     = 
                     
                       
                         
                           K 
                           1 
                         
                          
                         
                           ( 
                           
                             
                               ω 
                               1 
                             
                             - 
                             ω 
                           
                           ) 
                         
                       
                       - 
                       
                         
                           K 
                           2 
                         
                          
                         ω 
                       
                     
                   
                 
               
               
                 
                   ( 
                   3 
                   ) 
                 
               
             
           
         
       
     
         [0000]    where J is the inertia moment of the part  31 . Speed will be stabilized when the right portion of equation (3) is equal to zero. As such, the equation for the speed ω can be written: 
         [0000]        K (ω 1 −ω)− K   2 ω=0  (4)
 
         [0000]    and, finally, the part&#39;s  31  rotational speed ω will be expressed through the spindle shaft&#39;s  22  and the technological shaft&#39;s  23  rotational speeds ω 1  in the following way: 
         [0000]    
       
         
           
             
               
                 
                   ω 
                   = 
                   
                     
                       
                         K 
                         1 
                       
                       
                         
                           K 
                           1 
                         
                         + 
                         
                           K 
                           2 
                         
                       
                     
                      
                     
                       ω 
                       1 
                     
                   
                 
               
               
                 
                   ( 
                   5 
                   ) 
                 
               
             
           
         
       
     
         [0024]    It should be noted that the machine  16  disclosed in  FIG. 3  can employ any hydrostatic journal bearings between the part  31  and the technological shaft  23 . For example stepped hydrostatic bearings that do not require separately inlet restrictors could be used. One type bearing that also increases a radial stiffness and load capacity of the bearing is a journal stepped bearing similar to that disclosed in the U.S. Pat. No. 3,387,899 by Robert Hahn and David Youden. 
         [0025]    Referring to  FIGS. 4   a  and  4   b , a partial cross-sectional view of a technological shaft  51  of an alternate embodiment of the machine disclosed herein is illustrated. The shaft  51  provides radial support to a part  50 . The shaft  51  has two independent stepped journal bearings  62 ,  63  with each having a cylindrical portion  52  and non-cylindrical portion  53 . The non-cylindrical portions  53  have a number of inclined surfaces  60  defining gaps  58  having varying radial dimensions between the inclined surfaces  60  and the part  50  (as best seen in  FIG. 4   b ). The minimal gap  64  between the inclined surfaces  60  and an internal surface  66  of the part  50  is larger or equal to annular gaps  65  defined between the cylindrical portions  52  and the internal surface  66 . High pressure liquid media, such as oil, for example, is supplied to annular chamber  55  through passage  54 . From the chamber  55  oil moves through the gaps  58  and  65  to annular chambers  56  and  57 . From chamber  56 , oil is collected and returned back to a hydraulic power unit (not shown). Oil moving to the chamber  57  can either be collected and returned to the hydraulic power unit or be used as a coolant for a grinding process. 
         [0026]    A hydrostatic component of the radial stiffness is generated by a difference between a size of the annular gap  65  in the cylindrical portions  52  and an average size of the gaps  58  in the non-cylindrical portions  53  (in a similar manner as is used in a typical stepped hydrostatic bearings). 
         [0027]    A hydrodynamic component of the radial stiffness is generated by oil pressure distributed to the inclined gaps  58  of the non-cylindrical portions  53 . The hydrostatic portion of stiffness is defined mainly by supply pressure, while the hydrodynamic portion is defined mainly by and is proportional to differences in rotational speeds between the shaft  51  and the part  50 . 
         [0028]    While the invention has been described with reference to an exemplary embodiment or embodiments, it will be understood by those skilled in the art that various changes may be made and equivalents may be substituted for elements thereof without departing from the scope of the invention. In addition, many modifications may be made to adapt a particular situation or material to the teachings of the invention without departing from the essential scope thereof. Therefore, it is intended that the invention not be limited to the particular embodiment disclosed as the best mode contemplated for carrying out this invention, but that the invention will include all embodiments falling within the scope of the claims. Also, in the drawings and the description, there have been disclosed exemplary embodiments of the invention and, although specific terms may have been employed, they are unless otherwise stated used in a generic and descriptive sense only and not for purposes of limitation, the scope of the invention therefore not being so limited. Moreover, the use of the terms first, second, etc. do not denote any order or importance, but rather the terms first, second, etc. are used to distinguish one element from another. Furthermore, the use of the terms a, an, etc. do not denote a limitation of quantity, but rather denote the presence of at least one of the referenced item.