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Title:
IMPROVED MONITORING SYSTEM FOR WORKPIECE AND TOOL CARRIAGE MOVEMENT
Document Type and Number:
WIPO Patent Application WO/2000/066322
Kind Code:
A1
Abstract:
A machine tool has a carriage (28), has a workpiece carriage (28) for carrying a workpiece (32) from which material is removed by a tool (54) carried by a tool carriage (48). A two-axis scale (86; 88) is attached to one of the carriages, and cooperates with a reading head (96; 98) attached to the other carriage. The output from the reading head is processed by signalling processing means to provide an indication of the position and/or movement of the carriages relative to each other and for generating positional data about one or both of the carriages to assist in controlling their movement in order to perform a machine operation. By directly measuring the relative positions of the two carriages, problems arising from, for example, distortions of the machine frame on which the carriages are mounted are at least mitigated. A preferred embodiment of the machine incorporates a second reading head attached to one carriage and incorporating the scale on another carriage so that the outputs from the two reading heads can be used to determine whether there has been any relative angular displacement of the paths followed by the carriages. There is also provided a method of determining the linear movement of one of the carriages relative to the other, and the machining process achieved using the machine tool.

Inventors:
PIERSE MICHAEL GEORGE (GB)
Application Number:
PCT/GB2000/001237
Publication Date:
November 09, 2000
Filing Date:
March 31, 2000
Export Citation:
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Assignee:
UNOVA UK LTD (GB)
PIERSE MICHAEL GEORGE (GB)
International Classes:
B23Q1/62; B23Q17/24; G05B19/404; (IPC1-7): B23Q23/00; G05B19/401; G05B19/404
Domestic Patent References:
WO1997030381A11997-08-21
Attorney, Agent or Firm:
KEITH W NASH & CO. (90-92 Regent Street Cambridge CB2 1DP, GB)
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Claims:
CLAIMS
1. A method of reducing or eliminating machine induced errors which affect the orthogonality of the axes of a first and a second carriage of a machine tool, the carriages being movable substantially orthogonally with respect to one another, each carriage carrying a respective one of a workpiece and a tool for machining the workpiece, characterised by the steps of attaching a twoaxis scale means to one carriage so as to move therewith, attaching a reading head which cooperates with the scale means to the other carriage to move therewith, the reading head being disposed in substantially the same plane as the twoaxis scale means, deriving positional data from the reading head and scale means for the first carriage, exerting a force on at least one of the two carriages to effect a movement thereof relative to the machine, and deriving a value for the linear displacement of the first carriage relative to the second carriage by determining the difference between the positional data at the beginning and at the end of the carriage . e movement.
2. A machine tool when cperated in accordance with the method of claim 1.
3. A method of reducing or eliminating machine induced errors in a machine tool substantially as herein described with reference to, and as shown in, the accompanying drawings.
4. A machine tool substantially as herein described with reference to, and as shown in, the accompanying drawings.
Description:
Title: Improved monitoring system for workpiece and tool carriage movement Field of invention This invention concerns a method of monitoring the movement of workpiece and tool carriages in machine tools, and machine tools when fit with such improved monitoring systems. By machine tool is meant any machine in which a tool is used to remove material from a workpiece and wherein the tool and/or the workpiece are moved relative to one another during the machining operation, typically involving rotation and also linear displacement of one or both.

Background to the invention Currently the means of obtaining carriage positional feedback in a two-axis machine, such as a lathe, has involved fitting a linear position sensing device between each moving axis and the base of the machine. Thus the relationship of position between a tool and a workpiece is derived from two sets of feedback information, namely 1. a point or the workpiece carriage which is monitored for change of position with respect to the base, and 2. a point on the tool carriage which is monitored for change in position with respect to the base.

However, the position on the base which is checked against the point on the tool carriage is not the same as that which is used as the reference for monitoring the change in position of the point on the workpiece carriage. As a consequence errors can arise in the computation of the position of the tool relative to the workpiece at the point of engagement due to the following possibilities: A) variations in the relationship between the machining point and the reference point of the work-feed measuring system, B) similar variations in the relationship between the machining point and the tool feed measuring system, C) any static or dynamic changes in the relationship between the two points on the base to which the two axis measuring systems are attached, and D) any variation in the orthogonality between the axes of the workpiece and tool carriages.

It is a general object of the present invention to provide an improved method of measuring the position of workpiece carriage and tool carriage, so as to reduce the error in the computation of the tool/workpiece point of engagement and to provide a machine capable of high precision machining.

It is also an object of the invention to provide a design of machine in which the orthogonality between the carriage axes is at least reduced, and so does not require the same degree of build accuracy as is necessary using conventional carriage monitoring systems. This should also result in a machine which is cheaper to build.

Although the invention may be applied to machine tools in which the workpiece carriage and/or the tool carriage move through considerable distances during workpiece machining, the invention is in fact of primary application to machine tools having a small working volume, in which both the workpiece carriage and the tool carriage only move through relatively small distances during the machining operation.

Summary of the invention According to the present invention there is provided a method of reducing or eliminating machine induced errors which affect the orthogonality of the axes of a first and a second carriage of a machine tool, the carriages being movable substantially orthogonally with respect to one another, each carriage carrying a respective one of a workpiece and a tool for machining the workpiece, characterised by the steps of attaching a two-axis scale means to one carriage so as to move therewith, attaching a reading head which cooperates with the ? cale means to the other carriage to move t~.. e ewith, the reading head being disposed in substantially the same plane as the two-axis scale means, deriving positional data from the reading head and scale means for the first carriage, exerting a force on at least one of the two carriages to effect a movement thereof relative to the machine, and deriving a value for the linear displacement of the first carriage relative to the second by determining the difference between the positional data at the beginning, and at the end, of the carriage movement.

The invention also extends to a machine tool when operated in accordance with such a method.

The invention thus provides a system where the following machine induced errors are substantially reduced, if not eliminated, as possible sources of machining errors: 1. orthogonality of the axes of the tool carriage and workpiece carriage, since the monitoring of the positions of the carriages will be derived from the orthogonality of the grating lines of the two-axis scale means and not from the machine base or the alignment of the carriage guideways; 2. errors contributed by the machine base, including static low frequency dynamic compliance, geometric stability, thermal expansions and distortions (all of which can affect the angle of one of the said axes relative to the other); and 3. lateral axial and angular deviations and disturbances of the guideways.

The remaining errors in the machining system can now be seen to be attributable as follows: (A) distortions, deflections, expansions etc, occurring in the machine mechanics situated in the direct path between the cutting tool and grating reference point, and between the wo>piece cutting zone and the direct path to th. grating reference point.

(B) errors in the grating itself. These errors are not necessarily trivial. Scaling errors, orthogonality of the X and Z fringes, interpolation errors and any other errors in the grating will be directly applied to the workpiece.

Error correction of scaling and orthogonality (listed under (B)) can be carried out electronically using computer control.

By careful machine design, errors arising from distortions and deflections etc, identified in (A) above, can be reduced to a minimum.

Remaining errors under heading (B) tend to be very small and in general can be ignored.

Without prejudice to the generality of the expression"machine tool", the invention may be applied to lathes and grinding machines.

Brief Description of the Drawings The invention will now be described by way of example, with reference to the accompanying drawings, in which: Figure 1 is a plan view of part of a machine tool embodying the invention, with selected parts removed and with other parts cut away, for clarity; Figure 2 is an end view of the machine in the direction of arrow A in Figure 1, again with selected parts removed for clarity; Figure 3 is a front view of the machine in the direction of arrow B in Figure 1, again with selected parts removed for clarity.

Figure 4 is a block diagram of a control system for the machine tool; and Figures 5 and 6 are block diagrams each showing a respective part of the system of Figure 4 to an enlarged scale.

Detailed Description With reference to Figures 1 to 3, part of the main frame of a machine tool is denoted by 10. Typically this is a casting with flat orthogonal faces machined thereon at 12 and 14 to which are attached upper and lower slideways, best seen in Figures 2 and 3 for carrying tool and workpiece supports (carriages). Thus as face 12 is shown in Figure 3, are mounted two parallel rails 16,18 on which two pairs of upper and lower slides 20,22 and 24,26 respectively are mounted for sliding movement therealong. A workpiece support 28 is carried by the slides and a chuck 30 protrudes from one end thereof in which is secured a workpiece (such as a spindle 32).

Rotational drive for driving the chuck and therefore the workpiece about the workpiece axis 34 is provided within the support 28 and indexing drive means for incrementally advancing or retracting the support 28 in a direction parallel to the axis 34 is also provided (but not shown). The indexing drive (not shown) is selected to permit high accuracy positioning of the support 28 relative to the casting rails 16,18.

Two similar rails 36,38 are mounted on the adjoining orthogonal casting face 14 and these provide slideways for two further pairs of slides 40,42 and 44,46 (see Figure 1) which carry between them a tool support (carriage) 48. Mounted on the latter (and visible in Figure 1) is an indexing drive 50 by which a tool capstan (or turret) 52 bearing eight tools 54 to can be rotatably indexed as required to brinX ny one of the eight tools into a workpiece engaging position, as is tool 54 in Figure 3. Only tools 54 and 62 are shown in the plan view of Figure 1, which shows more clearly than does Figure 3, the machining engagement of the tool 54 with the workpiece 32.

Further drive means (not shown) is mounted on the casting 10 or the support 48, for incrementally indexing the support 48 along the tool axis 70, towards and away from the workpiece 32.

Also mounted between each support carriage 28,48 and its respective mounting face 12,14 is linear position determining means (200,202 in Figures 4 to 6). for indicating the position of each carriage 28,48 relative to its axis 34,70 respectively and if moved therealong the displacement of either support carriage 28,48 relative thereto. The outputs of the position determining means can thus be used to calculate the carriage velocities relative to the casting 10.

The corner of the casting 10 is defined by the two mounting faces 12,14 in cut-away to form a cavity 72 defined by horizontal faces 74,76 and vertical walls 78,80. Wall 78 is visible (in section) in Figure 2, together with the upper and lower horizontal faces 74,76 whilst in Figure 1 both walls 78 and 80 are shown (in section) together with the lower horizontal face 76-the upper region of the casting (including the upper face 74) having been cut-away. The cavity provides the space into which the position indicating means of the invention can protrude.

In accordance with the invention, a horizontal platform 82 is secured to the workpiece support carriage 28 at 84 and carries two separate two-axis scales (gratings) 86 and 88 whilst secured at 90 to the tool support carriage 48 is a rigid arm 92 which is positioned so as to extend laterally from the support 48 to overlie the platform 82 and be parallel thereto. Although not illustrated, vertical may be formed on the upper face of the arm 92 to improve its rigidity. Its underside is substantially flat.

In a similar way the underside of the platform 82 is provided with strengthening ribs one of which is shown at 94 in Figure 2.

Carried by the arm 92 are two reading heads 96,98 which are positioned thereon so as to overlie and cooperate with the scales 86,88 respectively, to provide X and Z axis coordinates. Since the scales move with the workpiece support carriage 28 and the reading heads move with the tool support carriage 48, the difference between X1, Z1 and X2, Z2 (the X and Z coordinates at the beginning and ending of the linear movement of one of the two carriages 28,48 relative to the casting 10) will in fact be the movement of the one carriage relative to the other. Thus, for example, if the workpiece support carriage is stationary (i. e. is fixed in position along the Z axis 34), then if the tool support carriage 48 advances by 2 microns along the axis 70 (the X axis), the value of Z1 and Z2 would be the same, and the value of X2 will be 2 microns greater than the value of X1.

If however the reaction at the engagement of the tool and workpiece to the application of a driving force to the support carriage 48 to advance the tool 54 by 2 microns causes a tiny distortion of the structure mounting the support carriage 48 and/or in the casting 10 and/or in the structures mounting the support carriage 28, the result may be that the actual movement of the tool 54 relative to the workpiece 32 will be greater than 2 microns in order to achieve a 2 micron change in the X axis coordinates from the primary reading head 98. This will result in an excess of material being removed from the diameter of the workpiece.

For some applications, the errors caused by such distortions can b isregarded, and for such applications the machining increments may be determined simply by monitoring the X axis coordinates from the reading head 98 after calibrating the start position of the carriage 48 (i. e. its position when the tool 54 just touches the workpiece for the first time as the carriage 48 is advanced).

Where such errors are unacceptable, the X axis readings from the second reading head 96 may also be taken into account and if the coordinate value for 96 begins to get out of step with that from 98, an error signal is computed in a computing device which is indicative of the magnitude of the distortion occurring along the X axis due to the reaction to the machining forces at the tool/workpiece point of engagement.

By utilising a trigonometric analysis of this error signal, the drive t : o the tool support carriage 48 may be adjusted and released or removed sooner than would have otherwise been the case, to prevent extra unwanted advancement of the tool along its axis 70.

In order to accommodate the platform 82 the inboard face of the support carriage 48 is recessed at 100 (see Figures 1 and 2) and the region of attachment 90 between the arm 92 and the carriage 48 is in fact on the internal face 102 of the recess 100.

Different tools such as 56,58 etc can be brought into use by restricting the carriage 48 to remove the tool assembly from the region of the workpiece and indexing the capstan until the desired tool is in the"working"position, after which the carriage can be advanced once again so that the new tool engages the workpiece.

The invention is of particular application to machining operations and workpieces requiring very short axial movement (stroke) of tool relative to workpiece and workpiece relative to tool. Machining tiny parts such as spindles for computer disc drives, in one such application, where high machining accuracy is required to achieve accurate finished diameters and minimal high and low points.

Where high accuracy is required drives for achieving X and Z axis displacement of the carriages 28 and 48 may be High Traction Friction Drives such as have been developed and supplied by Cranfield Precision Engineering Ltd of Wharley End, Cranfield, Bedford, England. Such drives allow incremental steps of less than 0.1 micron to be achieved.

In a typical application the tool carriage X basic stroke may be of the order of 20mm and the workpiece Z axis stroke some 50mm.

Referring again to Figure 1, the full advantage of the second reading head 96 is obtained if the distance between the reading head 98 and the point of engagement of the tool and workpiece (104 in Figure 1) is the same as the distance between the reading head 98 and the reading head 96.

Parallax errors can arise if the point of engagement of tool and workpiece is not in the same plane as the scales and reading heads.

Since the scales and reading heads have finite depth, and a small gap must exist between the head (s) and the surface of the scale (s), it is not possible for the scales and head to occupy the same horizontal plane. However the configuration shown in the drawings minimises parallax errors which might otherwise arise by positioning the support platform 82 for the scale (s) just below the horizontal plane 106 which contains the workpiece axis and the point of tool of engagement 104 (see Figure 1), and positioning the arm 92 which carries the reading heads by the same distance above that horizontal plane as the platform 82 is below. In this way the horizontal plane 106 lies n the gap between the reading heads and the scal* : w.

Two-axis X, Z coordinate measuring device are manufactured inter alia by Heidenhain Dr Johannes Heidenhain GmbH which utilise diffraction gratings and optical sensors for accurately determining movement in two orthogonal directions.

With reference to Figures 4 to 6, the carriages 28 and 48 are respectively driven by"voice coil"type motors 204 and 206.

Power for operating the motors 204 and 206 is provided by amplifiers 208 and 210 under the control of a (rack MTD PC) computer 212 connected to the motors 208 and 210 via digital signal processing interface cards 214 which allow the computer to send control signals to the motors 208 and 210. The cards 214 also allow the computer 212 to control a spindle amplifier 216 which, in turn, supplies the power for operating a spindle motor 218 for rotating the chuck 30.

The position determining means 202 comprises a linear scale 220 mounted on the carriage 48, and a Heidenhain encoder 222 which is mounted on the casting 10 and is arranged to read the scale 220. Further information on the position of the carriage 48 relative to the casting 10 is provided by a datum switch 224 which is mounted on the casting 10 and is closed by a portion of the carriage 48 (not shown) when the latter is at one end of its range of movement along the axis 70. The determining means 200 similarly comprises a linear scale 226 on the carriage 28, and a sensor 228 and datum switch 230 mounted on the casting 10.

The outputs from the sensors 98,222 and 228 are fed to the computer 212 via a Heidenhain splitter box 232, as is the output from an encoder 234 mounted on the workpiece spindle (on which the chuck 30 is also mounted) of the machine and arranged to provide velocity and position information on the spindle, and hence the workpiece 32. The splitter box 232 also enables those sensors to communicate with the amplifiers 208,210 and 216.

The computer 212 is also connected to the indexing drive 50 for the capstan 52 through control circuitry 236, and information on the angular position of the capstan 52 is derived by the computer from the output from kaman probes 238 connected to the computer 212 through an interface unit 240. The dimensions of parts of the workpiece mounted on the machine can be measured by means of air probes 242 which are also connected to the computer 212.

An operator can control the operation of the computer 212 by means of a Man Machine Interface 244, which in this case takes the form of a monitor 246, keypad 248 and control panel 250. The machine can also produce various control and information signals and receive various other signals, for example loader or metrology signals through I/O interface modules 252,254 and 256 connected to the computer 212. The present example of machine includes a 2-axis loader robot 258 which is connected to and controlled by the computer 212 using control circuitry 260.

In the event of an interruption in the mains power supply to the machine, the power supply to the computer 212 is maintained by an uninterruptable power supply 262, which permits controlled stops of the machine and prevent data being lost from the volatile memory of the computer 212.

The machine may also be equipped with a grooving tool (not shown) which can be advanced to the workpiece by means of a grooving system generally indicated at 264.

The encoder 96 is also connected to the computer 212 through the splitter box 232, but has been emitted from Figures 4 to 6 for the sake of simplicity.

Each of the carriages 28 and 48 may carry a respective plate which iC llsed to provide damping for the carriage mover, ; ç) The plates may be disposed just above the bottom wall 76 and below the strengthening rib 94 at positions generally indicated at 300 and 302, each of which respectively refers to the plate attached to the carriage 48 and the carriage 28. For the sake of clarity, the plates are not shown in the drawings. The plate attached to the carriage 28 overlies that attached to the carriage 48, and a viscose fluid, such as oil, is introduced between the two plates to provide damping of the carriage movements. In an alternative arrangement, the two plates do not overlie each other, but each plate instead partially overlies a respective tray mounted on the bottom of nut 76, the trays containing the viscose fluid for providing said damping.

In such a case, each tray may be movable to vary the proportion of the respective plate which overlies it so as to enable the amount of damping of the respective carriage to be fine tuned.

Two examples of the operation of the grinding machine will now be described with reference to the following definitions of the various offset and reference values which are used to determine the correct path for a working tool on the capstan 52 relative to a workpiece mounted on the carriage 28: X and Z axes'reference points These are the positions along the X and Z axes respectively of the carriages 48 and 28 which is defined by a given reference point. Initially, the reference point can be defined by the positions of the carriages at which the datum switches 224 and 230 are closed. The reference line (s) on either of the grids 86 and 88 corresponding to those positions can then be stored by the machine to enable it to find the reference positions in subsequent operations.

X and Z axes'home positions These are the positions which are cons. dered to be the retracted ends of the strokes of the carriages 28 and 48. At these positions, the displays on the Man Machine Interface 244 are set to indicate a value of +35 for X and +50 for Z.

X axis cutting point This is the position of the carriage 48 at which a tool (which requires no offsets) will be positioned on the axis 34, and therefore corresponds to the farthest forward end of the stroke of the carriage 48, i. e. when X = 0.

Z axis cuttinq point A tool (requiring no offsets) on the capstan 52 would be placed lOmm beyond (into) the front face of the jaws of the chuck 30 at this point, which is where the carriage 28 is at the farthest forward end of its working stroke (at which Z = 0).

Chuck Z reference offset This is the difference in Z values (a distance along the axis 34) between the front face of the jaws of the chuck 30 actually fitted to the machine and that of 15mm notional chuck jaws.

This offset can be varied to compensate, for example, for skimming of the jaws.

Toolset X and Z offsets These are the measured differences between the ideal position of a cutting edge of a tool in the capstan 52 and its actual position when fitted to the machine. If the offsets are zero, the tool edge is placed on the cutting points when X and Z = 0. These offsets are measured on an offline tool referencing fixture and fed to the computer 212. Each tool requires its own X and Z offset values.

Index X and Z tool offset This is the detected difference between the position at which a tool on the capstan 52 is actually placed at the cutting point, and the corresponding position for previous operations of the machine. These offsets represent the non-repeatability of the movement of the tool and workpieces relative to each other. For a given capstan 52, there will be eight pairs of X and Z tool offset values, one set for each position on the capstan.

X and Z metrology tool offset After a workpiece has been operated on by the machine, it is transferred to a post-process metrology station (not shown) where the workpiece dimensions are measured and compared with theoretical dimensions. the metrology station therefore produces a set of constantly updated values which represent the offset necessary to keep the dimensions of the finished workpiece within a predetermined tolerance as conditions change with time. Errors arising from gentle thermal drifts, tool wear etc will be corrected in this manner. These corrections can be automatically input into the computer through the module 256 or manually input should offline metrology features not measured at the metrology station indicate a drift out of working limits.

During the construction and setting up of the machine, the stroke of each of the carriages 28 and 48 can be adjusted, within soft limits, by changing the amount of movement required to take the carriages from the reference point positions and home positions to the cutting points. This will be reflected by changes in the differences between the X values corresponding to the reference/home positions and cutting positions.

The computer 212 can then be programmed to define the start and finish points of the path of movement of the tool with respect to the X and Z axes cutting points, i. e. h respect to the axis 34 and the face of the jaws of the chuck 30. The machine automatically makes further corrections by monitoring the finished workpiece and also by checking for non-repeatability of the capstan 52.

Example 1: Turning a diameter To form a cylindrical workpiece of 10mm diameter, the following steps are taken: 1. The carriages 28 and 48 are moved into their respective home positions; 2. the toolset X offset of a tool is measured by placing the tool in a tool holder of an off-machine tool referencing device (not shown). The tool (for example 54) is then mounted in a given receptacle in the face-plate of the capstan 52 and the measured toolset X offset is entered into the computer 212 which places that figure in a tool offset data-table applicable to that receptacle; 3. the tool is then advanced on the carriage 48 to a position of X = 5.000 (i. e. at which the end of the tool is 5mm away from the axis 34), and the tool is then in a position to turn the lOmm diameter, since the computer 212 will have incorporated the toolset X offset into the position coordinates of the tool; 4. during the initial turning, the index X tool offset is set to zero; 5. after the 10mm turned diameter workpiece is produced, it is transferred to the metrology station.

The accuracy of the finished component will be limited by the accumulated errors in the position of the X axis cutting point, the determined toolset X offset value, and errors introduced from non-'repeatability of the positions of the receptacle í the capstan 52, both in relation to the face-plate of the capstan and the reference points of the carriages 28 and 48.

However, the metrology X tool offset is calculated at the metrology station and fed back into the computer 212, which will then use the metrology X tool offset value to revise the tool position for subsequent workpieces.

Before such workpieces are formed, the machine will also calculate a value of the index X tool offset by moving the carriage 70 until the sensors 96 and 98, operating in cooperation with the scales 86 and 88, indicate that the tool is at the X axis cutting point, and then comparing that measurement with the position measurement given by the determining means 202. This data is then used to revise the tool position, again to correct for non-repeatability of the tool index.

Should all other functions on the machine remain unchanged, and the calculated value of the offsets be correct, the second part, in theory, will be turned exactly to size.

Subsequent parts can be produced in the same manner, the metrology X tool offset in these cases being subjected to a smoothing algorithm to stabilise the correction process.

Example 2: turning a face To turn a face with a positional dimension relative to a pre- machined feature, the feature's position relative to the front of the jaws of the chuck 30 needs firstly to be established.

In the following example, this dimension is 3mm.

1. The carriages 28 and 48 are first moved to their home positions as before.

2. The tool is then placed in an off-machine tool referencing fixture, so that the toolset _ offset can be measured. The tool and its holder are then mounted in a given receptacle in the capstan 52, and the toolset Z offset figure entered into the computer which uses the figure in an offset data table for that receptacle.

3. The carriage 28 is then moved until a position of Z = 13.000 is reached, and as a result the tool is then in a position to turn the face as the controller will have incorporated the toolset X offset into the actual Z position of the tool relative to the workpiece. If there is carrently a valid chuck Z reference offset in the memory of the computer 212, the latter will also use this figure to modify the Z position of the tool when at the cutting face.

4. The index Z tool offset figure is set to zero during the turning of the first face.

5. The part produced by the process is then transferred to the metrology station and can also be subsequently manually measured.

The accuracy with which the part is formed will be limited by the accumulated errors in the position of the Z axis cutting point, the toolset Z offset value and the calculated chuck Z reference of said offset, and the errors introduced from the non-repeatability in the locations of the tool holder receptacles (and the capstan 52).

If it is found that, for subsequent parts, the position of the cut face has to be moved, the chuck Z reference offset or the metrology Z tool offset can be manually adjusted by inputting suitable commands into the computer 212.

To turn a second part, the machine will automatically use new offsets to revise the tool position. The machine will also take the value currently found in the index Z tool offset (which is calculated in a similar fashion to the index X tool offset) revise the tool position again to correct rs, non-repeatability of the tool index for subsequent parts. Should all other functions on the machine remain unchanged, and the value of the offsets be correctly calculated, the second and subsequent parts will theoretically be turned exactly to size.