referring now to the drawings and , in particular , to fig5 one embodiment of a spindle in accordance with the present invention is shown and designated generally by the numeral 14 &# 34 ;. parts similar to those shown in fig1 and 4 are designated by the same numerals but with a double prime . in particular , this spindle unit 14 &# 34 ; has a rotor shaft 101 &# 34 ; with an outer diameter d 2 and a built - in copper core 110 &# 34 ;, and a thrust flange 103 &# 34 ; with a diameter d 1 integral with and at the top of the shaft 101 &# 34 ;. radial air bearings 102 &# 34 ; are spaced axially along the rotor shaft 101 &# 34 ;. a thrust air bearing 105 &# 34 ; arranged in the thrust bearing assembly 38 &# 34 ; supports the flange 103 &# 34 ;. a selectively energized motor coil 106 &# 34 ; surrounds the core 110 &# 34 ;. a supply of pressurized air to the radial air bearings 102 &# 34 ; is provided through ports in the spindle housing 104 &# 34 ; in the direction shown by the arrow 111 &# 34 ;. the pressurized air is also supplied to the thrust bearing 105 &# 34 ; through a port in the assembly 38 &# 34 ; as shown by the arrow 116 &# 34 ;. air is supplied to the bearings 102 &# 34 ;, 105 &# 34 ; at pressure p b and also to air bearing 117 &# 34 ; on the outer peripheral face of the assembly 38 &# 34 ; through radial air grooves 118 &# 34 ; arranged in the assembly 38 &# 34 ; whose diameter is d 2 . the spindle housing at the upper end has a diameter d 3 . a rod 32 &# 34 ; mounted on the assembly 38 &# 34 ; is actuated in the axial direction by a z - axis unit ( fig8 and 9 ) and moves the drill bit 25 in an axial or z - axis direction shown by double - headed arrow 119 &# 34 ; by the above described air bearing system . a spring - biased diaphragm 120 &# 34 ; similar to but of smaller diameter d 1 than diaphragm 107 in fig1 is provided in a cavity of the thrust bearing assembly 38 &# 34 ; and is supplied with pressurized air at pressure p d through a port in the direction indicated by the arrow 112 &# 34 ;. during an atc process , collet - actuating air at the pressure p d is supplied through the port in the assembly 38 &# 34 ; to the a diaphragm 120 &# 34 ; which is connected with a push rod 114 &# 34 ; to push a stopper 122 &# 34 ; normally biased upward by a disk spring 121 in the downward direction indicated by arrow 113 &# 34 ; and thereby open the taper collet 24 &# 34 ; which is normally spring biased toward a chucking position within the shaft 101 &# 34 ; to allow changing of the drill bit 25 &# 34 ;. the air supply pressure p b for each bearing 102 &# 34 ;, 105 &# 34 ; is approximately 4 . 8 to 5 . 0 kg / cm 2 , and the air supply pressure p d for the collet actuation diaphragm 120 &# 34 ; is approximately 5 . 5 to 6 . 0 kg / cm 2 . fig5 e shows details of the tapered collet mechanism used in the spindle depicted in fig5 . the main body of the rotor shaft 101 &# 39 ; has a cylindrical shape and a clamp or grip portion 28a provided with a tapered hole 27a opening forwardly . the grip portion 28a is placed at the front end of the cylindrical rotor 101 &# 34 ; so as to extend outwardly . the tapered hole 27a is concentric with the rotor 101 &# 34 ; and communicated with the interior of the rotor 101 &# 34 ;. the collet 24 &# 34 ; is inserted into the tapered hole 27a formed in the clamp portion 28a in a manner to allow removal from the inserted position . the collet 29a has a tool holding portion 26a placed in the tapered hole 27a at the front end of the chuck so as to hold the tool 25 and an expanded portion or stopper 122 &# 34 ; at its rear end adapted so as to movably fit in the rotor 101 &# 34 ;. the tool holding portion 26a has a through - hole 29a opening to the front end of the holding portion 26a , through which the tool 25 is inserted . the tool holding portion 26a has a cylindrical shape and an axial slit 125 &# 34 ; formed on the outer circumference of the portion 26a . when the collet 24 &# 34 ; moves toward the rear end of the spindle mechanism , the tapered hole 27a of the grip portion 28a gradually becomes smaller , and consequently the tool holding portion 26a is clamped or pressed inwardly to close the through hole 29a . when the collet 24 &# 34 ; is moved toward the front end , the tool holding portion 26a is released from its clamped condition due to the tapered hole 27a opening outwardly . the disk spring 121 is adapted to be placed in the space between the expanded portion or stopper 122 &# 34 ; formed at the rear end of the collet 24 &# 34 ; and a stepped front end portion of the rotor 101 &# 34 ; in order to urge or press the collet 24 &# 34 ; rearwardly . the resilient force of the disk spring 121 normally presses or urges the collet 24 &# 34 ; along the rearward axial direction , and the tool holding portion 26a is kept at its closed condition . when the collet 24 &# 34 ; moves forwardly by means of a collet opening - and - closing mechanism against the resilient force of the spring 121 , the tool holding portion 26a opens . accordingly , the moving weight or mass with the arrangement of fig5 has been decreased from more than 15 kg to 2 . 8 kg . as a result , acceleration controls and noise reduction are greatly improved without any compromise in the drill bit sizes which can be used to obtain high quality holes . during the drilling process with the spindle unit 14 &# 34 ; of fig5 only the rotor shaft 101 &# 34 ;, the collet 24 &# 34 ;, the drill bit 25 , the push rod 114 &# 34 ;, the diaphragm 120 &# 34 ; and the assembly 38 &# 34 ; are driven instead of the entire spindle unit as is the case with the unit 14 of fig1 which also requires movement of a spindle saddle 13 . as a result , the spindle moving weight or mass is decreased to 2 . 8 kg , and spindle saddle 13 of fig1 can be eliminated . fig7 shows another embodiment of the spindle unit in accordance with the present invention which is substantially the same as the embodiment of fig5 but which has a smaller upper portion to further reduce the moving mass . parts similar in construction and operation to parts in fig5 are designated by the same numerals but are triple primed and will not be further described except to the extent set forth hereinafter . the air supplied to the diaphragm 120 &# 39 ;&# 34 ; is at pressure p 1 , and the air supplied to the radial bearings 102 &# 39 ;&# 34 ; and axial thrust bearings 105 &# 39 ;&# 34 ; is at pressure p 2 . the outer diameter of the rotor shaft 101 &# 39 ;&# 34 ; is d 2 &# 39 ; and of the thrust flange 103 &# 39 ;&# 34 ; is d 1 &# 39 ;. the diaphragm 120 &# 39 ;&# 34 ; has a diameter d 1 &# 39 ;, the assembly 38 &# 39 ;&# 34 ; has a diameter d &# 34 ;, and the upper portion of the spindle housing 104 &# 39 ;&# 34 ; has a diameter d 3 &# 39 ;. therefore , if ( d 1 2 - d 2 2 ) p b =( d &# 39 ; 1 2 - d &# 39 ; 2 2 ) p 2 [ where p 2 is 5 ˜ 10 kg / cm 2 ], and d 1 2 p d = d &# 39 ; 1 2 p 1 [ p 1 is 9 ˜ 18 kg / cm 2 ], the flange diameter d 1 &# 39 ; is reduced to 75 % of d 1 , and the diaphragm diameter d 1 &# 39 ; is reduced to 70 % of d 1 . accordingly , d 2 &# 39 ; and d 3 &# 39 ; are also reduced to near 70 % of d 2 and d 3 , and the moving weight is significantly reduced in the fig7 embodiment from 2 . 8 kg to 2 . 0 kg . as a result , the overall dimensions of the spindle unit 14 &# 39 ;&# 34 ; are substantially reduced or miniaturized . ordinary typical high speed spindles have two types of dynamic run - out characteristic as shown in fig6 and 6a . the dynamic run - out characteristic curves of fig6 are known as the supercritical characteristic , i . e . the critical run - out point between minimum and maximum speed . fig6 a shows curves of another run - out characteristic known as the sub - critical characteristic , i . e . the critical run - out point over maximum speed . the characteristic curves shown by the solid lines a in fig6 &# 39 ; and 6a are shifted rightwardly as shown by the dashed lines b as the pressure of the air supplied to the air bearings is increased . for example , with regard to fig6 the critical point for the supercritical characteristic shifts rightwardly from curve a to curve b . thus , the supercritical run - out characteristic ( measured in μm ) is significantly improved in the speed range of 60 to 80 krpm ( thousand revolutions per minute ) for small holes of from 4 to 40 mils and is only slightly worse in speeds between 80 to 120 krpm . futhermore , fig6 a shows that the sub - critical characteristic is also greatly improved in speed ranges at or above 80 krpm so that the run - out reaches maximum only at much higher speeds than is the case with conventional spindles . at the same time , however , adequate collet actuation chucking force can be maintained for larger diameter drill bits . fig8 and 9 show a presently preferred embodiment of the more compact z - axis unit used for the spindles shown in fig5 and 7 . more specifically , drive motor 7 &# 39 ; is mounted on the unit base 6 &# 39 ; and drives the screw shaft 11 &# 39 ; supported by ball bearing 10 &# 39 ; and the housing 9 &# 39 ; which is also mounted on the unit base 6 . the screw shaft 11 &# 39 ; drives the screw nut 12 &# 39 ; in the axial or z - direction . the screw nut 12 &# 39 ; is mounted on the plate 31 &# 39 ; which is supported by a pair of guide shafts 34 &# 39 ; arranged in a housing 35 &# 39 ; and linear bearings 36 &# 39 ;. plate 31 &# 39 ; reciprocates the radial air bearing - supported spindle rotor assembly , via the rod 32 &# 39 ; in the axial or z - direction comprising the rotor shaft , the collet , and diaphragm , including the thrust bearing assembly , described in fig5 and 7 . the plate 31 &# 39 ; also drives the pressure foot 20 &# 39 ; supported and guided by a pair of brackets 37 &# 39 ;, air cylinders 16 &# 39 ;, swivel joints 17 &# 39 ;, and shafts 19 &# 39 ; located at both sides of the spindle unit 33 ( of the type shown in fig5 and 7 as 14 &# 34 ; and 14 &# 39 ;&# 34 ;, respectively ) in a manner similar to the conventional z - axis units . by virtue of the foregoing , the spindle saddle 13 and spindle body 4 which constitute a significant weight or mass are not driven . consequently , these mechanisms exceed an acceleration of 2g &# 39 ; s with the result that the feed / retract time for z - axis movement can be substantially reduced . in addition , the drilling of holes between about 0 . 004 &# 34 ; to 0 . 25 &# 34 ; in diameter can now be achieved with this unit because the collet chucking force is maintained the same as in the conventional range of drill bit diameters . while we have shown and described several embodiments in accordance with the present invention , it should be clearly understood that the same is susceptible of changes and modifications without departing from the scope of the invention . therefore , it is not intended that the invention be limited to the details shown and described herein but that it should cover all such changes and modifications falling within the scope of the appended claims .