EP4003644A1

EP4003644A1 - Device for processing the borders of flat workpieces

Info

Publication number: EP4003644A1
Application number: EP20746131.0A
Authority: EP
Inventors: Johannes ZEHETHOFER; Christoph LUEGER; Franz Haselmayr
Original assignee: Lisec Austria GmbH
Current assignee: Lisec Austria GmbH
Priority date: 2019-07-22
Filing date: 2020-07-20
Publication date: 2022-06-01
Also published as: WO2021013779A1; AT17015U1; US20220266407A1; CN114080298A

Abstract

In a device (1) for trimming panel-type workpieces (8), such as glass panes, a grinding ring (25) is used which is caused to rotate about an axis (2) by a drive. The grinding surfaces (7), engaging in a material-removing manner on the edges (9) of the border (10) of the workpiece (8), are designed such that they move in the axial direction, so that they can follow the edges (9) of the workpiece (8) during trimming. The grinding surfaces (7) automatically rest on the edges (9) of the workpiece (8) to be trimmed, even when the edges (9) are not in the predefined target position. The grinding ring (25) is floatingly mounted on its carrier (12) via a hydrostatic bearing or a gas bearing.

Description

DEVICE FOR PROCESSING THE EDGES OF FLAT WORKPIECES

The invention relates to an apparatus for processing the

Edges of flat workpieces, such as panes of glass, with the features of the introductory part of claim 1.

The inventive device includes for ablative

Processing of the edges on the edges of flat workpieces, such as glass panes, grinding surfaces, which attack the edges of the edges of the flat workpiece. The device according to the invention can also be designed and set up for polishing the edges of workpieces.

Devices for processing the edges of flat

Workpieces, in particular glass panes, are known in various embodiments. So there are devices with

Grinding wheels that are grooved, in which context reference can be made to WO 2015/055671 A1, EP 1 607 177 B1 and EP 1 488 886 B1.

For removing machining of flat workpieces,

In particular, glass panes, in order to trim their edges, are also known belt grinders, as is known, for example, from EP 1 344 604 B1 or DE 44 19 963 CI.

It has also already been proposed to have cup-shaped grinding wheels attack the edges of the glass panes, one grinding wheel attacking one edge and the other grinding wheel attacking the other edge. This is known from US Pat. No. 9,555,516 B2, for example.

Trimming devices with sanding belts (so-called

"Belt grinders"), in particular with grinding belts arranged in a cross shape, have the advantage that the grinding belts lie flexibly on the glass edges, so that the precision of the Infeed of the glass pane to the tool is not decisive. In this way, interruptions and interruptions can be added to the level of

Glass pane not at right angles, but at an angle

Aligned edge surfaces or shapes that differ slightly from the shape that result from cutting tolerances, as well as warped (not flat) workpieces can be seamed without any problems. Deviations of the flat object, such as the

Glass pane of the given shape and size can be compensated for by the flexibility of the sanding belts.

Trimming devices that use grinding wheels, the grinding wheels usually having a V-profile and for

Different glass thicknesses can be used, are usually rigid, so that inaccuracies in the format and size of the flat workpiece to be processed (glass pane) as well as deformations of the workpiece (the workpiece is then discarded, i.e. no longer flat) must be compensated for by the machine. It is therefore necessary to take measures to trace the edges to be machined like this

is known for example from EP 2 512 732 B1. The well-known hemming disks (grinding disks with V-profile) often cause the problem that interruptions and interruptions are not as desired

can be processed evenly.

No. 2,733,553 A shows and describes a tool for grinding knives or the like. The tool has two grinding wheels, which are fixed on two sleeves with the help of nuts. The sleeves are arranged on a shaft which is set in rotation by a motor and are held by springs in a central position in which they lie against one another.

When grinding, the grinding wheels can be moved against the force of the springs, so that the edges on both sides of a knife or the like can be processed (column 1, lines 18 to 25 and column 2, lines 50 to 59). When cutting flat workpieces, in particular glass panes, deviations from the desired size and shape, gaps and interruptions, and deviating geometry (e.g. a diamond with beveled edges is cut instead of a rectangle) can occur. When trimming such edges that deviate from the specified position and size, a problem arises because without further, rather complex,

mechanical engineering measures on the plate-shaped workpiece (glass pane) no exact seam can be achieved.

The invention is based on the object of providing a device with which flat workpieces, such as

Glass panes can also be processed (trimmed / polished) successfully and to the desired extent if the shape of the edges and the position of the edges of the desired shape or the

Setpoint position differ, with an advantageous storage of the

Grinding wheel is given on its carrier.

This object is achieved according to the invention with a device which has the features of claim 1.

Advantageous and preferred embodiments of the

The device according to the invention are the subject of

Subclaims.

The device according to the invention, which is designed essentially similar to a grinding wheel, has a slip ring with an outwardly open groove with grinding surfaces. The slip ring with the grinding surfaces is adjustable in the direction of the axis about which the device is set in rotation by its drive. So can in the invention

Sanding surfaces the edges of the edges of the workpiece

(Glass pane) also follow if the edge deviates from the target position in the direction of the axis. This can occur when the Workpiece is discarded. In the invention, the slip ring with the grinding surfaces automatically follows the edge of the workpiece. Movements of the carrier (shaft) on which the slip ring sits, with which movements the device according to the invention is tracked to the course and the position of the edges of the workpiece, are no longer required. This is because according to the invention in the direction of the (rotary) axis there is no rigid connection of the

Slip ring is provided with the carrier of the device.

It is advantageous that the slip ring is mounted in a floating manner on the carrier (the inner diameter of the slip ring is larger than the outer diameter of the carrier) so that the

Slip ring relative to its carrier in the direction of the

(Rotary) axis can move freely.

The floating bearing of the slip ring on the carrier is designed as a hydrostatic bearing or as a gas (air) bearing.

The inventive design of the device with a hydrostatic bearing or gas bearing has the advantage that the coupling of the slip ring with its carrier, with which the torque is transmitted from the carrier to the slip ring, can be designed so that the floating bearing of the slip ring is not adversely affected.

In the context of the invention it can be provided that the

Grinding surfaces are elastically resiliently loaded, so that when the device is used they preferably rest against the edges of the edges of the workpiece with elastic pretension.

If springs are provided, in a possible embodiment of the invention, these have the effect that the slip ring with its grinding surfaces is moved back into the starting position of the grinding surfaces after the device has been used. In addition, independent (resilient)

Grinding surfaces the possibility of following the edges of the workpiece even if the distance between the edge of the workpiece and the axis around which the device is rotated changes

(becomes larger or smaller), i.e. does not remain in the target position. This is possible, for example, if the slip ring is divided into two slip ring parts.

The inventive device combines in the exemplary embodiment with resilient grinding surfaces, the advantages of belt grinders with those of grinding wheels, since the

In this embodiment, grinding surfaces are designed to be elastically resilient, that is to say rest against the edges of the edges of the workpiece with elastic (resilient) prestress.

The adjustability of the grinding surfaces of the device according to the invention can be achieved in different ways within the scope of the invention.

In one embodiment of the invention it is provided that the pin in the bore or recess with sliding guide

is added, it being preferred that the grinding surfaces are elastically resilient in the direction of the axis.

The possible in one embodiment of the invention

Design of the coupling between the grinding wheel and its carrier in the form of at least one pin attached to the carrier

is attached and in a hole or recess in the

Grinding wheel engages, it allows to design the floating bearing of the grinding wheel in the form of a hydrostatic bearing or a gas bearing without the influence of the coupling between the grinding wheel and its carrier so that a good bearing of the grinding wheel is given. In one embodiment of the invention is a grooved

Slip ring with sliding surfaces on the carrier, which serves as a shaft for the rotary drive, adjustable, e.g. floating, mounted. In this embodiment, the slip ring can be moved in the direction of the (rotary) axis without the slip ring being loaded into its starting position by springs. In this way, the grinding surfaces can match the edges to be trimmed on the edges of the

Workpiece (the glass pane) if edges,

for example due to warping of the workpiece (the

Glass pane), deviate from the nominal position in the direction of the (rotary) axis in one direction or the other.

In another embodiment of the invention, the

Grinding surfaces provided on a slip ring, which is attached to the

Carrier is for example resiliently supported.

In another embodiment of the invention, the

Sliding surfaces are provided on two slip ring parts, which are arranged to be movable relative to one another and on the carrier in the direction of the (rotary) axis and are resiliently loaded towards one another.

In a further embodiment that of the invention

underlying object can be achieved in that a grooved slip ring with its grinding surfaces forming

Groove walls in the direction of the (rotational) axis of the carrier against

Spring force is arranged displaceably. This can be achieved, for example, that the slip ring on its carrier in the direction of the axis of rotation of a carrier against the force of springs which act on both sides of the slip ring,

is slidably mounted.

A slip ring, which optionally comprises two slip ring parts, is generally provided on the carrier of the device according to the invention. In the context of the invention, however, embodiments are also considered in which on a Carriers more than one slip ring and / or more than one pair

Slip ring parts are provided. Even if on one carrier two or more than two slip rings and / or pairs of

Slip ring parts are provided, one-piece slip rings and slip rings divided into slip ring parts can be combined. Furthermore, in the context of the invention is considered on a

Carrier slip rings with different grooves (trapezoidal, V-shaped etc.) and / or differently shaped grinding surfaces to be arranged.

The slip rings provided within the scope of the invention can be designed for removing machining (e.g. trimming) and also for polishing the edges of workpieces.

With the term "spring" used herein, any type of elastic means that acts on a slip ring or

Slip ring parts act, includes. Examples are metallic springs (coil springs), gas springs (pneumatic springs) and liquid springs.

In embodiments, the invention offers one or more of the following advantages:

The quality of the hem remains constant if the shape / size of the object to be processed differs from the specified shape / size,

the seam quality is significantly better than with conventional grinding wheels,

the quality of the hem can be reliably maintained,

when the grinding surfaces on a slip ring or on

Slip ring parts are provided, which are for example resiliently supported on the carrier of the device, changing is simple and inexpensive, since only slip rings / slip ring parts have to be exchanged, The inventive device can be used in all machines and allows conventional grinding wheels in existing machines by the inventive

To replace device,

serving for example as a rotary drive for the slip ring / the slip ring parts needs the edge of the

Workpiece cannot be tracked.

Further details and features as well as advantages of the invention emerge from the following description of the FIGS

Drawings partially shown schematically

Embodiments. It shows:

Fig. 1 to 4 in axial section an embodiment in

different working positions when hemming glass panes,

5 to 9 show a further embodiment in various forms

Job positions and details,

10 and 11 show a further embodiment in different forms

Working positions and

12 shows an embodiment with a floating bearing

Slip ring.

The embodiment shown in FIGS. 1 to 4 a

Device 1, which is designed in the manner of a grinding wheel, comprises a carrier 12 serving as a (drive) shaft and a slip ring 25 made of two slip ring parts 6

Slip ring parts 6 are arranged on the carrier 12, which is embodied as a shaft, so as to be displaceable in the direction of the axis 2 of the carrier 12, as is indicated in FIGS. 3 and 4 by the arrows 13.

In the carrier 12, a line 14 for the supply of liquid (supply of water) is provided so that the slip ring parts 6 of the slip ring 25 are mounted on the carrier 12 via hydrostatic bearings (floating). Instead of hydrostatic bearings for the slip ring 25 or the slip ring parts 6 can also be provided with gas (air) bearings. In the case of gas bearings, a gas (for example air) is supplied via line 14.

It is also possible that supplied liquid (water) emerges through the gap 15 between the slip ring parts 6 in the direction of the workpiece 8 (the glass pane to be processed), so that the workpiece 8, e.g. a glass pane, with the

Liquid is cooled during processing in order to trim edges 9 at its edge 10.

The slip ring parts 6 have grinding surfaces 7 which are conically or concavely curved and, when the device 1 is used for trimming the edges 9 of an edge 10, attack the workpiece 8 (glass pane) to be machined.

The slip ring parts 6 of those shown in FIGS

Embodiment are of springs 16, in the example

Coil springs between the slip ring parts 6 and

Shoulders 17 of the carrier 12 are arranged, loaded in the sense of a movement towards one another.

Since the slip ring parts 6 are supported on the carrier 12 by springs 16, the slip ring parts 6 can follow the course of the edge 10 of the workpiece 8 (glass pane) to be machined without special guiding measures being required. The reason for this is that the grinding surfaces 7 of the slip ring parts 6 are resiliently resilient and, under resilient preload, also apply to the edges 9 of the workpiece 8 to be trimmed, such as a pane of glass, when the workpiece 8 is of the desired size, position and / or Shape differs.

In order to couple the slip ring parts 6 with the carrier 12 in rotation, pins 18 are used as

Serve driver and / or guide pins, which are arranged on a flange 19 of the carrier 12 and with Grip the sliding guide through holes 20 in the slip ring parts 6.

In Fig. 1, the ideal case is shown in which the to

processed workpiece 8 (the glass sheet to be processed) to the plane of symmetry (plane perpendicular to the axis 2, which lies in the middle between the slip ring parts 6) of the device 1 exactly

(symmetrically) aligned.

Fig. 2 shows an offset of a workpiece 8, as often occurs in practice, the grinding surfaces 7 of the

Slip ring parts 6 attack evenly (centered) edges 9 of the edge 10 of the workpiece 8 and are offset in relation to the position shown in FIG. 1.

In Fig. 2, 3 and 4, for clarity, in each case above the machined workpiece 8, which is offset larger, a

Workpiece 8, which is not offset larger, is shown.

In Fig. 3 the case is shown in which the workpiece 8 is laterally offset with respect to the target position and is also larger than it corresponds to the target size (blank with oversize).

In this case, too, the grinding surfaces 7 of the device 1 follow the edges 9 of the edge 10 of the workpiece 8, the slip ring parts 6 moving out of it in the direction of the axis 2

Move the basic position (Fig. 1). Since the workpiece 8 to be machined is oversized, ie larger than it corresponds to the nominal size, the slip ring parts 6 are moved apart against the force of the springs 16 and the grinding surfaces 7 automatically align themselves into the correct position.

In Fig. 4 the case is shown in which the workpiece 8 (the glass pane) is correctly aligned, i.e. not offset laterally, but is oversized, i.e. larger than that Target dimension, in which case the grinding surfaces 7 of the slip ring parts 6 are correctly aligned on the edges 9 and engage the edges 9 in a resilient manner.

The springs 16 acting as restoring elements, which act on the slip ring parts 6 and resiliently move them into their in Fig.

1 load the basic position shown, in the embodiment shown in Figs. 1 to 4, the grinding surfaces 7 of the

Slip ring parts 6 of the slip ring 25 are designed to be resilient. The grinding surfaces 7 are automatically directed towards the edges 9 of the flat to be machined

Workpiece 8 (glass pane), as it is under elastic

Pretension on the workpiece 8 (glass pane).

FIGS. 5 to 9 show an embodiment of the device 1 according to the invention which is modified compared to the embodiment of FIGS. 1 to 4 and which essentially takes the form of a grinding wheel

is formed, shown. The slip ring 25 includes two

Slip ring parts 6 with conical grinding surfaces 7 which are arranged on a carrier 12 serving as a base body so as to be displaceable in the direction of the axis 2 of the device 1.

The spring forces that the slip ring parts 6 in their

Moving the active position and additionally pressing elastically resiliently against the edges 9 to be trimmed of the edge 10 of the flat workpiece 8 (glass pane), in the embodiment shown in FIGS , upset. For this purpose, an annular space 21 is provided for each slip ring part 6, into which liquid or gas is introduced. The annular space 21 is delimited by the carrier 12, the slip ring parts 6 and a sleeve-shaped element 22 (tubular part) provided on the slip ring parts 6. Thus, hydraulic springs or gas springs acting in the axial direction are formed by pressure, which move the slip ring parts 6, and thus their grinding surfaces 7, elastically towards one another in the sense of a movement burden. By changing the pressure of the liquid / gas, the pressing of the grinding surfaces 7 of the slip ring parts 6 - and thus the extent of the abrasive machining - can be changed to produce either smaller or larger chamfers (see FIGS. 5 and 6).

The embodiment shown in FIGS. 5 to 9 has the advantage, due to the liquid springs or the gas springs (the spaces 21 acted upon with liquid or gas (air)), that the slip ring parts 6 of the slip ring 25 and thus their grinding surfaces 7 through the workpiece 8 (the glass pane) can be moved in the axial direction without changing the contact force (if the pressure of the medium or gas does not change). This allows the slip ring parts 6 with the grinding surfaces 7 to adapt to different geometries of the

machining workpiece 8, in particular the glass pane

(Oblique break, cutting tolerances, glass warpage).

In the embodiment of the device 1, essentially designed as a grinding wheel, shown in FIGS. 5 to 9, provision is made for the sleeve-shaped elements 22 (tubular parts) provided on the slip-ring parts 6 to have openings 23 (holes). Usually (see. Fig. 5 and 6) the openings 23 are outside the annular spaces 21, which

Liquid or gas for the liquid springs or the

Gas springs is supplied, arranged. Only when the position according to FIGS. 7 to 9 is reached, the openings 23 in the sleeve-shaped (ring-shaped) elements 22 are arranged so that liquid or gas through the openings 23, which as

Leakage holes act, can escape and the pressure drops, whereupon the slip ring parts 6 resume their starting position (position according to FIGS. 5 and 6).

The slip ring parts 6 of those shown in FIGS Embodiment are coupled to the carrier 12 for rotation. For example, pins 18, similar to pins 18 shown in FIGS. 1 to 4, are used for torque transmission

Embodiment provided.

In the embodiment shown in FIGS. 10 and 11, the device 1 has an undivided slip ring 25 with a trapezoidal groove 5, the lateral (conical)

Groove surfaces are designed as grinding surfaces 7. The

Slip ring 25 is secured by pins 18 attached to flange 19 of carrier 12 and in recesses, e.g.

Bores 20, of the slip ring 25 slidingly engage, coupled to the carrier 12 for rotation so that a

Torque transmission is given.

In the embodiment shown in FIGS. 10 and 11 too, springs 16, for example helical springs, are provided as elastically resilient restoring elements which align the slip ring 25 in its starting position (standby position), which is shown in FIG.

In the embodiment shown in FIGS. 10 and 11, a line 14 is for the supply of a liquid or gaseous

Medium for a hydrostatic bearing or a gas bearing of the slip ring 25 (floating bearing), which allows its displacement relative to the carrier 12 in the axial direction, is provided.

The slip ring 25 of FIGS. 10 and 11 is rotationally coupled to the carrier 12 by pins 18.

11 shows the case in which the workpiece 8 (the glass pane to be processed) deviates from the desired position (indicated at the top in FIG. 10), for example because of a discarded workpiece. The slip ring 25, which can be displaced on the carrier 12 counter to spring force, and thus its grinding surfaces 7, close automatically the edges 9 by the slip ring 25 moving on the carrier 12 in the direction of the axis 2. Thus, in the embodiment shown in FIGS. 10 and 11, the grinding surfaces 7 are elastically resilient, follow the edges 9 and lie under elastic bias on the edges 9 of the to be trimmed

Workpiece 8 evenly.

In the context of the invention, an embodiment in

Considered when the grinding wheel 25 with their

Grinding surfaces 7 is floatingly mounted on the carrier 12 without springs 16 or the liquid springs / gas springs provided in the embodiment of FIGS. 6 to 10 being provided.

Such an embodiment is shown by way of example in FIG. 12

shown.

The device 1 shown in Fig. 12 for trimming the

Edges 9 of edges 10 of a flat workpiece 8, such as a glass pane, is essentially designed in the form of a grinding wheel and essentially corresponds to the embodiment shown in FIGS. 10 and 11, but the springs 16 are not provided.

The floating mounting of the slip ring 25 on the carrier 12 results in an arrangement of the slip ring 25 that is movable in the direction of the (rotary) axis 2, so that it

can automatically follow the edge 10 of the workpiece 8, even if it deviates from the desired position, as shown by the arrows in FIG. This is particularly the case when the edge 8 deviates in the direction of the axis 2 about which the device 1 with its slip ring 25 is set in rotation, because the workpiece 8 (the glass pane) is warped, that is, it is not flat.

The groove 5 of the slip ring 25 can - instead of as shown trapezoidal - also be V-shaped.

Slip rings 25 with a trapezoidal groove 5 can be used for trimming the edges 9 and for processing (grinding and / or polishing) the edge surfaces of the workpiece 8 aligned transversely to the plane of the workpiece 8. In this case, the bottom of the groove 5 has a machining, for example polishing, effect on the edge surface of the workpiece 8.

Slip rings 25 with a V-shaped groove 5 are used, for example, when only the edges 9 on the edges 10 of workpieces 8 are to be machined (trimmed).

In summary, an embodiment of the invention can be described as follows:

In a device 1 for trimming plate-shaped

Workpieces 8, such as panes of glass, a slip ring 25 set in rotation by a drive about an axis 2 is used. The grinding surfaces 7 that act on the edges 9 of the edge 10 of the workpiece 8 are designed to be movable in the axial direction, so that when they are trimmed the edges 9 of the

Workpiece 8 can follow. The grinding surfaces 7 automatically lie against the edges 9 of the workpiece 8 to be trimmed, even if the edges 9 are not in the predetermined target position.

Claims

Expectations :

1. Device (1) for removing edges (9) on the edges (10) of flat workpieces (8), for example glass panes, with at least one slip ring (25) which has grinding surfaces (7), one around an axis (2 ) rotationally driven carrier (12) is provided for the slip ring (25) and wherein the slip ring (25) with the

Carrier (12) is coupled to rotate, the slip ring (25) is arranged on the carrier (12) movable in the direction of the axis (2), characterized in that the

Slip ring (25) is floatingly mounted on the carrier (12) and that the slip ring (25) is floatingly mounted on the carrier (12) via a hydrostatic bearing or gas bearing.

2. Apparatus according to claim 1, characterized in that the coupling has at least one pin (18) as a driver and / or guide, which is attached to the carrier (12) and in a bore (20) or recess in the slip ring (25) intervenes.

3. Device according to claim 2, characterized in that the pin (18) is received in the bore (20) or recess with sliding guide.

4. Device according to one of claims 1 to 3, characterized

characterized in that the grinding surfaces (7) are elastically resilient in the direction of the axis (2).

5. Device according to one of claims 1 to 4, characterized

characterized in that the slip ring (25) is resiliently loaded into its starting position.

6. Device according to one of claims 1 to 5, characterized characterized in that the slip ring (25) has two

Comprises slip ring parts (6) and that the grinding surfaces (7) are provided on the slip ring parts (6).

7. Device according to one of claims 1 to 6, characterized

characterized in that the grinding surfaces (7) are conical or concave.

8. Apparatus according to claim 6 or 7, characterized in that the slip ring parts (6) of springs (11) are loaded towards one another.

9. The device according to claim 7, characterized in that the slip ring parts (6) of pneumatic or

hydraulic springs are loaded.

10. Device according to one of claims 6 to 9, characterized

characterized in that the slip ring parts (6) are arranged on the carrier (12) for the slip ring (25) so as to be displaceable in the direction of the axis (2).

11. Device according to one of claims 6 to 10, characterized

characterized in that the slip ring parts (6) on the carrier (12) are loaded by springs in the sense of a movement towards one another.

12. Device according to one of claims 1 to 11, characterized

characterized in that in the carrier (12) at least one line (14) for the supply of liquid or gaseous medium, such as water in the air, is provided and that of the

Line (14) branch off line branches (24) which open between the inner surface of the slip ring (25) and the outer surface of the carrier (12).

13. Device according to one of claims 1 to 12, characterized characterized in that the slip ring (25), in particular the slip ring parts (6), is coupled to rotate with the carrier (12).

14. The device according to claim 13, characterized in that the coupling is at least one in a bore (20) or recess in the slip ring (25) or the

Slip ring parts (6) engaging pin (18) which is attached to the carrier (12) for the slip ring (25),

includes.

15. The device according to claim 14, characterized in that the pin (18) in the slip ring (25) or the

Slip ring parts (6) is added with sliding guide.

16. Device according to one of claims 1 to 15, characterized

characterized in that springs (16) on the carrier (12)

are provided that the slip ring (25) or the

Load slip ring parts (6) resiliently into its original position.

17. Device according to one of claims 1 to 16, characterized

characterized in that at least one annular space (21) is provided, which is delimited in some areas by a slip ring part (6), and that the line (14) for supplying the liquid or gaseous medium opens into the annular space (21).

18. The device according to claim 17, characterized in that on at least one slip ring part (6) a carrier (12) encompassing, sleeve-shaped element (22) which the

annular space (21) is provided and that at least one opening (23) is provided in the sleeve-shaped element (22) which is in the region of the annular space (21) when the slip ring part (6) is in its The starting point is.

19. Device according to one of claims 1 to 5, characterized

characterized in that the slip ring (25) a

Has grinding surfaces (7) having groove (5) which is open to the outside.

20. The device according to claim 19, characterized in that the groove (5) is trapezoidal or V-shaped.