MACHINE TOOL FOR AND METHOD OF PROVIDING A SURFACE WHICH IS NOT ROTATIONALLY SYMMETRICAL ON A WORKPIECE, AND CONTROL FOR SUCH A MACHINE TOOL

Abstract: A machine tool (1, 227) with a spindle (27, 229) which extends parallel to Z-direction, is rotatable about an axis of rotation (29, 231) which runs parallel to the Z-direction, and is provided with a holder (33, 235) for a workpiece (35, 237) to be manufactured. The machine tool (1, 227) has a holder (11) for a tool (13) which is displaceable in an X-direction perpendicular to the Z-direction. The spindle (27, 229) and the holder (11) for the tool (13) are mutually displaceable parallel to the Z-direction as a function of the X-position of the tool (13) and an angle of rotation of the spindle (27, 229), so that the workpiece (35, 237) is provided with a surface which is not rotationally symmetrical relative to the axis of rotation (29, 231). According to the invention, the spindle (27, 229) and the holder (11) are mutually displaced parallel to the Z-direction in that exclusively the spindle (27, 229) is displaced parallel to the Z-direction. The workpiece (35, 237) is thus provided with a desired basic surface and a desired correction which is not rotationally symmetrical, while a series of workpieces having different basic surfaces and corrections can be manufactured by means of only a single tool.

Description: Machine tool for and method of providing a surface which is not rotationally symmetrical on a workpiece, and control for such a machine tool. The invention relates to a machine tool with a spindle which extends parallel to a Z-direction and a tool holder which is movable relative to the spindle, this spindle being rotatable about an axis of rotation which is directed parallel to the Z-direction and being provided with a holder for a workpiece, while a displacement of the tool holder has at least a component which is parallel to an X-direction directed perpendicularly to the Z- direction, and the spindle and tool holder are mutually displaceable parallel to the Z-direction as a function of an angle of rotation of the spindle so as to provide the workpiece with a surface which is not rotationally symmetrical relative to an axis of the workpiece which coincides with the axis of rotation. The invention also relates to a method whereby a workpiece is provided with a surface which is not rotationally symmetrical relative to an axis of the workpiece, the workpiece being mounted on a spindle which extends parallel to a Z-direction, and the spindle being rotated about an axis of rotation directed parallel to the Z-direction and coinciding with the axis of the workpiece, whereupon a tool is displaced relative to the workpiece in a direction which has at least a component which is parallel to an X-direction directed perpendicularly to the Z-direction, and the spindle and the tool are mutually displaced parallel to the Z-direction as a function of an angle of rotation of the spindle. The invention also relates to a control suitable for use in a machine tool according to the invention. A machine tool and a method of the kind mentioned in the opening paragraphs are known from EP-A-0 370 788. The spindle of the known machine tool is fastened in a bush by means of two elastically deformable membranes, the bush being rotatably supported in a bearing block by means of ball bearings. The spindle is supported parallel to the Z-direction by means of a further ball bearing of which a stationary part is fastened to the bearing block by means of a further elastically deformable membrane. The known machine tool further comprises an electromagnetic actuator of which a magnetic circuit is fastened to the bearing block and of which an electric coil is fastened to the stationary part of the further ball bearing. The spindle is displaceable over a limited distance parallel to the Z-direction by means of the electromagnetic actuator under elastic deformation of said membranes. The tool holder of the known machine tool is fastened to a carriage which is rotatable about a Y-axis which extends at right angles to the X-direction and Z- direction. T e known machine tool and the method which can be carried out with the known machine tool are used for the application of a so-called astigmatic surface on a lens such as, for example, a contact lens or spectacle glass. Such an astigmatic surface has a spherical basic surface with an astigmatic correction which is not rotationally symmetrical relative to an optical axis of the lens. For this purpose, the tool is rotated about the Y-axis by means of the carriage, so that the tool is displaced along the lens in accordance with a circular arc of a defined radius and the lens is provided with the spherical basic surface, while at the same time the spindle is displaced parallel to the Z-direction by the actuator as a function of the angle of rotation of the spindle, so that the spherical basic surface is simultaneously provided with the astigmatic correction. The spherical basic surface thus has a radius which corresponds to the radius of the circular arc. The limited distance over which the spindle is displaceable parallel to the Z-direction by means of the actuator under elastic deformation of said membranes is sufficient, because the displacements of the spindle parallel to the Z-direction, which are necessary for applying the astigmatic correction, are comparatively small in relation to the displacements of the tool parallel to the Z-direction, which are necessary for applying the spherical basic surface and are achieved by rotation of the tool about the Y-axis. It is a disadvantage of the known machine tool and the known method that the tool is displaceable exclusively along a circular arc with a previously defined radius, so that exclusively workpieces can be manufactured by the known machine tool and method which have a spherical basic surface of a previously defmed radius. If a series of lenses is to be manufactured by the known machine tool or known method, the basic surfaces of which have mutually different radiuses adapted to the relevant users of the lenses, the tool must be readjusted for each lens or the carriage must be provided with a large number of tools each fastened at a different distance from the Y-axis. In addition, it is not possible with the known machine tool or known method to provide a workpiece with a rounded edge which merges fluently into a rear side of the workpiece from the surface of the workpiece to be manufactured. The application of such a rounded edge in a contact lens considerably improves the wearing comfort of the contact lens. It is furthermore practically impossible in the known machine tool or known method to provide a workpiece with a different type of basic surface, so that the known machine tool or known method does not allow for, for example, the manufacture of a dynamic groove bearing with a pattern of grooves which is present on a plane basic surface. It is an object of the invention to provide a machine tool and a method of the kind mentioned in the opening paragraphs with which the disadvantages mentioned above are avoided as much as possible, so that it is possible to manufacture workpieces with different basic surfaces by means of the machine tool or method, and the number of machining possibilities of the machine tool and the method is increased. According to the invention, the machine tool is for this purpose characterized in that the spindle and the tool holder are mutually displaceable parallel to the Z-direction in that exclusively the spindle is displaceable parallel to the Z-direction. The method according to the invention is for this purpose characterized in that the spindle and the tool are mutually displaced parallel to the Z-direction in that exclusively the spindle is displaced parallel to the Z-direction. Since it is exclusively the spindle which is displaced parallel to the Z- direction, while the tool is displaced exclusively parallel to the X-direction, the surface to be applied on the workpiece is determined exclusively by the displacements carried out by the spindle parallel to the Z-direction during an operation as a function of the angle of rotation of the spindle and the X-position of the tool. Thus it is possible by means of the machine tool or by the method, for example, to manufacture a series of astigmatic lenses whose basic surfaces have mutually differing radiuses adapted to the relevant users of the lenses in that the Z-position of the spindle is controlled in a suitable manner as a function of the X-position of the tool and the angle of rotation of the spindle. For example, when a tool having a bent rod is used, it is also possible by means of the machine tool or by the method to machine a portion of a rear side of the workpiece, so that, for example, contact lenses can be provided with rounded edges. In addition, the machine tool or method also allows for the manufacture of workpieces having a plane or aspherically curved basic surface such as, for example, a dynamic groove bearing with a pattern of grooves present on a plane basic surface, which pattern is not rotationally symmetrical relative to an axis of rotation of the groove bearing. A further advantage of the machine tool and the method according to the invention is that the Z-position of the spindle is controllable as a function of the X-position of the tool and the angle of rotation of the spindle in accordance with a comparatively simple mathematical relation. Since the Z-position of the tool relative to the workpiece is dependent exclusively on the Z-position of the spindle, the calculated Z-position need not be corrected as a function of the X-position of the tool, as is necessary in the machine tool disclosed by EP-A-0 370 788. Calculation times required by a control unit for the calculation of the Z- position of the spindle are reduced thereby. A special embodiment of a machine tool according to the invention is characterized in that the spindle is a hollow shaft which is supported perpendicularly to the Z-direction by a radial fluid bearing, which fluid bearing is bounded by a circular-cylindrical outer wall of the hollow shaft. Owing to the use of the hollow shaft, the spindle has a comparatively small mass, so that a comparatively high frequency and a comparatively great stroke of the spindle displacements parallel to the Z-direction are achieved. Such a comparatively great axial stroke of the radially supported spindle is constructionally possible owing to the use of the radial fluid bearing. As a result of its comparatively small mass, the spindle has a great mechanical bandwidth as regards displacements parallel to the Z- direction, so that the displacements of the spindle parallel to the Z-direction are particularly accurate. A further embodiment of a machine tool according to the invention is characterized in that the spindle is supported parallel to the Z-direction by means of an axial fluid bearing with two cooperating bearing surfaces which extend perpendicularly to the Z- direction, a first of the two bearing surfaces being coupled to the spindle and a second of the two bearing surfaces being coupled to an actuator by means of which the spindle is displaceable parallel to the Z-direction. The use of the axial fluid bearing couples the spindle to the actuator in a constructionally simple manner, while a linear drive unit which is known and usual per se may be used as the actuator. A yet further embodiment of a machine tool according to the invention is characterized in that the spindle is supported and displaceable parallel to the Z-direction by means of only one electromagnetic actuator, which actuator is provided with a permanent magnet fastened to the spindle and with an electric coil fastened to a frame of the machine tool. The electromagnetic actuator thus has a dual function, so that the machine tool is of a particularly simple construction. When the electromagnetic actuator is controlled in a suitable manner, a particularly small rotation error and a particularly high axial stiffness of the spindle are provided by the electromagnetic actuator. Owing to these favourable properties, the workpiece can be provided by means of the machine tool with a surface of optical quality which requires no aftertreatment. When the machine tool is used, for example, for the manufacture of lenses, lenses manufactured by the machine tool need not be polished any more, so that the manufacturing process of the lenses is strongly simplified. A particular embodiment of a machine tool according to the invention is characterized in that the machine tool comprises a control provided with a control unit for supplying a first electrical output signal which corresponds to a desired X-position of the tool, and a second electrical output signal which corresponds to a Z-position of the spindle calculated by the control unit in accordance with a mathematical algorithm as a function of the X-position of the tool, so as to provide the workpiece with a desired basic surface which is rotationally symmetrical relative to the axis of the workpiece, while the control is further provided with a processor for supplying an electrical output signal which corresponds to a correction of the Z-position of the spindle which is stored in table form in the processor as a function of the X-position of the tool and the angle of rotation of the spindle so as to provide the workpiece with a desired correction on the basic surface which is not rotationally symmetrical relative to the axis of the workpiece, and the control is further provided with an electronic adder circuit for supplying an electrical output signal which is the sum of the second output signal of the control unit and the output signal of the processor. A special embodiment of a method according to the invention is characterized in that a desired Z-position of the spindle is calculated through addition of a Z- position calculated in accordance with a mathematical algorithm as a function of an X- position of the tool, whereby the workpiece is provided with a desired basic surface which is rotationally symmetrical relative to the axis of the workpiece, and a correction of the Z- position which is laid down in table form as a function of the X-position of the tool and the angle of rotation of the spindle, whereby the basic surface is provided with a desired correction which is not rotationally symmetrical relative to the axis of the workpiece. The control unit of said control controls the X-position of the tool and the Z-position of the spindle necessary for providing the desired basic surface, and carries out a new calculation of said X-position and Z-position once or a limited number of times per revolution. The correction of the Z-position necessary for applying the desired non- rotationally-symmetrical correction of the basic surface is to be carried out a great number of times, for example, a hundred times per spindle revolution. Since the correction of the Z- position of the spindle is stored in the processor of the said control in table form as a function of the X-position of the tool and the angle of rotation of the spindle, a fast determination of the Z-position correction is possible, so that also at a comparatively high spindle speed the correction can be carried out a sufficient number of times per spindle revolution. A further embodiment of a machine tool according to the invention is characterized in that the angle of rotation of the spindle, as a function of which the processor determines the correction of the Z-position of the spindle, is the sum of a measured angle of rotation of the spindle and a rotation angle correction calculated by the processor as a function of a rotation speed of the spindle. Owing to the required calculation time of the processor and the inertia of the actuator by means of which the spindle is displaceable parallel to the Z-direction, a difference will occur between the measured angle of rotation of the spindle, for which the processor determines the desired correction of the spindle Z- position, and the angle of rotation of the spindle at which the desired correction of the spindle Z-position is actually carried out by the actuator. Owing to this difference, which increases with an increase in the spindle speed, an undesirable distortion of the correction of the spindle Z-position about the workpiece axis will take place relative to a reference axis of the workpiece. Since the angle of rotation of the spindle as a function of which the processor determines the correction of the Z-position of the spindle is the sum of the measured angle of rotation of the spindle and said rotation angle correction, said difference is compensated by the rotation angle correction, so that said undesirable distortion of the correction of the spindle Z-position relative to the reference axis is avoided. It is noted that EP-A-0 602 724 discloses a machine tool provided with a spindle extending parallel to a Z-direction with a workpiece holder and a tool holder which is displaceable parallel to an X-direction perpendicular to the Z-direction, while the spindle and the tool holder are mutually displaceable parallel to the Z-direction in that exclusively the spindle is displaceable parallel to the Z-direction. The spindle of the machine tool known from EP-A-0 602 724, however, is not displaceable relative to the tool as a function of the angle of rotation of the spindle, so that the known machine tool is not used for providing a workpiece with a surface which is not rotationally symmetrical relative to an axis of the workpiece which coincides with the axis of rotation. The invention will be explained in more detail below with reference to the drawing, in which Fig. 1 is a plan view of a first embodiment of a machine tool according to the invention for carrying out a method according to the invention, Fig. 2 in cross-section shows a spindle, an axial fluid bearing, a coupling member, and a rotation angle sensor of the machine tool of Fig. 1, Fig. 3 diagrammatically shows a control for the machine tool of Fig. 1 , Fig. 4a shows an astigmatic contact lens manufactured by the machine tool of Fig. 1 , Fig. 4b is a cross-section of the contact lens taken on the line IVb-IVb in Fig. 4a, Fig. 4c diagrammatically shows the manufacture of a rounded edge of the contact lens of Fig. 4a, Fig. 4d shows a surface of a dynamic groove bearing manufactured by the machine tool of Fig. 1, Fig. 5 is a plan view of a second embodiment of a machine tool according to the invention for carrying out a method according to the invention, Fig. 6 diagrammatically shows a spindle, an electromagnetic actuator, and a rotation angle sensor of the machine tool of Fig. 5, Fig. 7 shows in cross-section the spindle, the electromagnetic actuator, and the rotation angle sensor of Fig. 6, and Fig. 8 diagrammatically shows a control for the machine tool of Fig. 5. The first embodiment of a machine tool 1 according to the invention shown in Figs. 1 to 3 is provided with a frame 3 which can be placed on a support surface. A guide block 5 with a straight guide 7 extending parallel to an X-direction is present on the frame 3. The machine tool 1 comprises a carriage 9 which is displaceably guided along the guide 7 by means of a static fluid bearing which is not visible in Fig. 1. A holder 11 for a tool such as, for example, a cutting tool 13, is present on the carriage 9. The carriage 9 is displaceable along the guide 7 by means of a drive unit 15, so that the holder 11 with the cutting tool 13 is displaceable parallel to the X-direction. The drive unit 15 comprises a drive rod 17 which extends parallel to the X-direction, is coupled to the carriage 9, and is guided in a housing 19 fastened to the frame 3 by means of a number of guide wheels 21 which are indicated diagrammatically only in Fig. 1. A friction wheel 23, which has its rotation bearings in the housing 19 and can be driven by an electric motor 25 fastened to the housing 19, bears with prestress on the drive rod 17, so that the carriage 9 is displaceable by means of the motor 25 parallel to the X-direction via the drive rod 17 and the friction wheel 23. As Fig. 1 further shows, the machine tool 1 comprises a spindle 27 which extends parallel to a Z-direction directed perpendicularly to the X-direction and which is rotatable about an axis of rotation 29 directed parallel to the Z-direction. The spindle 27 is provided with a holder 33, to which a workpiece 35 can be fastened, adjacent an end 31. As Fig. 2 shows, the spindle 27 comprises a hollow shaft 37 which is supported perpendicularly to the Z-direction by a radial static fluid bearing 39. The radial fluid bearing 39 comprises a feed channel 41 for the supply of a fluid, such as e.g. air, from a pressure source not shown in the Figures to an annular bearing gap 43 of the radial fluid bearing 39 which is bounded by a circular-cylindrical inner wall 45 of a bearing block 47 and by a circular-cylindrical outer wall 49 of the hollow shaft 37. As Fig. 1 further shows, the spindle 27 is coupled to a drive unit 55 via an axial static fluid bearing 51 and an elastically deformable coupling member 53. As Fig. 2 shows, the axial fluid bearing 51 comprises a central bearing plate 57 which is fastened to an end 61 of the hollow shaft 37 and is provided with a central opening 63. The bearing plate 57 is provided with a bearing surface 65, 67 at either side, these surfaces extending perpendicularly to d e axis of rotation 29. The axial fluid bearing 51 further comprises a first aerostatically supported foot 69 which is arranged in the hollow shaft 37 and is provided with a bearing surface 71 extending perpendicularly to the axis of rotation 29 for cooperation with the bearing surface 65 of the bearing plate 57, and a second aerostatically supported foot 73 which is provided with a bearing surface 75 which extends perpendicularly to the axis of rotation 29 for cooperation with the bearing surface 67 of the bearing plate 57. Between the bearing surfaces 65 and 71 there is a bearing gap 77, while a bearing gap 79 is present between the bearing surfaces 67 and 75. The bearing gaps 77 and 79 are each connected through a feed channel 81, 83 to a pressure source (not shown) for a fluid, such as e.g. air, the feed channel 81 for the bearing gap 77 extending through the central opening 63 of the bearing plate 57. The first aerostatically supported foot 69 is coupled to the second aerostatically supported foot 73 by means of a flexible tension rod 85 which also extends through the central opening 63 of the bearing plate 57 and through an opening 87 in the first aerostatically supported foot 69 and an opening 89 in the second aerostatically supported foot 73. The spindle 27 is supported and pretensioned parallel to the Z-direction by means of the axial fluid bearing 51. The coupling member 53 shown in Fig. 2 and mentioned above is of a kind known from EP-A-0 602 724 and is provided with a first fastening part 91, which is fastened to the second aerostatically supported foot 73, and a second fastening part 93, which is fastened to a drive rod 95 of the drive unit 55. The fastening parts 91 and 93 are interconnected by an elastically deformable bridge 97 which is rigid in a direction parallel to the Z-direction and is provided with a number of incision-defined hinges 99. The incision- defined hinges 99 are so provided in the bridge 97 that the first fastening part 91 is pivotable relative to the second fastening part 93 through limited angles about a first virtual pivot axis 101 shown in Fig. 2 which extends through a point of intersection 103 between the axis of rotation 29 and the bearing surface 75 of the second aerostatically supported foot 73 and which extends perpendicularly to the axis of rotation 29, and a second virtual pivot axis 105 not visible in Fig. 2 which also extends through said point of intersection 103 and which extends perpendicularly to die axis of rotation 29 and the first pivot axis 101. The use of the elastically deformable bridge 97 achieves that the second aerostatically supported foot 73 is self-adjusting relative to the bearing surface 67 of the bearing plate 57, so that inaccuracies in the perpendicularity of the cooperating bearing surfaces 67 and 75 relative to the axis of rotation 29 have no influence on the Z-position of the spindle 27 during the rotation of the spindle 27 about the axis of rotation 29. The use of the flexible tension rod 85 mentioned above achieves that also the first aerostatically supported foot 69 is self-adjusting relative to the bearing surface 65 of the bearing plate 57, so that also inaccuracies in the peφendicularity of the cooperating bearing surfaces 65 and 71 relative to the axis of rotation 29 have no influence on the Z-position of the spindle 27 during rotation of the spindle 27 about the axis of rotation 29. The drive rod 95 of the drive unit 55 shown in Fig. 2 and mentioned above extends parallel to the Z-direction and is guided along a number of guide wheels 107 which are shown diagrammatically only in Fig. 1 and which have their rotation bearings in a housing 109 fastened to the frame 3. The drive unit 55 further comprises a friction wheel 111 which also has its rotation bearings in the housing 109 and can be driven by an electric motor 113 fastened to the housing 109. The friction wheel 111 bears with prestress on the drive rod 95, so that the spindle 27 is displaceable parallel to the Z-direction via the drive rod 95, the coupling member 53, and the axial fluid bearing 51. As Fig. 1 further shows, the spindle 27 is rotatable about the axis of rotation 29 by means of a further electric motor 115, which is also fastened to the frame 3 and is coupled to the hollow shaft 37 via a pulley 117, a rope 119, and a pulley 121 integrated with the bearing plate 57 of the hollow shaft 37. The rope 119 has sufficient elasticity for being capable of following a displacement of the hollow shaft 37 and the pulley 121 parallel to the Z-direction. The control 123 of the machine tool 1 as shown in Fig. 3 shows a numerical control unit 125 which is usual and known per se, with a first electrical input 127 for receiving a first electrical input signal Uxx which corresponds to a measured X-position of the cutting tool 13, and a second electrical input 129 for receiving a second electrical input signal u 2 which corresponds to a measured Z-position of the workpiece 35. The first input signal u xx is supplied by a first optical position sensor 131 which is usual and known per se and which is shown diagrammatically only in Figs. 1 and 3. As Fig. 1 shows, the first position sensor 131 is provided with an optical source 133 and an optical detector 135 which are fastened to the housing 19 of the drive unit 15, and a reflecting surface 137 fastened to the carriage 9. The second input signal u^ is supplied by a second optical position sensor 139 which is usual and known per se and which again is shown diagrammatically only in Figs. 1 and 3. As Fig. 1 shows, the second position sensor 139 also comprises an optical source 141 and an optical detector 143, which are fastened to the housing 109 of the drive unit 55, and a reflecting surface 145 fastened to the drive rod 95 of the drive unit 55. The reflecting surface 145 of the second position sensor 139 is also visible in Fig. 2. As Fig. 3 further shows, the control unit 125 comprises a contour generator 147 which generates a first signal u x in accordance with a previously defined program, which signal conesponds to a desired X-position of the cutting tool 13, and a second signal U zo , which conesponds to a desired Z n -position of die workpiece 35 and is calculated by the contour generator 147 in accordance with a mathematical algorithm as a function of die desired X-position of die cutting tool 13. Since the desired Zn-position of the workpiece 35 is calculated exclusively as a function of the desired X-position of die cutting tool 13, the workpiece 35 as a result of the displacements of the cutting tool 13 and of the workpiece 35 in accordance with die desired X-position and the desired Zn-position, respectively, is provided with a basic surface which is rotationally symmetrical relative to an axis 149 of die workpiece 35 coinciding widi die axis of rotation 29 and shown in Figs. 4a, 4b and 4d. As Fig. 3 further shows, the control unit 125 comprises a first comparator 151 which compares die signal u x of die desired X-position of die cutting tool 13 with die input signal u^ of d e measured X-position of d e cutting tool 13. The first comparator 151 supplies an output signal u cx = u x - u^, which is multiplied by a factor K x by a first multiplier 153. The control unit 125 comprises a first electrical output 155 for supplying a first electrical output signal u^ = K *u cx = K x *(u x - u^). As Fig. 3 shows, die output signal u^ is offered to a first electrical amplifier 157 which supplies die electric motor 25 of die drive unit 15. The amplifier 157, die motor 25, die drive unit 15, and die first position sensor 131 together have a transmission factor H x , so diat d e first input signal u xx = Hχ*u κx = H x *K x *(u x - Uxx), and Uxx = u x *H x *K x /(l + H X *K X ). It is achieved dirough a suitable adjustment and choice of the factors H x and K x diat H x *K x > > 1, so diat u^, i.e. die measured X-position of die cutting tool 13, is substantially equal to u x , i.e. die desired X-position of d e cutting tool 13, and an accurate control of die X-position of me cutting tool 13 is obtained. As Fig. 3 further shows, the control unit 125 comprises a second comparator 159 which compares die signal u^ of me desired Zo-position of the workpiece 35 widi the input signal u^ of the measured Z-position of die workpiece 35. The second comparator 159 supplies an output signal u cz = u^, - u^, which is multiplied by a factor K z by a second multiplier 161. The control unit 125 comprises a second electrical output 163 for supplying a second electrical output signal u^ = K z *Uc Z = 1^* - u^). As Fig. 3 shows, the control 123 further comprises a processor 165, which is usual and known per se, widi a first electrical input 167 for receiving said first electrical input signal u xx , which conesponds to me X-position of the cutting tool 13 measured by the first position sensor 131, and a second electrical input 169 for receiving a second electrical input signal u^, which conesponds to a measured angle of rotation φ of die spindle 27 about die axis of rotation 29. The second input signal u^ is supplied by an optical rotation angle sensor 171 which is diagrammatically depicted in Fig. 2. The rotation angle sensor 171 comprises an annular collar 173 which extends concentrically around die axis of rotation 29 and which is integrated widi die bearing plate 57. In the collar 173 diere is a raster of slots 175 which are provided at mutually equal distances in die collar 173, while a single reference slot 177 is provided next to die slots 175, defining a zero value of die angle of rotation φ. The rotation angle sensor 171 further comprises a furcate holder 179 fastened to die second fastening part 93 of die coupling member 53. Two optical sources 181, 183 and two optical detectors 185, 187 are mounted in die furcate holder 179. The source 183 and the detector 187 are positioned next to die raster of slots 175 and detect me passage of die reference slot 177 during rotation of die spindle 27, φ being zero men. The source 181 and die detector 185 are positioned on either side of d e raster of slots 175 and detect die passage of die slots 175 during die rotation of die spindle 27, die measured angle of rotation φ increasing by a value δφ = 2π/N (N being die number of slots 175) each time upon me passage of a slot 175. Since d e sources 181 , 183 and die detectors 185, 187 are mounted on die holder 179, and me holder 179 is displaced parallel to die Z-direction simultaneously wid d e spindle 27, it is achieved d at die position of die sources 181 , 183 and d e detectors 185, 187 relative to die collar 173 does not change as seen in the Z-direction, so diat me rotation angle sensor 171 can function during die full stroke of die spindle 27. The processor 165 has an electrical output 189 for supplying an electrical ouφut signal u pr generated by d e processor 165 as a function of die input signals u xx and u^. The ouφut signal ιi pr conesponds to a conection of die Z-position of me workpiece 35, which is previously determined as a function of die X-position of the cutting tool 13 and the angle of rotation φ of die spindle 27, as stored in table form in me processor 165. Said conection of die Z-position of die workpiece 35 is performed so as to provide said basic surface of the workpiece 35 widi a conection which is not rotationally symmetrical relative to die axis 149 of die workpiece 35 shown in Figs. 4a, 4b and 4d. The ouφut signal U pr of die processor 165 for diis puφose forms a first input signal for an adder circuit 191 of die control 123 which has the second ouφut signal u^ of the control unit 125 as its second input signal. As Fig. 3 shows, an ouφut signal u z+az = u^ + U pr of die adder circuit 191 is applied to a second electrical amplifier 193 which supplies die electric motor 113 of the drive unit 55. The amplifier 193, me motor 113, me drive unit 55, and die second position sensor 139 togedier have a transmission factor H z , so d at die second input signal u H = H z *u z+όZ = H z *( Uκz + U pr ) = H z *K z *( Uzo - Uzz ) + H z *U p . and U Ώ = u ZD *H 2 *K z /(l + H 2 *Kz) + U pr *H z /(l + H z *Kz). Through programming of me processor 165 such diat u-, r = K z *u iZ , where u 4z = δZ*u Z0 /Z 0 (ZQ and δZ are die Z-positions of me basic surface and the conection of die basic surface, respectively), it is achieved diat u^ = (u^ + u az )*H z *K z /(l + H z *K z ). It is achieved by a suitable adjustment and choice of the factors H z and K z that H Z *K Z > > 1, so diat u Q , i.e. to me measured Z-position of me workpiece 35, is substantially equal to U-Q, + u az , i.e. die sum of the desired Zo-position of me workpiece 35 and d e desired conection δZ of d e Z-position of d e workpiece 35, and die rotationally symmetrical basic surface and me non-rotationally-symmetrical conection are provided on me workpiece 35 in an accurate manner. It is noted d at owing to me inertia of die processor 165, me adder circuit 191, die amplifier 193, the drive unit 55, and die rotation angle sensor 171, there will be a difference between die measured angle of rotation u^ of die spindle 27, as a function of which die processor 165 determines the desired conection δZ of me Z-position of die spindle 27, and die angle of rotation φ of me spindle 27 at which die desired conection δZ of the Z- position of d e spindle 27 is actually realised by die drive unit 55. Said difference increases wid an increase in the speed of d e spindle 27 and causes an undesirable distortion of d e conection δZ about die axis 149 of die workpiece 35 relative to die reference slot 177 of die rotation angle sensor 171. To prevent said undesirable distortion, a conector 195 is connected between d e rotation angle sensor 171 and d e second electrical input 169 of the processor 165. The conector 195 comprises a first electrical input 197 for receiving d e 13 signal u^ and a second electrical input 199 for receiving a signal u, which is supplied by a differentiator 201 for die signal u φφ and conesponds to die speed of die spindle 27. The differentiator 201 supplies an ouφut signal u^. = u w + u w , where u w conesponds to a rotation angle conection δφ = r*δt of the spindle 27 determined by die differentiator 201 as a function of the speed r of die spindle 27 and the total, previously determined time delay δt of me processor 165, adder circuit 191, amplifier 193, drive unit 55, and rotation angle sensor 171. Since die angle of rotation φ + δφ, as a function of which die processor 165 determines the conection δZ of me Z-position of d e spindle 27, is die sum of the measured angle of rotation φ and said rotation angle conection δφ, die desired conection δZ is realised at an angle rotation of the spindle 27 which conesponds to die conected angle of rotation φ + δφ, so that said undesirable distortion of me conection δZ about die axis 149 of die workpiece 35 is avoided. It was described above how die basic surface and the non-rotationally- symmetrical conection are provided on me workpiece 35 dirough a displacement of d e cutting tool 13 parallel to die X-direction and dirough a mutual displacement of die cutting tool 13 and the workpiece 35 parallel to die Z-direction in a suitable manner as a function of die X-position of me cutting tool 13 and me angle of rotation φ of the spindle 27. Since the cutting tool 13 is displaceable exclusively parallel to die X-direction, die workpiece 35 and die cutting tool 13 are mutually displaced parallel to d e Z-direction in d at exclusively die spindle 27 is displaced parallel to me Z-direction. Since the non-rotationally-symmetrical conection is provided as a function of the angle of rotation φ of die spindle 27, die displacements of the spindle 27 parallel to d e Z-direction have a frequency which is at least equal to die frequency of die rotational movement of die spindle 27. The spindle 27 has a comparatively small mass because it is provided wid a hollow shaft 37, so diat a comparatively high frequency in combination widi a comparatively great stroke of the displacements of the spindle 27 parallel to die Z-direction are achieved. Since there is no mechanical contact between the spindle 27 and die bearing block 47 of the radial fluid bearing 39, such a great stroke of d e spindle 27 is not hampered constructionally by d e radial fluid bearing 39. In addition, die control 123 of die Z-position of die spindle 27 has a great mechanical bandwidm owing to die comparatively small mass of the spindle 27, so diat me displacements of die spindle 27 parallel to die Z-direction are particularly accurate. The control unit 125 generates die X-position of die cutting tool 13 and die Zo-position of die workpiece 35 which are necessary for providing die desired basic surface. The calculation of said X-position and Z 0 -position is carried out only once or a comparatively small number of times per revolution of the spindle 27, so diat said calculation by die control unit 125 can be canied out in accordance wid an accurate mathematical algorithm. The conection of the Z- position of die workpiece 35 necessary for applying me desired non-rotationally-symmetrical conection on the basic surface, however, is to be carried out a comparatively large number of times per revolution of die spindle 27. Since die calculation speed of die control unit 125 is limited, die calculations for die non-rotationally-symmetrical conection cannot be canied out by the control unit 125. Since die conection of me Z-position of die workpiece 35 is stored in die processor 165 in table form as a function of the X-position of the cutting tool 13 and die angle of rotation φ of die spindle 27, a fast calculation of me conection of the Z- position of the workpiece 35 is possible by means of die processor 165, so diat said conection can also be canied out at comparatively high speeds of the spindle 27. Figs. 4a and 4b show a first example of a workpiece 35 manufactured widi die machine tool 1 by the method according to me invention. The workpiece 35 is a contact lens 203 manufactured, for example, from a transparent, oxygen-permeable medical syndietic resin. The contact lens 203 comprises a spherical, concave contact surface 205 by means of which d e contact lens 203 can be placed on an eye, and an outer surface 207 provided wid an astigmatic surface 209 and a spherical, convex positioning surface 211 which sunounds die astigmatic surface 209. The astigmatic surface 209 forms the effective optical part of the contact lens 203, which is present in front of die eye pupil during use, while die positioning surface 211 is partly covered by die eyelids during use. In d e manufacture of me contact lens 203, a circular-cylindrical initial product is fastened to die holder 33 of d e spindle 27, and die initial product is first provided wid me hollow contact surface 205 by means of die cutting tool 13. Then the contact lens 203 is provided widi a rounded edge 213 and wid a small portion of die positioning surface 211, the rounded edge 213 merging fluently from the contact surface 205 into me positioning surface 211. Such a rounded edge 213 leads to a considerable improvement in me wearing comfort of the contact lens 203. As Fig. 4c shows, a further cutting tool 215, placed at an acute angle relative to the Z-direction, is used for d e application of d e rounded edge 213. Since d e spindle 27 is displaceable parallel to die Z-direction over a comparatively great distance, die further cutting tool 215 can partly reach die positioning surface 211, so diat me rounded edge 213 and a small portion of me positioning surface 211 can be provided by means of me further cutting tool 215. After die contact surface 205, said portion of die positioning surface 211, and d e rounded edge 213 have been provided, me contact lens 203 is glued widi its contact surface 205 to a spherical carrier 217 of die holder 33 visible in Fig. 2, after which me astigmatic surface 209 and die remaining portion of the positioning surface 211 are provided by die cutting tool 13. As Figs. 4a and 4b show, the positioning surface 211 exclusively comprises a spherical basic surface with a radius R P , while the astigmatic surface 209 comprises a spherical basic surface with a radius R A and a conection δZ which is not rotationally symmetrical relative to the axis 149 of the contact lens 203. The non- rotationally-symmetrical conection δZ of the contact lens 203 has two maximum positive conections δZpos. which are present on a centreline 219, and two maximum negative conections δZ NEG , which are present on a centreline 221. The conections δZ decrease from a circumference of the astigmatic surface 209 linearly along a radius towards die centre of die astigmatic surface 209, where the conection δZ is zero. Between die maximum positive and negative conections δZpos and δZ NEG , the conections δZ have a fluent gradient, for example, in accordance widi a sine shape. Since it is exclusively die spindle 27 widi the contact lens 203 which is displaced parallel to die Z-direction, die basic surfaces of die positioning surface 211 and die astigmatic surface 209 as well as the non-rotationally-symmetrical conection δZ of die astigmatic surface 209 can be provided by die cutting tool 13 in a single operation in diat die Z-position of die spindle 27 is controlled by die control 123 in a suitable manner. In addition, die cutting tool 13 is capable of manufacturing a series of astigmatic contact lenses whose basic surfaces of the positioning surface and astigmatic surface have mutually differing radiuses adapted to relevant users of die contact lenses, and whose non- rotationally-symmetrical conections of the astigmatic surfaces are mutually different. Fig. 4d shows a second example of a workpiece 35 manufactured widi a machine tool 1 by me method according to die invention. The workpiece 35 is a bearing surface 223 of a dynamic fluid bearing which is usual and known per se and which is provided widi a pattern of grooves 225. The bearing surface 223 has a plane basic surface 226, while the grooves 225 constitute die conection δZ of die basic surface 226 provided by die machine tool 1 as a function of me X-position of the cutting tool 13, i.e. die radius r shown in Fig. 4d, and as a function of the angle of rotation φ of die spindle 27. It is noted diat die frequency of die Z-displacements of me spindle 27 necessary for die manufacture of d e bearing surface 223 and dependent on die number of grooves 225 is greater than die frequency of die Z-displacements of die spindle 27 necessary for die manufacture of me contact lens 203 discussed above, while die stroke of die Z-displacements for manufacturing the bearing surface 223 is smaller than the stroke of the Z-displacements for manufacturing the contact lens 203. It is further noted d at die bearing surface 223 may be provided widi a spherical basic surface instead of a plane basic surface, so d at die bearing surface 223 in combination with a smooth ball has a radial as well as an axial bearing function. The second embodiment of a machine tool 227 according to die invention shown in Figs. 5 to 7 is identical to die first embodiment of the machine tool 1 in a number of respects. Conesponding components of the machine tools 1 and 227 have been given the same reference numerals in the Figures. The differences only between die machine tools 1 and 227 will be discussed below. As Fig. 5 shows, me machine tool 227, like me machine tool 1, has a spindle 229 which extends parallel to die Z-direction and which is rotatable about an axis of rotation 231 directed parallel to die Z-direction. Adjacent a first end 233, die spindle 229 is provided widi a holder 235 for fastening a workpiece 237. As Fig. 7 shows, die spindle 229 is provided widi a hollow shaft 239, as is d e spindle 27 of the machine tool 1, which shaft is supported peφendicularly to me Z-direction by a radial static fluid bearing 241. The radial fluid bearing 241 is of a kind similar to the radial fluid bearing 39 of die machine tool 1. As Figs. 6 and 7 further show, d e machine tool 227 has an electromagnetic actuator 243. The actuator 243 comprises an annular magnetic circuit 245 which is fastened to d e spindle 229 and is provided widi a permanent magnet 247, a magnetizable closing yoke 249, and an annular gap 251. An annular electrical coil 253 is present inside d e annular gap 251 and is fastened to a bearing block 255 of die radial fluid bearing 241. The spindle 229 is supported by d e electromagnetic actuator 243 parallel to me Z-direction, while d e spindle 229 is displaceable parallel to die Z-direction also by means of die electromagnetic actuator 243. As Fig. 7 further shows, a pulley 257 is fastened near die actuator 243, and d e spindle 229 can be driven into rotation by an electric motor 263 visible in Fig. 5 via me pulley 257, a rope 259. and a pulley 261. The rope 259 has a sufficient elasticity for following a displacement of the spindle 229 parallel to the Z-direction. The Z-position of die spindle 229 is controlled by means of a control 265 of the machine tool 227 shown diagrammatically in Fig. 8, which control in the main is identical to die control 123 of d e machine tool 1. The differences between die controls 123 and 265 only will be discussed below. As Figs. 6, 7 and 8 show, die Z-position of die spindle 229 of die machine tool 227 is measurable by means of an optical position sensor 267 provided wid an optical source 269 and an optical detector 271 which are fastened to a earner 273 fastened to die bearing block 255, and provided widi a reflecting surface 275 which is provided on a second end 277 of die spindle 229. The angle of rotation φ of die spindle 229 of d e machine tool 227 is further measurable by means of an optical rotation angle sensor 279. As Fig. 6 shows, me rotation angle sensor 279 comprises an annular raster of reflecting marks 281 which are provided widi equal interspacings around die hollow shaft 239 near me second end 277 of the spindle 229, and a single reflecting reference mark 283 provided next to die marks 281 and defining a zero value for die angle of rotation of die spindle 229. The rotation angle sensor 279 further comprises a first optical source 285 and a first optical detector 287, which are provided in the bearing block 255 and detect die passage of die marks 281 during rotation of the spindle 229, and a second optical source 289 and a second optical detector 291, also provided in die bearing block 255 and detecting die passage of die reference mark 283 during rotation of ie spindle 229. As Figs. 6, 7 and 8 further show, die control 265 of me machine tool 227 also comprises a speed sensor 293 for measuring a speed of die spindle 229 directed parallel to die Z-direction. The speed sensor 293 comprises an annular magnetic circuit 295 which is fastened to me spindle 229 and is provided widi a permanent magnet 297, a magnetizable closing yoke 299 and an annular gap 301. In die annular gap 301 diere is an annular electrical coil 303 which is fastened to said carrier 273. When die spindle 229 is displaced parallel to die Z-direction, an electric cunent is induced in the coil 303 of the speed sensor 293 by me magnetic field present in die gap 301, which current is proportional to die speed of die spindle 229 parallel to die Z-direction. An ouφut signal Uw of die speed sensor 293 accordingly conesponds to said speed of die spindle 229. As Fig. 8 shows, die control 265 of die machine tool 227 comprises a control member 305 widi a first electrical input 307 for receiving the ouφut signal Uw of die speed sensor 293 and a second electrical input 309 for receiving d e ouφut signal U z+az of die adder circuit 191. The control member 305 has an electrical ouφut 311 for supplying an electrical ouφut signal U D = C,*u z+4Z + C 2 *u vv = C ι *U z+az + C 2 *u' zz , where u'zz = δuzz/δt. As Fig. 8 shows, the signal u D is applied to die amplifier 193. Owing to die use of die control member 305, the electromagnetic actuator 243 exerts not only the force necessary for reaching a desired Z-position but also a damping force on die spindle 229, so diat a particularly stable control of die Z-position of die spindle 229 is achieved by the control 265. The electromagnetic actuator 243 provides a particularly accurate support and positioning of die spindle 229 parallel to die Z-direction. The axial stiffness of die actuator 243 is particularly great. In addition, die so-called rotation enor of me spindle 229, i.e. d e undesirable axial displacements of die spindle 229 caused by axial forces arising from the rotation of die actuator 243 about d e axis of rotation 231 and from cutting forces, are negligibly small. The machine tool 227 is thus eminently suitable for the manufacture of products widi an accuracy in the sub-micron range or for me manufacture of surfaces of optical quality. When the machine tool 227 is used, for example, for the manufacture of the astigmatic contact lens 203 shown in Fig. 4a, an optical surface quality of the contact lens 203 is achieved such mat the contact lens 203 requires no aftertreatment and d e manufacturing process of me contact lens 203 is strongly simplified. It is noted diat instead of d e spindle 27, 229 widi die hollow shaft 37, 339 supported by a static fluid bearing 39, 241 an alternative type of spindle may also be used in die machine tool 1, 227 such as, for example, a solid spindle or a spindle provided widi two bearing parts coupled by a connecting rod. Instead of d e radial static fluid bearings 39, 241 , it is also possible to use, for example, dynamic groove bearings or electromagnetic bearings. The invention is also applicable to machine tools provided widi spindles supported by radial ball bearings. The axial stroke of a machine tool with such a spindle, however, is limited so diat only a limited number of different basic surfaces can be manufactured by means of such a machine tool. The invention is equally applicable to machine tools provided widi an axial ball bearing or an axial dynamic groove bearing. The stiffness of such bearings, however, is comparatively low, while the rotation accuracy of axial ball bearings is limited. It is further noted diat instead of die drive unit 55 or die electromagnetic actuator 243, an alternative type of actuator may be used for displacing die spindle 27, 229 parallel to die Z-direction. When die machine tool 1 , 227 is used for die manufacture of workpieces for which only a limited stroke of die workpiece is required, such as, for example, in the manufacture of bearing surfaces of dynamic groove bearings, it is possible, for example, to use a piezoelectric actuator. It is further noted diat instead of me controls 123 and 265 discussed above a different type of control may alternatively be used. Instead of d e numerical control unit 125 and the processor 165, for example, a microprocessor may be used which generates bom the basic surface and die correction which is not rotationally symmetrical. With die use of die conventional numerical control unit 125 in combination with the processor 165, however, d e machine tool 1 , 227 is controlled by die numerical control unit 125 in a known and usual manner for conventional rotationally-symmetrical operations, whereby a desired rotationally symmetrical basic surface can be programmed in a practical manner by means of a mathematical relation, while die use of die processor 165 for non-rotationally-symmetrical operations renders it possible to calculate a non-rotationally-symmetrical conection of the basic surface in a fast and effective manner. Furthermore, me control 123 just as the control 265 may be provided wid a feedback of die speed of die spindle 27 parallel to die Z- direction. Moreover, die controls 123 and 265 may be provided widi a feedback of die speed of die caniage 9 parallel to die X-direction. In die machine tools 1, 227 described above, examples mentioned for die workpiece 35, 237 were an astigmatic contact lens, whose basic surface is spherical, and a bearing surface for a dynamic groove bearing, whose basic surface is plane. It is finally noted diat basic surfaces of different shapes may also be provided widi die machine tool 1 , 227 and by the method according to die invention, for example, basic surfaces having an ellipsoidal or odier aspherical contour, in die case of aspherical lenses, or basic surfaces having a sawtooth contour, in the case of so-called fresnel lenses. It is also possible widi die machine tool 1 , 227 and by die method according to die invention to apply non-rotationally- symmetrical conections other than me conections described above, for example, conections of a decorative nature.

Claims: CLAIMS: 1. A machine tool with a spindle which extends parallel to a Z-direction and a tool holder which is movable relative to the spindle, diis spindle being rotatable about an axis of rotation which is directed parallel to die Z-direction and being provided widi a holder for a workpiece, while a displacement of the tool holder has at least a component which is parallel to an X-direction directed perpendicularly to die Z-direction, and die spindle and tool holder are mutually displaceable parallel to die Z-direction as a function of an angle of rotation of die spindle so as to provide die workpiece with a surface which is not rotationally symmetrical relative to an axis of the workpiece which coincides widi die axis of rotation, characterized in diat the spindle and die tool holder are mutually displaceable parallel to die Z-direction in mat exclusively the spindle is displaceable parallel to die Z-direction. 2. A machine tool as claimed in Claim 1, characterized in that the spindle is a hollow shaft which is supported perpendicularly to die Z-direction by a radial fluid bearing, which fluid bearing is bounded by a circular-cylindrical outer wall of die hollow shaft. 3. A machine tool as claimed in Claim 1 or 2, characterized in d at die spindle is supported parallel to die Z-direction by means of an axial fluid bearing widi two cooperating bearing surfaces which extend perpendicularly to die Z-direction, a first of die two bearing surfaces being coupled to die spindle and a second of d e two bearing surfaces being coupled to an actuator by means of which the spindle is displaceable parallel to d e Z- direction. 4. A machine tool as claimed in Claim 1 or 2, characterized in d at d e spindle is supported and displaceable parallel to d e Z-direction by means of only one electromagnetic actuator, which actuator is provided widi a permanent magnet fastened to die spindle and widi an electric coil fastened to a frame of the machine tool. 5. A machine tool as claimed in any one of die preceding Claims, characterized in that die machine tool comprises a control provided widi a control unit for supplying a first electrical ouφut signal which corresponds to a desired X-position of die tool, and a second electrical ouφut signal which corresponds to a Z-position of d e spindle calculated by d e control unit in accordance wid a mathematical algorithm as a function of the X-position of the tool, so as to provide die workpiece widi a desired basic surface which is rotationally symmetrical relative to the axis of the workpiece, while the control is further provided widi a processor for supplying an electrical ouφut signal which conesponds to a conection of die Z-position of die spindle which is stored in table form in me processor as a function of me X-position of die tool and die angle of rotation of die spindle so as to provide die workpiece with a desired conection on the basic surface which is not rotationally symmetrical relative to the axis of the workpiece, and the control is further provided widi an electronic adder circuit for supplying an electrical ouφut signal which is me sum of the second ouφut signal of the control unit and me ouφut signal of the processor. 6. A machine tool as claimed in Claim 5, characterized in mat the angle of rotation of the spindle, as a function of which die processor determines the conection of die Z-position of die spindle, is die sum of a measured angle of rotation of die spindle and a rotation angle conection calculated by the processor as a function of a rotation speed of die spindle. 7. A control suitable for use in a machine tool as claimed in Claim 5 or 6. 8. A memod whereby a workpiece is provided widi a surface which is not rotationally symmetrical relative to an axis of me workpiece, the workpiece being mounted on a spindle which extends parallel to a Z-direction, and die spindle being rotated about an axis of rotation directed parallel to me Z-direction and coinciding wid die axis of die workpiece, whereupon a tool is displaced relative to die workpiece in a direction which has at least a component which is parallel to an X-direction directed perpendicularly to die Z- direction, and me spindle and die tool are mutually displaced parallel to d e Z-direction as a function of an angle of rotation of d e spindle, characterized in diat d e spindle and d e tool are mutually displaced parallel to die Z-direction in diat exclusively me spindle is displaced parallel to die Z-direction. 9. A method as claimed in Claim 8, characterized in diat a desired Z- position of die spindle is calculated dirough addition of a Z-position calculated in accordance widi a mathematical algorithm as a function of an X-position of die tool, whereby die workpiece is provided wid a desired basic surface which is rotationally symmetrical relative to the axis of d e workpiece, and a conection of die Z-position which is laid down in table form as a function of the X-position of die tool and ie angle of rotation of the spindle, whereby die basic surface is provided widi a desired conection which is not rotationally symmetrical relative to the axis of die workpiece.

Inventors: RENKENS MICHAEL JOSEPHA MATHIJ, VAN LEEST JOHANNES HENRICUS FR, VAN TOOREN ARIE, VERHULST ANDRE ALOIS, RENKENS, MICHAEL, JOSEPHA, MATHIJS, VAN LEEST, JOHANNES, HENRICUS, FRANCISCUS, MARIA, VAN TOOREN, ARIE, VERHULST ANDRE, ALOIS
Applicants: PHILIPS ELECTRONICS NV, PHILIPS NORDEN AB, PHILIPS ELECTRONICS N.V.
Application year: 1995
Main classification: B24B13
IPC codes: B23B5, B23B19, B24B13