Abstract:
A compact surface self-compensated hydrostatic bearing includes a rotor assembly including a rotor plate having upper and lower fluid restricting faces, a rotor top and bottom, each having bearing surfaces angled with respect to an axis of rotation of the rotor assembly; a stator assembly including a stator top and a stator bottom housing the rotor assembly therebetween, the stator top and bottom having bearing surfaces facing and spaced apart from the rotor top and bottom bearing surfaces forming upper and lower bearing gaps, respectively, therebetween; the stator top and bottom including a lower and an upper fluid restricting surface, respectively, facing and spaced apart from the rotor upper and rotor lower fluid restricting faces, respectively, forming upper and lower restricting gaps, respectively, therebetween; and a fluid supply system configured to supply pressurized fluid to the bearing gaps and into the upper and lower fluid restricting gaps.

Description:
This application claims priority to U.S. Provisional Patent Application Ser. No. 60/813,084 filed Jun. 13, 2006, incorporated herein by reference. 

   FIELD OF THE INVENTION 
   The invention relates to hydrostatic bearings systems. More specifically, the invention relates to compact surface self-compensated hydrostatic bearing systems for use in, for example, precision machine tools. 
   BACKGROUND OF THE INVENTION 
   In order to exhibit static stiffness, hydrostatic bearings must regulate flow into the bearing pockets with a restrictor, feedback system, or the like. This enables the bearing to counteract externally applied loads by varying the fluid pressure in individual bearing pockets. Many hydrostatic bearings in machine tool applications use fixed resistance restrictors, such as orifices or capillaries, whose resistances are nominally equal to the flow resistance out of the bearing pocket. However, in order to achieve accuracy, the restrictors&#39; flow resistance must all be equal or of a specific ratio. Also, because, capillary resistance, for example, varies with the fourth power of the diameter, tuning all the restrictors can be time consuming. Further, because one restrictor is required for each bearing pocket, including as many bearing pockets as possible in order to enhance averaging and improve accuracy greatly increases cost. Thus, rolling element bearings are often used whenever possible in machine tools. 
   Hydrostatic bearings&#39; advantages and disadvantages were recognized early, and in the 1940&#39;s self-compensating bearing systems were developed using an opposed gap as a means to regulate flow to bearing pockets located on opposite sides of the bearing. In the 1960&#39;s, bearings were introduced that employed an atypical aerostatic bearing design that achieved compensation by including grooves of a precise depth on the surface of a shaft, which acted as flow restrictors. This form of regulating the flow on the surface also eliminated the need for separate restrictors. However, in such configurations, since the grooves act as restrictors, they must be machined or etched to a very precise depth and width that is matched to the radial clearance. One example of an aerostatic bearing design is the BlockHead™ aerostatic spindle developed by Professional Instruments Corp. 
   In contrast to aerostatic bearings, however, hydrostatic bearings offer substantially greater load capacity than aerostatic bearings. Conventional self-compensation methods for hydrostatic bearings were thus refined and incorporated into many different types of precision grinding machines developed primarily for machines used for grinding bearing rings. Self-compensation bearings were also developed that were used mainly for precision grinding and diamond turning machines. Other refinements of self-compensation were also developed, but required either cross-drilled holes or external plumbing to route the fluid from the compensating structures on one side of the bearing to the pockets on the other side. Alternatively, elastically deforming elements were also used to tune the compensation, but these designs add complexity and cost. 
   Conventional self-compensated bearings, which are less prone to clogging and have fewer parts, are desirable because their primary advantage is that their stiffness is not adversely affected by bearing gaps that are smaller or larger than intended; however, their stiffness is still finite and generally lower than ball or roller bearings. As a result, servostatic bearings were developed, where the fluid flow to the pockets was actively regulated by measurement of bearing gaps and the use of servo valves to achieve “infinite” stiffness. On the other hand, the rest of the machine structure is not infinitely stiff, and a valve on every pocket can become very expensive very quickly. Thus, this attempt to improve self-compensated bearings is also not without its drawbacks. 
   Moreover, the previous self-compensation designs required cross-drilling or the use of external fluid lines to connect the compensator to the opposed pad. Other designs evolved this general principle to create, for example, a thrust bearing where the compensation for the thrust lands came from features on the shaft radius. This was a forerunner of the present design; however, these designs still required the groove depths to be carefully tuned to the radial clearance. Ultimately, the first true surface self-compensating bearing was created where the compensating features are located opposite the pockets, so compensation is gap independent and the compensating features are then connected to the pockets via channels on the surface of the bearing. A high speed flow theory for this design concept was developed, and showed that it was robust enough that it could even be cast, including all the pockets and compensation features. Furthermore, surface self-compensation designs evolved to create a modular profile rail hydrostatic bearing. These designs, however, still do not lend themselves to low profile rotary tables, and hence angular surface self-compensated rotary bearings were initially developed. In this configuration, the assembly of elements used was evolved from the modular profile rail hydrostatic bearing, including the vertical orientation of the restrictor element; however, a simpler more accurate design still is needed in order to make the system mass-producible. 
   SUMMARY OF THE INVENTION 
   Accordingly, the present invention provides a surface self compensated hydrostatic bearing for use in precision machine tools, having, in combination, a rotor assembly, a stator assembly attached to a machine bed, a fluid pressure source and distribution system to supply pressurized fluid to keep the rotor assembly from making physical contact with the stator assembly. 
   In a first aspect, the invention provides a self-compensated hydrostatic bearing system comprising a rotor assembly including a rotor plate having an upper fluid restricting face and a lower fluid restricting face, and a rotor top and a rotor bottom having bearing surfaces angled with respect to an axis of rotation of the rotor assembly. Also included is a stator assembly including a stator top and a stator bottom attached to one another and housing at least a portion of the rotor assembly therebetween, the stator top having a bearing surface facing and spaced apart from the rotor top bearing surface forming upper bearing gaps therebetween, and the stator bottom having a bearing surface facing and spaced apart from the rotor bottom bearing surface forming lower bearing gaps therebetween. The stator top further includes a lower fluid restricting surface facing and spaced apart from the rotor upper fluid restricting face forming upper restricting gaps therebetween, and the stator bottom further includes an upper fluid restricting surface facing and spaced apart from the rotor lower fluid restricting face forming lower restricting gaps therebetween. The system further includes a fluid supply system configured to supply pressurized fluid to the upper and lower bearing gaps and into the upper and lower fluid restricting gaps. 
   In a second aspect, the invention provides a linear self-compensated hydrostatic bearing system. The system includes a rail assembly including a rail top and a rail bottom having bearing surfaces angled with respect to an axis of rotation of the rotor assembly; a carriage bearing assembly including a carriage bearing plate having an upper fluid restricting face and a lower fluid restricting face, a carriage bearing top and a carriage bearing bottom attached to one another and housing at least a portion of he rail assembly therebetween, the carriage bearing top having a bearing surface facing and spaced apart from the rotor top bearing surface forming upper bearing gaps therebetween; and the carriage bearing bottom having a bearing surface facing and spaced apart from the rail bottom bearing surface forming lower bearing gaps therebetween. The carriage bearing top further includes a lower fluid restricting surface facing and spaced apart from the rail upper fluid restricting face forming upper restricting gaps therebetween. The carriage bearing bottom further includes an upper fluid restricting surface facing and spaced apart from the rail lower fluid restricting face forming lower restricting gaps therebetween. The system also includes a fluid supply system configured to supply pressurized fluid to the bearing gaps and into the upper and lower fluid restricting gaps. 
   In a third aspect, the invention provides a method for providing self-compensation in a hydrostatic bearing system comprising the step of introducing a pressurized fluid to a concentrically mated rotor assembly and stator assembly having flowpaths formed therebetween. The flowpaths include upper and lower bearing gaps formed between rotor top and bottom bearing surfaces which are angled with respect to an axis of rotation of the rotor assembly, and corresponding bearing surfaces of a stator top and stator bottom of the stator assembly. The flowpaths further include upper and lower restricting gaps formed between rotor upper and lower fluid restricting surfaces and corresponding stator top and bottom lower and upper restricting surfaces, respectively. In response to displacement of the rotor assembly from an original position relative to the stator assembly, the pressurized fluid flowing through the flowpaths imparts pressure feedback to restore the rotor assembly to substantially the original position. 

   
     BRIEF DESCRIPTION OF DRAWINGS 
     The present invention will now be described with reference to the accompanying drawing in which: 
       FIG. 1  is an isometric cut-away view of the rotary hydrostatic bearing of the present invention; 
       FIG. 2  is an exploded view of the rotary hydrostatic bearing of the present invention; 
       FIG. 3  is a side view of the rotor assembly of the present invention; 
       FIG. 4  is a cross section of the hydrostatic bearing of the present invention showing the flowpath of fluid through the bearing gaps; 
       FIG. 5  is a close up view of a fluid restricting gap of the present invention; 
       FIG. 6  is a close up view of a bearing gap of the present invention; 
       FIG. 7  is a cross section illustrating how pocket pressures respond to oppose an axial displacement of the rotor; 
       FIG. 8  is a cross section illustrating how pocket pressures respond to oppose a radial displacement of the rotor; 
       FIG. 9  is a cross section illustrating how pocket pressures respond to oppose a tilt displacement of the rotor; 
       FIG. 10  is a cross section of the bearing of the present invention integrated with a brushless drive motor; 
       FIG. 11  is a cross section of a compact embodiment having a thinner rotor plate and no supply grooves or relief grooves; 
       FIG. 12  is a cross section illustrating the use of alignment pins as a means of achieving precise alignment between mated rotor parts and mated stator parts. 
       FIG. 13  is a cross section illustrating the use of shoulders as a means of achieving precise alignment between mated rotor parts and mated stator parts. 
       FIG. 14  is a cross section of the present invention applied to a compact linear bearing. 
       FIG. 15  is a cross section of the present invention applied to a linear bearing with a face-to-face bearing land configuration. 
   

   DETAILED DESCRIPTION OF THE INVENTION 
   The present invention relates to a rotary hydrostatic bearing system for use in precision machine tools, having, in combination, a rotor assembly, a stator assembly attached to a machine bed, a fluid pressure source and distribution system to supply pressurized fluid to keep the rotor assembly from making physical contact with the stator assembly. 
   In the present invention, flow restriction, or compensation, between the pressure supply and the load supporting surfaces is provided by a geometry that is an integral part of the system formed onto components that make up the assembly. In particular, the geometry is especially well suited for use in spindles and rotary tables, but it can also be used for linear motion systems. The invention establishes the relative position of a rotor assembly to a stator assembly with the use of a novel arrangement of precision surfaces, which result in a highly rigid and stable hydrostatic bearing, particularly in axial and tilt modes of loading. 
   For a rotary bearing application, such as in a spindle or a rotary table, the system provides concentric mating parts that, when viewed as a cross section with the bearing axis oriented vertically, form horizontal restricting gaps that feed acutely angled bearing pockets and bearing lands. By orienting the lands at an acute angle relative to the restricting gaps, preferably in the range of 40 to 50 degrees, the effective hydrostatic feedback due to axial and tilt displacements will be greater than a system that uses fixed restrictors, such as capillaries or orifices. This is because an axial displacement, by virtue of its orientation, will cause both the restrictor gaps to open and the bearing gaps to close (or visa versa), thus roughly doubling the pocket pressure increase (or decrease) that occurs as compared to a fixed restrictor scenario. The present invention exploits this principle to provide a remarkably simple and rigid bearing assembly. 
   The rotor assembly includes a rotor plate, such as a disk, sandwiched between a rotor top and a rotor bottom where the rotor plate with flat and parallel upper and lower faces act as fluid flow restriction surfaces. The rotor top has a lower face which mates with a portion of the upper fluid restricting face of the rotor plate. A conical bearing surface forms an acute angle with the upper fluid restricting face of the rotor plate and the conical bearing surface of the rotor top. Hydrostatic bearing pockets are formed thereon. The rotor bottom has a configuration including essentially mirror image hydrostatic surfaces of the rotor top. 
   The stator assembly has a stator bottom having a conical surface which forms an acute angle with the rotor plate&#39;s upper fluid restricting face, and a second upper face which is parallel to and located at a height “H” above the rotor plate&#39;s upper fluid restricting face where “H” is slightly larger than the thickness of said rotor plate. The stator top has a configuration that is essentially a mirror image of the hydrostatic surfaces of the stator bottom. The stator assembly houses at least a portion of the rotor assembly between the stator top and stator bottom, for example as shown in the cross-sectional view of  FIG. 4 . Alternatively, the entire rotor assembly may be housed in the stator assembly. 
   The rotor assembly parts and stator assembly parts are sized and assembled concentrically so that small gaps, for example, on the order of about 3 micrometers to about 100 micrometers, suitable for hydrostatic bearing operation, are present between the fluid restricting faces and the conical bearing surfaces. Supply passages direct pressurized fluid to the fluid restricting gaps. The stator assembly also has internal passages and one or more drain holes to allow fluid to exit the bearing. As a result, the system includes a large diameter to height ratio, making it highly compact and rigid and, it is believed, more dynamically stable, while using a minimal number of parts and precision surfaces. Thus, manufacturing costs and complexity are minimized while achieving ultra low error motion with high structural and hydrostatic rigidity in all modes of deflection, particularly in tilt mode—often the critical mode of compliance in practical precision machining operations. 
   In addition, the system is less prone to clogging by virtue of fluid restricting surfaces that move relative to one another, as compared to bearings with static fluid restricting orifices or capillaries. The surface self compensation of the present invention may also be applied to linear motion systems, where the cross section profile of the rotary bearing is essentially extruded linearly to define a carriage assembly. The carriage assembly comprises a left hand side, a right hand side and a top plate, and a rail assembly comprising a left hand side and a right hand side which are mirror images of each other. 
   The present invention will now be discussed in further detail, with reference to the Figures.  FIG. 1  is an isometric cut-away view of the hydrostatic bearing of the present invention.  FIG. 2  illustrates an exploded view of the hydrostatic bearing according to the present invention. As shown in  FIGS. 1 and 2 , the invention includes rotor assembly  1  and a stator assembly  2 . Rotor assembly  1  comprises rotor top  3 , rotor plate  4 , rotor bottom  5 , and motor adaptor plate  6 , all rigidly affixed to one another by bolts passing through bolt holes such as bolt hole  40 . Stator assembly  2  comprises stator top  7 , stator bottom  8 , and stator base  9 , all rigidly affixed to one another by bolts passing through bolt holes such as bolt hole  41 . Pressurized fluid enters supply port  10  and drains at atmospheric pressure through drain hole  11 . 
   Optionally, the invention further provides internal drainage passages where at least one can be switched from drainage to pressure to bias the pressure forces on the bearing which acts to lock the bearing in a fixed desired position. 
     FIG. 3  shows a side view of rotor assembly  1 , showing upper fluid restricting face  15  and lower fluid restricting face  23  on rotor plate  4 , conical bearing surface  13  on rotor top  3 , and conical bearing surface  14  on rotor bottom  5 . Hydrostatic pockets such as pocket  12  are present on both conical bearing surfaces  13  and  14 . Also present are bearing lands that restrict flow to the atmosphere such as bearing land  18 , and leakage lands that restrict flow between pockets such as leakage land  17 . 
     FIG. 4  illustrates cross-sectional view of the fluid flowpath through the bearing of the present invention. For illustrative purposes, the gaps shown between stator assembly  2  and rotor assembly  1  are greatly exaggerated relative to the depth of the pockets. Pressurized fluid enters supply port  10  and fills supply channel  21 , and then flows into upper restrictor gap  42  and lower restrictor gap  43 . On the upper bearing half, fluid flows from restrictor gap  42  into the upper pockets, such as pocket  46 , and then through bearing gap  44 , where it exists at atmospheric pressure. The fluid then drains via gravity through internal passages such as passage  32 , into trough  38 , and then through drain hole  11 . On the lower bearing half, after exiting restrictor gap  43 , fluid flows into the lower pockets, such as pocket  27 , then through bearing gap  45 , where it exits at atmospheric pressure. Fluid then drains via gravity into drain trough  38  and then through drain hole  11 . 
   Restrictor gaps  42  and  43  and bearing gaps  44  and  45 , as shown in  FIG. 4 , are to be manufactured to be equal to one another, with a target gap ranging from 10 micrometers to 20 micrometers, and with a tolerance of typically plus or minus 1 micrometer. Depending on the design requirements however, the gap target can be as small as 3 micrometers for a small bearing (e.g. an outer diameter of about 50 mm or less) designed to use water or air as the fluid, or as large as 100 micrometers for a very large bearing (e.g. an outer diameter of 1000 mm or greater) designed to use a high viscosity hydraulic oil as the fluid. The corresponding gap tolerance would typically be on the order of one tenth to one fifth of the target bearing gap. 
   An advantage of the present design is the relative ease with which the restrictor gaps and bearing gaps can be increased or decreased so as to match each other within a desired tolerance. If, after manufacturing, restrictor gaps  42  and  43 , and bearing gaps  44  and  45  are found to be out of tolerance, either rotor plate  4  can be re-ground to reduce rotor thickness  35 , or face  37  on stator bottom  8  can be re-ground to reduce the height  36  from fluid restricting face  24  on stator bottom  8 . When rotor plate  4  is re-ground, restrictor gaps  42  and  43  will increase and bearing gaps  44  and  45  will decrease. When face  37  of stator bottom  8  is re-ground, the opposite effect will result, i.e. restrictor gaps  42  and  43  will decrease and bearing gaps  44  and  45  will increase. By these means, the gaps can be adjusted and matched via relatively simple grinding operations. 
   In order to prevent shorting between adjacent pockets, sharp edge  33  on stator top  7  and sharp edge  34  on stator bottom  8  must be left sharp after grinding, and handled with care during assembly to prevent damage to them. Once the bearing is assembled, the sharp edges are protected, and no special handling precautions are needed. Alternatively, the sharp edges can be chamfered to a specific dimension, particularly if they are made of ceramic components. 
     FIG. 5  shows a close up view of the region around lower restrictor gap  43 . For illustrative purposes, the size of restrictor gap  43  and bearing gap  45  are shown greatly exaggerated as compared to depth  39  of supply groove  22  and depth  47  of bearing pocket  27 . In a practical bearing, depth  39  and depth  47  would be 10 times that of gaps  43  and  45 , or deeper, to minimize the pressure drop in those features. As shown, restrictor gap  43  is bounded by lower fluid restricting face  23  on rotor plate  4 , and by upper fluid restricting face  24  on stator bottom  8 . Bearing gap  45  is bounded by conical bearing surface  14  on rotor bottom  5  and conical bearing surface  25  on stator bottom  8 . Tracing the flowpath shown, fluid enters lower supply groove  22 , flows through restrictor gap  43 , and then flows into lower bearing pocket  27  located on conical bearing surface  14 . Some fluid also flows in the leakage land regions between the pockets where bearing gap  45  is present. 
     FIG. 6  shows a close up view of the region around lower bearing gap  45 . For illustrative purposes, the size of bearing gap  45  is shown greatly exaggerated as compared to depth  47  of bearing pocket  27 , and depth  48  of relief groove  49 . In practice, depth  47  and depth  48  would be 10 times that of gaps  43  and  45 , or deeper, to minimize the pressure drop in these areas. As shown, bearing gap  45  is bounded by conical bearing surface  14  on rotor bottom  5  and conical bearing surface  25  on stator bottom  8 . Tracing the flowpath, fluid in bearing pocket  27  flows through bearing gap  45  and exhausts at nearly atmospheric pressure into relief groove  49 . 
     FIG. 7  illustrates how the bearing pocket pressures respond to oppose an axial displacement of the bearing rotor. When rotor assembly  1  is displaced downward relative to stator assembly  2 , upper restrictor gap  50  opens, and upper bearing gap  51  closes. These both act to cause pocket pressures  52  and  55  in upper pockets  53  and  54  to increase. When rotor assembly  1  is displaced downward, lower restrictor gap  56 , conversely, closes, and lower bearing gap  57  opens. These both act to cause pocket pressures  58  and  61  in lower pockets  59  and  60  to decrease, as shown in  FIGS. 7-9  by the lengths of the elongated arrows. Both of the described pressure changes result in a net upward force on rotor assembly  1 , thus acting to restore it to its original undisplaced position. 
   For the axial mode of displacement, due to the fact that the restrictor gaps are modulated in addition to the bearing gaps, more pressure feedback occurs than would result from a conventional fixed restrictor bearing (which might include orifices or capillaries to provide the fluid restricting function). The factor of improvement in given axial displacement can be more than double, because the restrictor gaps are actually modulated at a faster rate than the bearing gaps. 
     FIG. 8  illustrates how the bearing pocket pressures respond to oppose a radial displacement of the bearing rotor. When rotor assembly  1  is displaced to the right relative to stator assembly  2 , bearing gaps  68  and  75  on the right close, and bearing gaps  63  and  70  on the left open. These act to cause pocket pressures  67  and  74  to increase in pockets  66  and  73  on the right, and pocket pressures  64  and  71  to decrease in pockets  65  and  72  on the left, respectively. Both of the described pressure changes result in a net leftward force on rotor assembly  1 , thus serving to restore it to its original undisplaced position. Restrictor gaps  62  and  69  remain constant during a radial displacement, and thus they do not contribute to hydrostatic stiffness in this case. 
   For the radial mode of displacement, due to the fact that the restrictor gaps remain constant, and only the bearing gaps are modulated, about the same pressure feedback occurs as would occur using conventional fixed restrictors feeding the bearing pockets on the conical bearing surfaces. 
     FIG. 9  illustrates how the bearing pocket pressures respond to oppose a tilt displacement of the bearing rotor. When rotor assembly  1  is tilted clockwise relative to stator assembly  2 , restrictor gaps  83  and  84  open, and their corresponding bearing gaps  82  and  85  close. This causes pocket pressures  81  and  86  to increase. Conversely, restrictor gaps  91  and  76  close, and corresponding bearing gaps  90  and  77  open, thus causing pocket pressures  89  and  78  to decrease. All of the described pressure changes result in a net counterclockwise torque on rotor assembly  1 , thus serving to restore it to its original undisplaced position. 
   Similar to the axial displacement case, for the tilt mode of displacement, due to the fact that the restrictor gaps are modulated in addition to the bearing gaps, more pressure feedback occurs than would result for a conventional fixed restrictor bearing (which may include orifices or capillaries to provide the fluid restricting function). The factor of improvement in this mode can be more than double, because the restrictor gaps are actually modulated at a faster rate than the bearing gaps. 
     FIG. 10  illustrates a bearing of the present invention integrated with a brushless DC motor and a non-contact rotary encoder, enabling an entirely non-contact ultra-precision rotary table capable of closed loop control. Brushless motor stator  93  is mounted to motor mount  92 , which is mounted to stator base  9 . Brushless motor rotor  94  is mounted to adaptor plate  6  on rotor assembly  1 . Encoder rotor  96  is mounted to rotor top  3 , and encoder stator  95  is mounted to motor mount  92 . Due to the lack of mechanical contact and the lack of wear and static friction associated with it, this configuration enables ultra precise sub micro-radian closed loop positioning control. Alternatively, a brushed motor could be used. 
     FIG. 11  illustrates a more compact embodiment of the present invention, comprising a rotor assembly  100  with a thinner rotor plate  103 , and a stator assembly  101  with a smaller height  104 . Fluid restricting faces  105  and  106  do not have supply grooves, and rotor plate outer edge  107  does not have a concave channel therewithin. Supply passage  108  can be sized to provide minimal pressure drop as fluid flows circumferentially through it. To further minimize supply passage pressure variations, multiple supply ports such as port  109  can be provided around the perimeter of stator bottom  110 . 
     FIG. 12  illustrates the use of alignment pins as a means of achieving precise alignment between mated rotor parts and mated stator parts. Precision alignment pins  111  and  112  pass through rotor top  113 , rotor plate  114 , and rotor bottom  115  to hold the parts in precise alignment with each other. Precision alignment pins  116  and  117  pass through stator top  118  and stator bottom  119  to hold the parts in precise alignment with each other as well. 
     FIG. 13  illustrates the use of shoulders as a means of achieving precise alignment between mated rotor parts and mated stator parts. Interior shoulder  120  on rotor top  121 , and interior shoulder  122  on rotor bottom  123  contact inner surface  124  on rotor plate  125 , thus holding the three parts in alignment with each other. Interior shoulder  126  on stator top  127  contacts inner surface  128  on stator bottom  129 , thus holding the two parts in alignment with each other. 
   Although the above preferred embodiments focused on rotary bearing applications, the invention can also be applied to a linear motion system, where essentially the diameters of the parts are infinite, i.e. in a segment of an infinite radius bearing, and the stator becomes two parts, a left hand part and a right hand part. In such configurations, for example, the cross section profile of the rotary bearing is essentially extruded linearly to define a carriage assembly comprising a left hand side, a right hand side, and a top plate, and a rail assembly comprising a left hand side and a right hand side which are mirror images of each other. 
     FIG. 14  illustrates the use of the surface self compensation of the present invention applied to a linear bearing. This configuration comprises a carriage assembly  130  and rail assembly  131  mounted to machine bed  132 . Carriage assembly  130  comprises carriage top  132 , carriage bearing parts  133 ,  134 ,  135  and  136 , and carriage plates  137  and  138 . Rail assembly  131  comprises rail top  139 , rail plate  140 , and rail bottom  141 . Rail assembly  131  is shown bolted to machine bed  132 . On the right side of carriage assembly  130 , pressurized fluid enters supply port  142 , flows into supply cavity  143 , and enters fluid restricting gaps  144  and  145 . Fluid then flows into pockets  146  and  147 , and exits through bearing gaps  148  and  149  into the atmosphere. Fluid is then captured in drain channel  150  in machine bed  132 . The left side of the bearing is a mirror image of the right, and essentially the same flowpath occurs on the left side. In addition to the flowpaths described, fluid can also flow out the ends of the bearing parallel to the rail. To maximize the resistance to fluid flow along endwise leakage paths, and hence minimize end leakage, edges such as  151 ,  152  on rail plate  140  must be left sharp after grinding, and edges such as  153  and  154  on bearing parts  133  and  134  must be left sharp as well after grinding. Leakage gaps  155  and  156  do not influence pocket pressure response, and hence their precision is less important. Leakage gaps  155  and  156  can be made larger than the restrictor gaps and bearing gaps to allow larger particles escape the supply cavities. 
     FIG. 15  illustrates a face to face embodiment of the linear bearing described in  FIG. 14 . Carriage assembly  160  comprises carriage top  162 , carriage bearing parts  163 ,  164 ,  165  and  166 , and carriage plates  167  and  168 . Rail assembly  161  comprises rail top  169 , rail plate  170 , and rail bottom  171 . Rail assembly  161  is shown bolted to machine bed  172 . On the right side of carriage assembly  160 , pressurized fluid enters supply port  173 , flows into supply cavity  174 , and enters fluid restricting gaps  175  and  176 . Fluid then flows into pockets  177  and  178 , and exits through bearing gaps  179  and ISO into the atmosphere. Fluid is then captured in drain channel  181  in machine bed  172 . The left side of the bearing is a mirror image of the right, and essentially the same flowpath occurs on the left side. 
   In another embodiment of the present invention, the rotor plate can be made a part of the stator assembly, hence then it would be called the stator plate. This configuration can enable the stator assembly to be made monolithic, for example using a machine that allows one angled side to be precision machined, then the part turned over to precision machine the other side. The rotor can then be made from two parts that when bolted together sandwich the stator plate between them. 
   The self-compensating hydrostatic bearings of the present invention are designed to achieve a design that inherently allows a large diameter to height ratio, making it highly compact and rigid and potentially more dynamically stable, while using a minimal number of parts and precision surfaces. The design is intended to thus minimize manufacturing cost and complexity to achieve ultra low error motion with high structural and hydrostatic rigidity, particularly in tilt mode. 
   It is also contemplated that the present invention can be turned inside out. Such configurations, however, will be apparent to those skilled in the art of precision machine design. 
   Although the invention is illustrated and described herein with reference to specific embodiments, the invention is not intended to be limited to the details shown. Rather, various modifications may be made in the details within the scope and range of equivalents of the claims and without departing from the invention.