Milling machine

The problem addressed by the invention is to provide a milling machine which can be used to machine eccentric end faces and peripheral faces and which ensures a short machining time despite its simple design. A milling machine of this king for machining workpieces and with means of clamping eccentric end faces or enveloping surfaces, e.g. of a crankshaft (1), with a bed (20), with two mutually facing chucks (21, 22) to accommodate the workpiece (1), at least one of these chucks being rotatable and positionable (C1 axis) by means of a headstock (23, 24), with a tool holder (25, 26) which can be moved at right angles to the Z axis and has a rotatable milling cutter (5, 6), and with a control mechanism is characterized by a plurality of tool holders which can be controlled independently of each other in terms of both milling cutter rotation and travel in a transverse direction, and in that the control mechanism controls not only the rotation of the workpiece but also the transverse movement of the tool holders and the rotation of the milling cutters.

BACKGROUND OF THE INVENTION
 The invention relates to milling machines which can be used to machine both
 eccentric end faces and circumferential faces, e.g. peripheral faces.
 A typical workpiece having such faces is a crankshaft, for which reason the
 following text always refers to a crankshaft, without limiting the
 possible workpieces to this alone.
 For crankshafts, metal-removing machining is known both with
 external-milling machines and with internal-milling machines, that is to
 say by means of a milling cutter which annularly surrounds the crankshaft
 and has inwardly directed teeth. In this case, the axis of rotation of the
 milling cutter lies parallel to the longitudinal axis of the crankshaft.
 In this case, the crankshaft is held at its ends, that is to say on one
 sides at its end flange and on the other side at its end journal,
 centrically, that is to say on the centre axis of its centre bearings, in
 chucks on both sides.
 In a known solution, the crankshaft does not move during the machining, and
 thus the chucks are not driven by a spindle head. For machining of the
 crankpin journals, the annular internal-milling cutter rotates, on the one
 hand, about its own centre point in order to generate the cutting speed
 and, on the other hand, on an orbit about the centre of the crankpin
 journal to be machined, in order to mill the peripheral face thereof. Web
 end faces and web circumferential surfaces can also be machined in this
 manner, as long as the radius of curvature is smaller than the radius of
 the circuit of the cutting edges of the internal-milling cutter. With the
 crankshaft stationary, the internal-milling cutter can be displaced in a
 defined manner in the X- and Y-directions.
 The mounting which annularly surrounds the internal-milling cutter is
 extremely stable, but has a relatively wide extent in the Z-direction, for
 which reason, for short crankshafts, the simultaneous deployment of two
 internal-milling cutters axially spaced apart on the same crankshaft can
 be problematical.
 It is also known in that solution to rotate the crankshaft slowly during
 the machining, that is to say to be able to drive at least one of the
 chucks in a defined manner by means of a spindle head and to set its
 rotational position. This realisation of the C-axis for the workpiece
 makes it possible to dispense with the movement of the tool slide rest in
 the Y-direction, so that therefore only the tool slide rest for the
 internal-milling cutter merely comprises a lower slide for movement in the
 Z-direction and an upper slide for movement in the X-direction.
 Furthermore, external-milling machines are known, in which the milling
 units--in addition to the displaceability in the Z-direction--were
 displaceable in a defined manner in the X-direction, and the chucks for
 the crankshaft were held in one or two spindle heads. Realisation of the
 C-axis on the workpiece meant that the external-milling cutter was guided
 on in a defined manner in the X-direction during the machining of
 eccentric surfaces. However, the machining of eccentric surfaces did not
 entail two or more external-milling units, operating independently of one
 another, being deployed on the same crankshaft. This was only possible
 when machining the eccentric surfaces, e.g. the centre-bearing journals.
 In the case of the known milling machines, work is carried out with a
 conventional, negative cutting-edge geometry and cutting speeds on
 workpieces made of grey cast iron (GGG60-GGG80) of at most 160 m/min. As a
 result, very high cutting forces are introduced into the workpiece, for
 which reason it is also necessary as a rule to support the centre of the
 workpiece by means of steady rests, etc. A further drawback consisted in
 the fact that a high proportion of the process heat was introduced both
 into the workpiece, and thus also into the tool, and only a small
 proportion was dissipated via the chips.
 SUMMARY OF THE INVENTION
 a) Technical Object
 It is therefore the object of the invention to provide a milling machine
 for machining both eccentric end faces and circumferential faces which,
 despite a simple design, ensures a short machining time.
 b) Solution to the Object
 This object is achieved by means of the characterizing features of claim 1.
 Advantageous embodiments result from the subclaims.
 Owing to the C-axis of the workpiece and the resultant possible defined,
 but relatively slow rotation of the workpiece of generally less than 60
 revolutions/minute, frequently only 15-20 revolutions/minute, it is
 sufficient that the tool slide rests has to be able to move the tool,
 generally an external-milling cutter, in a defined manner, in addition to
 in the Z-direction, only also in the X-direction.
 This rotation of the workpiece is so slow that any imbalances of the
 workpiece which may arise do not have a disadvantageous dynamic effect on
 the result of the machining.
 c) Advantages
 The short machining time is achieved due to the fact that, despite the
 rotation of the workpiece, e.g. of the crankshaft, two tool units can
 work, independently of one another, on eccentric surfaces whose rotational
 positions do not coincide, which effect is only possible by means of a
 machine control system which controls the independent tool slide rests as
 a function of the position and rotation of the workpiece, it preferably
 being possible to specify optimisation targets, such as for example the
 chip thickness or the cutting speed.
 In this case, for a specific workpiece it is possible even before machining
 to calculate, for each instant of the machining, the rotational position,
 direction of movement and speed of the workpiece, the rotational speed of
 the milling cutters, the X-position and direction of movement and speed of
 movement of the milling cutters, etc., and to store these parameters in a
 working program, for example as a table of settings for various states of
 the machining, which program can then be executed by the machine control
 system.
 d) Further Configurations
 Another possibility consists in taking into account at the same time the
 current actual position and actual movement of the workpiece during the
 machining and, as a function of these, controlling the tool slide rests.
 However, this is considerably more complex in terms of the sensor
 technology and the control outlay.
 Owing to the relatively low rotational speed of the workpiece, slip errors,
 that is to say deviations between the desired and the actual position,
 during the movement of the workpiece are relatively low.
 In order also to achieve this on the tool side, for example when using a
 side-milling cutter, the diameter is designed to be larger than would be
 necessary for the penetration depth for milling the big-end journal of a
 crankshaft. This enlargement of the side-milling cutter results in a
 likewise relatively low rotational speed of the milling cutter, so that in
 addition the rotational speed of the tool can be constantly adjusted with
 slip errors which are only negligibly low.
 For machining a passenger-car crankshaft with a throw of 10-15 cm, the
 diameter of a side-milling cutter used for this purpose is about 800 mm.
 This also results in thermal advantages, since a relatively long time is
 available for cooling between two successive deployments of one and the
 same cutting edge of the milling cutter.
 If suitable cutting materials and cutting-edge geometry are used, cutting
 speeds of 800 m/min and even significantly more can be achieved, and in
 addition the machine does not need any cooling lubricant at the machining
 location, since dry milling is possible, in particular with a positive
 tool geometry.
 Instead of a linear movement of the milling cutter in the X-direction, it
 is also possible to pivot the milling cutter about an axis parallel to the
 Z-axis, which is necessary in particular when using a slotting cutter, the
 axis of rotation of which is arranged perpendicular to the longitudinal
 axis of the crankshaft. The cutting edges on the front end face of a
 slotting cutter of this kind machine circumferential faces, that is to
 say, for example, the peripheral faces of the crankpin journals of a
 crankshaft, and its cutting edges on the circumferential face machine the
 side faces, for example the web end faces.
 The use of a side-milling cutter, in which therefore cutting edges are
 arranged on its circumferential region and/or in the transition region
 between the circumferential face and the end face of the cylindrical base
 body, is to be preferred to an internal-milling cutter, since even with a
 width of the side-milling cutter in the Z-direction of only about 20-25 mm
 and a diameter of about 800 mm such a side-milling cutter is sufficiently
 stable to be mounted free on only one side. If two side-milling cutters
 which act on the workpiece from the same side but are axially spaced apart
 are used, these two side-milling cutters can thus be mounted driveably on
 mutually remote sides on their respective slide rests, so that these two
 side-milling cutters can in theory be moved towards one another in the
 axial direction as far as until their cutting edges make contact on the
 end side.
 In the case of an internal-milling cutter mounted and surrounded along the
 outer circumference, it is not possible to achieve such a narrow design in
 the Z-direction and to bring two milling units so close together.
 Moreover, cylindrical external-milling cutters are easier to equip, and
 also to adjust and exchange, which is an extremely important factor in
 view of the fact that in currently possible processes the idle times and
 non-cutting times of a machine compared to the cutting times are becoming
 ever more significant.
 The cutting edges in milling cutters of this kind are usually positioned
 along the circumference as screwed-on throw-away cutting-tool tips. In
 principle, a distinction is made here between three different types
 cutting tip with regard to their use: The so-called web-cutting tip
 machines end faces, that is to say, for example, web side faces, the
 so-called journal-cutting tip machines circumferential faces, that is to
 say, for example, the peripheral face of a bearing journal of a crankshaft
 or the outer circumferential contour of a web, possible peripheral faces
 being any desired convexly curved contour and plane, for example surfaces
 arranged tangentially with respect to the Z-axis and even concave
 surfaces, as long as their radius of curvature is greater than the radius
 of the side-milling cutter used.
 The milling of planar surfaces as fastening surface for additional weights
 or for balancing operations is a particularly important advantage of
 external milling over internal milling.
 Furthermore, to produce the so-called undercut, that is to say a recess at
 the transition between the peripheral face of the journal and the end-side
 web end face, special undercut-cutting tips are present.
 It is possible, for example, to arrange only journal-cutting tips on a
 side-milling cutter, which provides the possibility of additionally
 displacing such a side-milling cutter in a defined manner in the
 Z-direction during the machining, and thus of being able to mill bearing
 journals of virtually any desired width using a narrow side-milling cutter
 without annularly encircling machined shoulders. In this case, the
 undercut has to be produced by a separate milling cutter.
 Another possibility consists in arranging the undercut-cutting tips
 directly on one circumferential edge, or even on both circumferential
 edges, of the milling cutter which bears the journal-cutting tips, and
 thus in milling the undercut together with the peripheral face of the
 journal. If the two-sided undercut-cutting tips are arranged on a milling
 cutter, the milling cutter corresponds to the finished axial length of the
 bearing location, that is to say only to a specific workpiece to be
 produced. If one milling cutter is used for the left-hand undercut and the
 left-hand half of the peripheral face of the journal and another milling
 cutter is used for the right-hand half of the journal face, it is possible
 to produce variable bearing widths in the Z-direction using one and the
 same pair of side-milling cutters by means of variable intersection in the
 centre.
 The web-cutting tips are mostly arranged on a separate side-milling cutter,
 and again preferably on both end faces of the side-milling cutter, in
 order to be able to machine side faces which are directed both in the +Z
 and in the Z-direction. Arrangement on a separate side-milling cutter is
 sensible, since relatively large volumes are to be removed along the web
 side faces and thus these web-cutting tips wear more quickly than, for
 example, the journal-cutting tips or the undercut-cutting tips.
 The milling machine according to the invention may, for example, comprise
 only two milling units, which can be moved independently of one another
 and which work on the crankshaft from approximately the same side, merely
 being spaced apart axially. As a rule, the movement in the X-direction
 will be directed obliquely from above or even perpendicularly towards the
 crankshaft, in that either the bed of the milling machine itself or at
 least the transverse guide along which the upper slide runs on the lower
 slide of the tool slide rest is already positioned either obliquely or
 steeply.
 However, it is also possible for two independently operating tool units to
 work on the workpiece from opposite sides or else with transverse
 movements directed towards one another in the manner of a V.
 If, in these cases, in addition a plurality of tool slide rests are
 arranged one after the other, spaced apart in the Z-direction, it is also
 possible for four or even more tool units to work simultaneously on one
 and the same workpiece.
 In addition, a single tool unit may have a multiple tool, that is to say,
 for example, two side-milling cutters which are spaced apart in the
 Z-direction but can only be moved synchronously with one another, for
 example as a tandem tool. This is useful in particular if the crankshaft
 to be machined has two crankpin journals which are aligned with one
 another, such as for example the crankshafts of four-cylinder in-line
 engines. However, since multiple tools of this kind are coupled in terms
 of their transverse movement and rotation, they are only to be considered
 as a single tool unit.
 In the case of the double-sided driving of the crankshaft held in the
 chucks, the double-sided spindle drives are preferably electrically
 synchronised.
 Even when machining the workpiece using a machining program worked out
 prior to the machining and stored in the machine control system, this
 machining program can be corrected subsequently on the basis of the
 measurements of the first finished parts:
 It is known that the result of the machining is in practice slightly
 out-of-round, despite the machining of a precise cylindrical surface,
 owing to the deflection of the crankshaft in the transverse direction by
 the cutting forces. It is attempted to compensate for this by milling a
 theoretically out-of-round contour which, owing to the deflection of the
 crankshaft in the transverse direction which occurs in practice, then
 results in a very close approximation of a completely cylindrical
 peripheral face. Since this in theory can only roughly be taken into
 account when establishing the machining program, the machine control
 system includes the possibility, after producing the first samples, of
 inputting the out-of-roundness still present with regard to size and
 angular position into the control system using an input panel, the control
 system them automatically, and preferably for each bearing journal
 individually, if necessary even beyond its axial length, adjusting the
 transverse movements of the milling units differently for the respective
 angular position of the workpiece.
 If two milling units which are drivable and operate independently of one
 another are machining different, eccentric surfaces for machining on one
 and the same rotatable and drivable crankshaft, and it is intended to
 maintain an optimum value or range for the chip thickness, under certain
 circumstances it is only possible to achieve the desired maximum cutting
 speed, for example the cutting speed of HS milling, at one machining
 point.
 In order to keep the chip thickness or average chip thickness within the
 optimum range at the other machining points, under certain circumstances
 the rotational speed of the milling cutter has to be reduced there, and
 consequently so too does the cutting speed. For this reason, at the start
 of the journal machining the milling cutter is not moved immediately
 radially as far as the desired dimension, but rather is moved slowly as
 far as the radial desired dimension while the crankshaft is rotating
 slowly, over the course of a rotation of the journal to be machined of
 30-90, preferably of 50-70.degree.. As a result, the stipulation with
 regard to the chip thickness is observed even at the beginning of the
 machining of a bearing journal, and inadmissibly high transverse forces
 are not introduced into the workpiece at the start of the machining. After
 reaching the radial desired dimension, it is necessary to execute a
 complete cycle of the journal surface, preferably about 100.degree.
 circumferential surface, in order to achieve an optimum machining result.
 If there is no optimum value for the chip thickness with regard to the
 life-cycle performance of a tool, the independent tool units would be
 optimised with a view to maximum cutting speed. These laws, which were
 determined primarily for machining grey cast iron (GGG60-GGG80), may under
 certain circumstances also be valid for other workpiece materials, such as
 steel, for which other groups of cutting materials are also employed.
 The additional use of a positive tool geometry instead of the negative tool
 geometry which was previously used in milling and which nevertheless,
 primarily in connection with the low average or maximum chip thicknesses,
 leads to a sufficient tool life of the cutting means, in turn results in a
 reduction in the cutting forces and consequently also in a reduction in
 the driving powers required for the tool, which powers, for the size
 ratios indicated, is only about half to one third of the power required
 for internal milling or rotary turn broaching. In addition to the lower
 energy costs, this also minimises the waste heat problems of the drives,
 which always have a negative effect on the overall machine and the
 machining result.
 The high-speed milling according to the invention may in this case be
 carried out, in particular, not only on the unhardened workpiece but also
 on the hardened (e.g. Rockwell hardness H.sub.RC of 60 to 62, in
 particular fully hardened) workpiece. In this case, the cutting material
 preferably used is cermet or polycrystalline boron nitride (PCB), and in
 the case of the latter in particular cubic boron nitride (CBN). In this
 case, it is preferable firstly to sinter a carbide cutting tool tip as
 usual which, however, has cavities in the cutting-edge area, e.g. in the
 tool face open towards the cutting edge. CBN powder is placed in these
 cavities in the base body and is then sintered.
 It is not only the noses of throw-away cutting tool tips which can be
 reinforced in this manner, but also an entire cutting edge can be
 reinforced by arranging a plurality of CBN pallets next to one another
 along a cutting edge, or else by providing a bar-shaped CBN insert. It is
 consequently also possible to machine unhardened steel or cast iron, even
 by milling.
 These cutting materials can also be used without cooling lubricant, that is
 to say dry, thus saving on disposal costs and environmental problems.
 It is thus possible even as early as during the metal-removing machining to
 eliminate the distortion of the workpiece which due to the hardening
 process occurs in conventional production (metal-removing machining prior
 to hardening). Since, when using high-speed milling and in particular when
 using high-speed milling on the hardened workpiece, it is possible to
 achieve surface qualities which are acceptable as the final state of the
 workpiece, it is consequently possible to dispense with at least the
 rough-grinding operation altogether.
 When machining the journal and web surfaces on crankshafts which consist of
 cast iron or steel and are machining in the unhardened state by means of
 an external circular-milling cutter, in particular by means of a disc-like
 milling cutter with cutting edges on the circumferential region, it has
 proven particularly advantageous to observe the following parameters:
 Cutting speed during the roughing machining: at least 180, preferably
 250-600 m/min,
 Cutting speed during the finishing machining: at least 200, preferably
 300-800 m/min,
 Chip thickness: 0.05-0.5 mm, in particular 0.1-0.3 mm.
 The tool used here is generally a disc-like tool body driven in rotation
 and having inserted throw-away cutting-tool tips. In this case, the
 configuration of the cutting-tool tips differs depending on their intended
 purpose (machining of the end faces on the webs, machining of the
 peripheral surfaces on the journals of the main bearing point and big-end
 journal points, production of the undercuts at the transition between
 peripheral surfaces and end faces) and they are also positioned
 differently with respect to the tool carrier or to the workpiece:

DESCRIPTION OF THE PREFERRED EMBODIMENT
 The milling machine illustrated in FIGS. 1a and 1b comprises a bed 20 with
 a chip trough 34 and a chip conveyor 45 accommodated therein. Two spindle
 heads 23, 24, which are spaced apart in the Z-direction and are directed
 towards one another, are positioned above the chip trough 34, at least one
 spindle head 24 being displaceable in the Z-direction.
 The spindle heads in turn bear chucks 21, 22, which are directed towards
 one another, can be driven in rotation and are electronically synchronised
 with one another in terms of their rotation.
 A crankshaft 1 is chucked in between the two chucks 21, 22, which
 crankshaft is chucked by the chuck 21 on its end flange and by the chuck
 22 on its end journal, that is to say on the centre axis MA of the
 crankshaft 1, which thus coincides with the spindle-head axis. The belt
 surfaces, that is to say the circumferential faces on the end-bearing
 flange and on the end-bearing journal, have been rough-machined, in
 particular rough-machined with the removal of metal, and in addition
 corresponding stop faces have been rough-machined on the crankshaft for
 the purpose of inserting the crankshaft into the chucks in a defined
 rotational position.
 Since the spindle heads 23, 24 not only drive the crankshaft in rotation
 but are also able to set its rotational position (C-axis formed), the
 crankshaft 1 chucked therein can at any time during the machining be
 brought into the desired rotational position, and moreover at a defined
 speed.
 Viewed in the direction of FIG. 1a, Z-guides 33 are arranged on the bed 20
 of the milling machine, behind the chip trough 34 and rising obliquely
 backwards out of the latter, on which Z-guides the lower slides 29, 30,
 which can be seen in FIG. 1a, of the tool slide rests 25, 26 can be
 displaced in the Z-direction.
 On each of the lower slides 29, 30 there runs an upper slide 27, 28 which
 in each case supports a side-milling cutter 5, 6 such that it can be
 driven in rotation about an axis parallel to the Z-axis.
 The upper slide 27, 28 can be moved from above in the X-direction onto the
 centre axis MA at a relatively steep gradient, at an angle of less than
 45.degree. to the perpendicular. The X-guides between upper slide 27, 28
 and the lower slide 29, 30 here preferably coincides with the connection
 of the centre points of the side-milling cutters 5 and/or 6 and the centre
 axis MA.
 In order to be able to use such a milling machine with an externally
 toothed side-milling cutter to machine the circumference of a crankpin
 journal H1, H2 over the entire circumference, the crankshaft 1 chucked on
 the centre axis MA must complete at least one full revolution during the
 machining.
 As can best be understood with reference to FIG. 1a, during the rotation of
 the crankshaft 1 the side-milling cutters 5, 6 which are simultaneously in
 use at different machining locations are constantly guided on in the
 X-direction with the aid of the tool slide rests 25, 26.
 As will be explained in more detail later, the movements of the two tool
 slide rests 25, 26 are thus indirectly dependent on one another, in that
 they depend on the rotation of the crankshaft which they are both
 machining and the geometry of the eccentric surfaces to be machined.
 If in the process it is intended to carry out optimisations to the
 machining by means of these several slide rests which can be controlled
 independently of one another, for example with regard to a specific chip
 thickness, the side-milling cutters 5, 6 not only move differently in the
 X-direction but also rotate largely with different, constantly adjusted
 rotational speeds.
 The milling cutters 5, 6, and also their slide rests 25, 26 and the machine
 control system which controls the joint rotation of the spindle heads,
 i.e. of the crankshaft 1, can additionally be recorrected by correction
 values using an input panel 36 on the machine, on the basis of the
 results, determined in practice, of the machining of the first components
 of a series of workpieces.
 In FIG. 1b, the tool slide rests 25, 26, and thus also the directions of
 movement of the milling cutters 5, 6 and of the upper slides 27, 28, are
 aligned one behind the other in the direction of viewing.
 By contrast, FIG. 2 shows a different configuration of the machine in
 which, by contrast to FIG. 1b, the slide rests 25, 26, which are of
 similar design, are arranged in mirror-image fashion with respect to a
 centre plane ME, namely the vertical plane through the spindle-head axis.
 The directions of movement of the milling cutters 5, 6 in the X-direction
 towards the workpiece are thus positioned in a V-shaped manner with
 respect to one another.
 Owing to the relatively large diameter of the milling cutters 5, 6, it is
 here possible for the milling cutters 5, 6 to operate simultaneously at
 different axial positions of the crankshaft, and in addition, in the
 direction of viewing of FIG. 2, the same tool slide rests 25', 26' may
 again be arranged behind the tool slide rests 25, 26, axially spaced
 apart. The fact that four side-milling cutters 5, 5', 6, 6' can then
 machine the crankshaft simultaneously permits optimally short machining
 times for crankshafts and similar parts.
 Viewed in the same direction as FIG. 1, namely in the Z-direction, FIG. 3
 shows another machine design, in which the slide rests 25, 26 act on the
 workpiece from opposite sides. The directions of movement of the two
 side-milling cutters 5, 6 are in this case on a line which runs through
 the spindle-head axis and are thus inclined just as much with respect to
 the perpendicular as the solution in accordance with FIG. 1b. On the
 inclined bed, one slide rest 25 is situated above the spindle heads 23, 24
 and the other slide rest 26 is situated below the spindle heads 23, 24.
 In this machine configuration too, in the direction of viewing of FIG. 3,
 identical slide rests may again be arranged behind the slide rests 25, 26,
 axially spaced apart, so that here too more than two, for example four or
 even six, milling cutters, which can be controlled independently of one
 another, can act on the workpiece.
 FIG. 4 shows an illustration similar to that of FIG. 1a, but in which three
 side-milling cutters can be seen. However, two of the three side-milling
 cutters are coupled together to form a multiple tool 42, in that the two
 side-milling cutters, which are assigned to the tool slide rest 26, are
 connected to one another in an axially spaced but rotationally fixed
 manner and are driven jointly by this slide rest 26. It is thus possible
 to machine simultaneously machining locations which are aligned in the
 Z-direction, for example the second and third big-end journals of a
 crankshaft for a four-cylinder in-line engine.
 The machine shown in FIG. 4 thus has three side-milling cutters, but only
 two milling units which can be driven independently of one another.
 FIG. 5 shows a side view of a milling machine similar to that of FIG. 2.
 Here, the slide rest 25 is of identical construction to that in FIG. 2,
 that is to say it is equipped with a side-milling cutter 5 which can be
 driven in rotation about an axis which is parallel to the Z-direction,
 i.e. to the spindle-head axis.
 In this case, the centre point of the side-milling cutter 5 moves in the
 X-direction, that is to say parallel to the X-guides between lower slide
 29 and upper slide 27, on a plane which runs above the spindle axis. This
 results in a more compact structure of the milling machine owing to the
 tool slide rest being reduced in height.
 In contrast to this, the tool slide rest 26, which like the slide rest 25
 comprises a lower slide 30 and an upper slide 28, bears a slotting cutter
 37, the axis of which runs transversely to the spindle-head axis. This
 slotting cutter 37 is mounted such that it can pivot in the upper slide
 rest 28 about an axis which is parallel to the Z-direction, that is to say
 to the spindle-head axis. As a result, it is possible to machine eccentric
 peripheral faces, for example to machine a crankpin journal of the
 centrically chucked crankshaft, in that during the slow rotation of the
 crankshaft the slotting cutter 37 is constantly guided on by pivoting with
 respect to the upper slide 28 and the traversed X-direction of the upper
 slide 28 with respect to the lower slide 30.
 Instead of the traversing movement of the slotting cutter 37 with the upper
 slide 28 in the X-direction, an additional pivoting, i.e. virtually a
 pivoting of the upper slide 28 with respect to the lower slide 30, is also
 possible for compensation in the X-direction.
 The machine depicted in FIG. 5 may, instead of being fitted with
 side-milling cutters and slotting cutters, also be equipped only with
 slotting cutters; this, incidentally, also applies to all other machine
 designs in accordance with the present invention.
 FIG. 6 shows the surfaces which are typically to be machined on a
 crankshaft and the corresponding fitting of the base bodies 5a, 6a, 7a of
 the side-milling cutters 5, 6 with exchangeable cutting tips:
 In FIG. 6a, the web-cutting tips 39 for machining web side faces 3 are
 arranged on both end faces of the cylindrical base body 6a of a
 side-milling cutter 6, the web-cutting tips 39 obviously also protruding
 radially beyond the base body 6a.
 Due to the arrangement of the web-cutting tips on both sides of the base
 body 6a, it is possible to machine both left-hand and right-hand web faces
 3 and 3'.
 The arrangement of the web-cutting tips 39 on their own base body 6a is to
 be recommended, since owing to the high volume of metal removed from the
 web side faces 3, 3' these tips wear and have to be exchanged more quickly
 than, for example, the journal-cutting tips 40. In FIG. 6a, the latter are
 arranged on the circumferential face of a cylindrical base body 5a of a
 side-milling cutter 5 in two axially spaced apart paths which overlap in
 the Z-direction and on the respective outer side also protrude in the
 Z-direction beyond the base body 5a.
 With such a side-milling cutter 5 which is exclusively fitted with
 journal-cutting tips 40, only peripheral faces, for example the journal
 face 16, are machined. Such a side-milling cutter 5 in accordance with
 FIG. 6a can also be used--by means of an additional controlled
 displacement of the side-milling cutter 5 in the Z-direction--to machine a
 journal face 16 which is significantly wider in the Z-direction than the
 width of the side-milling cutter 5. Due to the spiral machining path,
 annular shoulders between axially spaced-apart machining areas of a
 journal face 16 are avoided.
 FIG. 6b shows another solution. In this figure too, the web-cutting tips 39
 are arranged on their own base body 7a of a milling cutter. However, two
 separate side-milling cutters 5, 6 for the left-hand and right-hand
 halves, respectively, of the journal face are provided for machining the
 journal face 16 and the undercuts 15 which adjoin the latter on both
 sides:
 In this case, journal-cutting tips 40 which are in each case arranged on
 the circumference are situated on the base body 5a and/or 6a, while
 undercut-cutting tips 41 for producing the undercut 15 or 15' are arranged
 on the end face of the base body, i.e. for the right-hand half in the
 +Z-direction and for the left-hand half in the -Z-direction. Obviously, in
 this case the undercut-cutting tips 41 again protrude radially beyond the
 base body 5a and/or 6a. The machining width of the two milling cutters 5,
 6 in the Z-direction is in this case so great that in the centre of the
 journal the machined areas overlap. In order to avoid an annular shoulder
 here, in this case the journal-cutting tips 40 are designed to fall off
 slightly towards the centre of the bearing journal, i.e. they are
 chamfered or even rounded, in order in the centre of the bearing location
 to produce only a rounded elevation instead of a sharp shoulder.
 The undercut-cutting tips 41, which are not shown in FIG. 6a, are in this
 figure arranged on a separate milling cutter, in order to produce the
 undercuts 15, 15' separately.
 In the direction of viewing of the Z-axis, FIG. 7 shows the fundamental
 situation for the machining of a circumferential surface, for example of
 the journal of a crankshaft, but also of an out-of-round circumferential
 surface, by means of external milling. An enlarged illustration of the
 machining point is depicted in the right-hand part of FIG. 7.
 The workpiece is intended to be machined from the larger base dimension to
 the smaller final dimension.
 In this case, the cutting edges S, only one of which is drawn in, protrude
 radially beyond the tool body, in order to be able to effect this
 abrasion. The tool body is in this case displaceable in a defined manner
 in the X-direction and rotates anticlockwise. Since the milling is
 intended to take place on a climb-cutting basis, the workpiece rotates in
 the clockwise direction, so that at the machining point tool and workpiece
 are moving in the same direction.
 As shown by the enlarged depiction, the new cutting edge S will produce a
 chip 1 , which is delimited in cross-section by two convex and one concave
 curved segments and has the form of a flat, irregular triangle.
 In this case, the concave side is the flank produced by the preceding cut,
 and the long convex side is the flank produced by the the new cutting edge
 S. The short convex flank is the length .DELTA.I.sub.U measured along the
 circumference of the branch piece, that is to say the circumferential
 length between two successively arranged cutting edges of the tool
 striking the circumference of the workpiece.
 In practice, of course, the chip 1 does not retain the shape which can be
 seen in FIG. 7, but rather is rolled up spirally owing to the deflection
 at the tool face of the cutting edge.
 It can be seen from FIG. 7 that the chip thickness, e.g. h.sub.1, of the
 chip 2--viewed in the passage direction of the cutting edge--increases
 rapidly up to the maximum chip thickness h.sub.max. From there, the chip
 thickness decreases relatively slowly and continuously to the end (e.g.
 h.sub.x).
 If the difference between the base dimension and the final dimension
 remains the same and the rotational speed of the workpiece likewise
 remains the same, it can be seen from this illustration that a reduction
 in the rotational speed of the tool has the effect of increasing the cut
 distance .DELTA.I.sub.U, and thus also of increasing h.sub.max.
 Again viewed in the Z-direction, FIG. 8 illustrates, for example, a
 crankshaft for a 6-cylinder in-line engine having three crankpin journals
 H1-H3 with different rotational positions with respect to the centre
 bearing ML.
 Two separate tools, for example disc-like external-milling cutters (WZ1,
 WZ2), are being used on this crankshaft at different axial positions. One
 of the tools could, for example, machine the crankpin journal H1, and the
 other the crankpin journal H2, as illustrated in FIG. 8, but it would also
 be possible for one of the tools to machine a crankpin journal and the
 other of the tools to machine the end face of a web.
 In the latter case, the machining of the web could in theory take place
 partially with the crankshaft stationary, in that the relevant tool WZ1 or
 WZ2 works along the end face of the web in the feed direction, that is to
 say in the X-direction. However, since if the crankshaft is stationary it
 is not possible to achieve any progress with the machining, taking place
 at a different axial position, of a peripheral surface, whether of a
 crankpin journal H or of a centre bearing ML, the machining of the web
 surface is preferably also carried out with the crankshaft rotating.
 If the machining of the web starts in that position of the crankshaft which
 is illustrated in FIG. 8 and then the crankshaft rotates further, the
 result is the cutting paths s.sub.a, s.sub.b, s.sub.m, s.sub.x, some of
 which are drawn in FIG. 8.
 As can be seen, these cutting paths, owing to the climb-cutting operation
 of the milling cutter, together with the rotation of the workpiece, are at
 a greater distance apart at the point where they begin than at the point
 where they end, that is to say the point at which the cutting edge leaves
 the side face of the web.
 FIG. 9 shows the relationships when two separate tools WZ1, WZ2 are
 simultaneously machining two different crankpin journals H1, H2.
 Independently of one another the tools WZ1 and WZ2 can move in a defined
 manner in the X-direction and their rotational speed can be controlled.
 However, the parameter which links them is the rotation of the crankshaft,
 as the workpiece, which is driven in rotation, likewise in a controlled
 manner, about the centre bearings, which rotation can also be stopped for
 certain machining operations.
 In the situation illustrated in FIG. 9, crankpin journal H2 is situated in
 line with the centre bearing ML1 and the centre point M.sub.1 and M.sub.2
 of the tools WZ1 or WZ2. The crankpin journal H1 is offset through about
 120.degree. in the clockwise direction with respect to the centre bearing.
 If, as indicated, the tools WZ1 and WZ2 are each rotating anticlockwise and
 the crankshaft--as drawn in at its centre bearing ML--is rotating in the
 clockwise direction, the big-end journal H1 is clearly being milled by a
 climb-cutting method, which effect is desirable for the reasons given
 above.
 For the big-end journal H2, one could gain the impression that it is
 subject to ordinary milling, since at this point the tool WZ2 is moving
 downwards but the crankpin journal H2 is moving upwards.
 However, the absolute movement of the crankpin journal is not the deciding
 criterion in assessing whether ordinary or climb-milling is taking place,
 but rather the important factor is whether the big-end journal H2 is
 rotating about its own centre point allowing its surface at the machining
 point still to move in the same direction as the milling cutter.
 However, viewed in absolute terms, the crankpin journal H2, which is
 migrating upwards in FIG. 9, is clearly rolling upwards along the tool
 WZ2, so that, therefore, the big-end journal is rotating in the clockwise
 direction relative to the centre point of the big-end journal H2 and
 therefore de facto climb-cutting is the prevailing circumstance at the
 machining point.
 FIG. 9 furthermore shows the relationship which is necessarily present
 between the machining on the two big-end journals H1 and H2, which
 relationship is to be taken into account primarily in optimizing a
 plurality of machining operations which take place simultaneously with
 regard, for example, to a specific chip thickness.
 It has been assumed that the milling cutter WZ2 in relation to the
 crankshaft 1--of which only the centre bearing ML and the two crankpin
 journals H1 and H2 currently being machined are shown in FIG. 9, for the
 sake of clarity--are rotating so quickly with respect to one another that
 the crankshaft has been rotated further through the angle .DELTA..alpha.
 between the engagement of two successive cutting edges of the tool WZ2 on
 the big-end journal H2. Since in FIG. 9 the centre point of the big-end
 journal H2 and the centre point of the crankshaft, that is to say of the
 centre bearing ML, are in line with the centre M2 of the tool WZ2, the
 pivot angle .DELTA..alpha. provides an offset a.sub.2 of the point where
 the new cutting edge strikes with respect to the old cutting edge, which
 runs almost precisely in the Y-direction.
 As a result, it is only necessary for there to be a very small X-component
 x.sub.2 by means of a corresponding X-movement of the tool WZ2, and the
 resultant cutting distance .DELTA.I.sub.U2 determines a chip
 cross-section, the thickness of which is intended to correspond to the
 optimum chip thickness.
 It is also intended, as far as possible, for the same chip thickness to be
 achieved at the machining point of the crankpin journal H1. Assuming that
 the rotational speed and diameter of the tools WZ1 and WZ2 are the same,
 the centre point of the crankpin journal H1 has also been pivoted through
 the angle .DELTA..alpha. with respect to the centre of the big-end journal
 by the time that the next cutting edge of the tool WZ1 comes into action.
 The offset a.sub.1, thus brought about at the machining point is in this
 case greater to only a negligible extent than a.sub.2, since the distance
 from the centre of the centre bearing ML to the machining point on the
 big-end journal H1 is slightly greater than the distance to the centre of
 the big-end journal H.sub.1. This offset a.sub.1 has a pronounced
 component x.sub.1 in the X-direction, which component has to be
 compensated for by a corresponding movement of the tool WZ1 in the
 X-direction. Thus only a relatively small component of a.sub.1 remains as
 the cutting distance .DELTA.I.sub.U1 in the Y-direction. This would result
 in the thin chip, which is illustrated to the outside on the right-hand
 side in FIG. 9, with a maximum thickness of only H.sub.1max, which is much
 smaller than the optimum chip thickness.
 In order to reach the optimum chip thickness at this machining point too,
 the rotational speed of the tool WZ1 has to be reduced by comparison with
 the rotational speed of WZ2, so that the cutting distance .DELTA.I.sub.U1
 increases to such an extent that the desired chip thickness is also
 achieved on the crankpin journal H.sub.1. It is necessary here to reduce
 the rotational speed of tool WZ1 to a maximum of about 30% of the
 rotational speed of tool WZ2.
 In addition to the first optimization target described of a
 specific--average or maximum--chip thickness, the secondary optimization
 target could be a cutting speed which is intended to move within a
 predetermined target corridor or is intended not to exceed a specific
 maximum value.
 In the former case, this would lead, in the case of the machining
 illustrated in FIG. 9, to the rotational speeds of the workpiece and of
 the tool WZ2, during the machining of the big-end journal H2, being
 increased with respect to one another--such that the desired chip
 thickness is maintained on the big-end journal H2, to such an extent that
 the rotational speed of tool WZ2 moves at the upper end of the specified
 range for the cutting speed. This also results in an increase in the
 rotational speed of the tool WZ1, as a result of which the cutting speed
 on the crankpin journal H.sub.1 should likewise still lie within the
 specified range for the cutting speed.
 By contrast, if an upper limit is specified for the cutting speed, this
 upper limit would be applied to the machining on the crankpin journal
 H.sub.2, which has the higher cutting speed by comparison with the
 machining on the crankpin journal H.sub.1, so that, as a result, an
 absolute upper limit of the cutting speed is automatically observed at
 both machining points present.
 In the event of more than two points on a crankshaft being machined
 simultaneously, in an analogous manner the limiting criterion for absolute
 maximum or minimum values is always to be applied to the machining point
 which has the relatively highest or lowest corresponding value.
 When specified ranges of certain cutting parameters are being applied, it
 may be that it is not possible to observe this range for all the machining
 points. In this event, either the specified range width should be
 increased or a third-priority optimization parameter has to be specified.
 This third optimization variable could, for example, be the chip length
 (primarily in the case of the machining of web side faces).
 The mutual dependencies illustrated in FIG. 9 when observing a specific
 chip thickness occur to an increased extent when one of a plurality of
 simultaneous machining points on the crankshaft is the machining of an end
 face of a web, as illustrated in FIG. 10. The illustration in FIG. 10
 shows a crankshaft, for example for a four-cylinder in-line engine, in
 which the crankpin journals H1 and H2 are situated opposite one another,
 in the radial direction, with respect to the centre bearing ML.
 If, in the position illustrated in FIG. 10, one were to begin machining the
 web surface 3 by means of the tool WZ, the crankshaft would rotate further
 in the direction indicated (in the clockwise direction) about the centre
 of the centre bearing ML, while the tool WZ is rotating anticlockwise, in
 order to bring about climb-cutting milling.
 Some of the resultant cutting paths s.sub.a, s.sub.b, s.sub.m, s.sub.x are
 drawn in on the web surface 3.
 The simultaneous rotation of the crankshaft results in chip cross-sections
 which are again considerably larger at the start of the chip than towards
 the end of the chip, and in addition the chips differ considerably in
 their length, depending on the respective position of the cutting path on
 the web surface 3.
 As a rule, it is not possible to dispense completely with a rotation of the
 crankshaft, since otherwise a machining operation, currently taking place
 at a different point of the crankshaft, on a bearing journal would no
 longer produce any progress in the machining.
 Therefore, if, on a crankshaft, a plurality of web side faces or one web
 side face takes place at the same time as the machining of a bearing
 journal, the discrepancies in chip thicknesses between the various
 machining points, given identical rotational speeds and diameters of all
 the tools, which discrepancies were illustrated with reference to the
 example of FIG. 9, occur to an increased extent, so that it is necessary
 to an increased extent for the rotational speeds, and/or in the case of
 the machining of a web also the movement in the transverse direction, that
 is to say the X-direction, by the milling cutter, to be adjusted
 continually, in order to observe the desired optimum chip thickness in
 each phase of the machining and at all the machining points at the same
 time.
 As shown by FIG. 11, in order to protect the workpiece, the procedure is as
 follows even at the start of the machining of the peripheral surface, for
 example of a bearing journal:
 Despite the rotation of the workpiece, the milling cutter is fed in
 relatively slowly as far as the desired radial dimension. A radial in-feed
 which is too quick would not only increase the chip thickness to
 unacceptable levels but also, above all, the corollary transverse forces
 which are introduced into the workpiece would become relatively high, due
 to the chip length, which is then considerable owing to the relatively
 great wrap between a disc-like external-milling cutter, which rotates
 about an axis parallel to the bearing-journal axis, and the current
 machining point.
 As shown by FIG. 11, the milling cutter is moved forwards radially towards
 the centre point of the bearing journal to be machined so slowly that the
 existing extent is acted on by the milling cutter only after a traverse-in
 angle of about 50-70, preferably about 60.degree., of the bearing-journal
 circumference. Starting from this point, it is necessary to execute a
 complete revolution of the bearing journal to be machined, and preferably
 slightly more, that is to say about 370.degree., in order to achieve
 optimum adaptation of the actual contour to the desired contour of the
 journal. The milling cutter can then traverse directly radially outwards.
 In addition, in FIG. 11 correction points with an intervening angle of
 about 10-15.degree. with respect to the centre point of the crankpin
 journal to be machined are arranged along the machining path.
 After producing the first components of a series to be machined, the extent
 to which the actual circumferential contour approaches the desired
 circumferential contour can be measured and the actual contour achieved
 can subsequently be corrected empirically by modifying each of the
 individual correction points, by entering corresponding correction values
 for the individual correction points into the machine control system.
 Furthermore, in FIG. 10 the circumferential contour of the web is flattened
 off at one point in a planar manner. The circumferential contour of the
 web surface is also partially machined by means of external milling. The
 external milling according to the invention makes it possible--by means of
 a corresponding control of the rotational position, that is to say of the
 rotational speed of the crankshaft in relation to the X-displacement of
 the milling cutter--not only to achieve any desired (that is to say
 outwardly curved) contour, but also to achieve planar flattened portions
 which lie, for example, tangentially with respect to the centre bearing ML
 of the crankshaft. Planar milled areas of this kind are required either
 for the subsequent attachment of, for example, counterweights, or else for
 balancing the crankshaft directly in the chucking of the metal-removing
 machining operation.
 It is even possible to produce concave, that is to say recessed,
 circumferential contours, as long as the radius of curvature thereof is
 greater than the radius of the disc-like external-milling cutter.
 FIG. 12 shows a section through a metal-removing tool WZ, for example a
 turning tool, most designations and angles applying both to turning and to
 milling. Here, the cutting edge, for example the main cutting edge S, is
 formed by the edge formed by the tool face A.sub..gamma. and the main
 flank A.sub..alpha., and the secondary cutting edge S' is formed by the
 tool face A.sub..gamma. and the secondary flank A'.sub..alpha. running at
 an angle to the main flank A.sub..alpha.. The cutting edge S, which in
 FIG. 12 is shown as a sharp edge, is in practice never completely sharp,
 but rather has to have a certain degree of rounding, the cutting edge
 rounding (CER), in order to prevent the cutting edge chipping.
 Various directions and planes with respect to the tool are defined in FIGS.
 13 and 14.
 In these Figures, the tool reference plane P.sub.r is a plane through the
 selected cutting-edge point, specifically perpendicular to the assumed
 cutting direction. The tool reference plane P.sub.r is in this case as far
 as possible selected such that it lies parallel or perpendicular to an
 axis of the tool. It has to be stipulated individually for each type of
 tool. In the case of turning tools, the tool reference plane P.sub.r is a
 plane parallel to the base of the shank for conventional turning tools,
 while in the case of milling tools it is a plane which contains the axis
 of the milling tool.
 The assumed working plane P.sub.f is a plane through the selected
 cutting-edge point, perpendicular to the tool reference plane P.sub.r and
 parallel to the assumed feed direction.
 The tool rear plane P.sub.p is a plane through the selected cutting-edge
 point, perpendicular to the tool reference plane P.sub.r and perpendicular
 to the assumed working plane P.sub.f. P.sub.r, P.sub.p and P.sub.f thus
 form a coordinate system through the assumed cutting-edge point.
 The tool cutting-edge plane P.sub.s (see FIG. 14) is a plane through the
 cutting-edge point, tangential with respect to the cutting edge S and
 perpendicular to the tool reference plane P.sub.r. If the tool cutting
 edge S is at right angles to the feed direction, tool cutting edge plane
 P.sub.s and tool rear plane P.sub.p coincide.
 The tool orthogonal plane P.sub.c is a plane through the cutting-edge
 point, perpendicular to the tool reference plane P.sub.r and perpendicular
 to the tool cutting-edge plane P.sub.s. Therefore, if the tool cutting
 edge S is at right angles to the feed direction, tool orthogonal plane
 P.sub.c and assumed working plane P.sub.f coincide.
 The orientation of the individual tool cutting edges with respect to the
 workpiece can be seen more clearly from FIGS. 15 and 16, separately for
 plain turning and face turning. Considered in this plan view, the tool has
 at its cutting-edge point a tool nose angle .epsilon..sub.r between the
 tool cutting-edge plane P.sub.s of the main cutting edge and the tool
 cutting-edge plane P'.sub.s of the secondary cutting edge, measured in the
 tool reference plane P.sub.r.
 In this case, the main cutting edge is at a tool adjustment angle
 .kappa..sub.r between the tool cutting-edge plane P.sub.s and the assumed
 working plane P.sub.f, measured in the tool reference plane P.sub.r.
 FIGS. 18a-18f directly show the position of the individual sections and
 views, some of which are from FIGS. 15 and 16.
 The relevant angles here are:
 Tool side rake .gamma..sub.f : angle between the tool face A.sub..gamma.
 and the tool reference surface P.sub.r, measured in the working plane
 P.sub.f ;
 Tool rear rake .gamma..sub.p : angle between the tool face A.sub..gamma.
 and the tool reference plane P.sub.r, measured in the tool rear plane
 P.sub.p ;
 Tool normal cutting rake .gamma..sub.n : angle between the tool face
 A.sub..gamma. and the tool reference plane P.sub.r, measured in the tool
 cutting-edge normal plane P.sub.n ; the value of this angle .gamma..sub.n
 (positive or negative) is usually referred to in a generalized way as
 "positive/negative tool geometry".
 Tool cutting-edge angle of inclination .lambda..sub.s (FIG. 18e): angle
 between the cutting edge S and the tool reference point P.sub.r, measured
 in the tool cutting-edge plane P.sub.s.
 This tool cutting-edge angle of inclination .lambda..sub.s is an acute
 angle, the point of which faces towards the tool nose. It is positive when
 the cutting edge, to be viewed starting from the tool nose, lies on that
 side of the tool reference plane P.sub.r which faces away from the assumed
 cutting direction.
 .alpha. generally denotes the clearance angle of a cutting edge.
 FIG. 19 shows a web-cutting tip, which is screwed on the end side,
 preferably on both sides, onto the disc-like base body of the milling
 cutter and thus protrudes beyond the base body both radially and on the
 end side. In order to abrade the material from the end face of the web,
 with the milling cutter rotating the latter is moved forwards in the
 X-direction, that is to say radially with respect to the workpiece, as the
 feed direction. Here, the plane of the bit-like web-cutting tip, i.e. the
 tool cutting-edge plane P.sub.s, is positioned at a small angle .kappa. to
 the working plane P.sub.f, which is composed of the feed direction
 (X-direction) and the cutting direction, which lies in the X-Y plane. As a
 result, the outer edge, which is rounded with the nose radius R of about
 1.6 mm, of the cutting bit projects obliquely outwards from the base body
 and forms the point which protrudes furthest axially with respect to the
 base body of the milling cutter.
 The larger the angle .kappa., the more wavy the machined end face of the
 web becomes, as can be seen from the already machined part in FIG. 19.
 In order to be able to machine the entire end face of a web, an additional
 rotation of the crankshaft may additionally be necessary as well as the
 feed, depicted in FIG. 19a, in the X-direction of the milling cutter, if,
 for example, it is intended to machine the web surface as far as the
 crankpin journal H.sub.2 and around the latter.
 In the case of a web-cutting tip as shown in FIG. 19a, the extent of the
 tip in the radial direction of the body of the milling cutter is referred
 to as the length of the cutting tip, the extent in the tangential
 direction of the disc-like base body of the tool is referred to as the
 width, and the extent in the direction of the cutting bit closest to the
 axial direction is referred to as the thickness.
 FIG. 19b shows, in the same direction of viewing as FIG. 19a, the machining
 of the peripheral surface of a journal of the crankshaft by means of a
 journal-cutting tip. For a tip of this kind, length and width are intended
 to mean the sides which can be seen in the plan view of FIG. 19b, square
 throw-away cutting-tool tips usually being used as journal-cutting tips;
 these throw-away cutting-tool tips can thus be used four times in
 succession.
 The journal-cutting tips can then be fastened with their external cutting
 edge at a small angle deviating from the Z-direction within the Z-X plane
 on the base body of the side-milling cutter if, at the same time, a
 deviation from the Z-direction is also provided within the Z-Y plane.