EP3191275A1

EP3191275A1 - Method for controlling a wall saw system when creating a separating cut

Info

Publication number: EP3191275A1
Application number: EP15757253.8A
Authority: EP
Inventors: Wilfried Kaneider; Dragan Stevic; Christian Bereuter; Dieter Profunser
Original assignee: Hilti AG
Current assignee: Hilti AG
Priority date: 2014-09-08
Filing date: 2015-09-01
Publication date: 2017-07-19
Also published as: EP2993011A1; US20170291324A1; WO2016037891A1; US10300629B2; JP2017527470A

Abstract

The invention relates to a method for controlling a wall saw system (10) when creating a separating cut in a workpiece (24) between a first and a second end point. The wall saw system (10) comprises a wall saw (12) having a saw head (14), a pivotable saw arm (17), a saw blade (16) and a blade guard (21). The separating cut is carried out in a plurality of main cuts, wherein the parameters of the main cuts (main cutting angles) are determined before the start in a main cutting sequence. The pivoting movement of the saw arm (17) in a main cutting angle is carried out in at least two steps with at least one intermediate angle, wherein a free cut of the saw blade (16) is carried out in the respective intermediate angle between the pivoting movements of the saw arm (17).

Description

Method for controlling a wall sawing system when creating a separating cut Technical field

The present invention relates to a method for controlling a wall sawing system when creating a separating cut according to the preamble of claim 1.

State of the art

From EP 1 693 173 B1 a method is known for controlling a wall sawing system when first creating a separating cut in a workpiece between a first end point and a second end point. The wall saw system comprises a guide rail and a wall saw with a saw head, a motor feed unit which moves the saw head parallel to a feed direction along the guide rail and at least one saw blade mounted on a saw arm of the saw head and driven by a drive motor about an axis of rotation , The saw arm is designed to be pivotable about a pivot axis by means of a swivel motor. By a pivoting movement of the saw arm about the pivot axis, the penetration depth of the saw blade is changed in the workpiece. The motorized feed unit comprises a guide rail and a feed motor, wherein the saw head is mounted on the guide carriage and moved along the guide rail via the feed motor. For monitoring the wall sawing system, a sensor device with a swivel angle sensor and a displacement sensor is provided. The swivel angle sensor measures the instantaneous swivel angle of the saw arm and the travel sensor measures the current position of the saw head on the guide rail. The measured values for the current swivel angle of the saw arm and the current position of the saw head are regularly transmitted to a control unit of the wall saw.

The known method for controlling a wall sawing system is divided into a preparation part and a processing of the separating cut controlled by the control unit. In the preparation part, the operator sets at least the saw blade diameter of the saw blade, the positions of the first and second end points in the feed direction and the final depth of the separating cut; other parameters can be the material of the machined Workpiece and the dimensions of embedded reinforcing iron. From the parameters entered, the separating cut control unit determines a suitable main cutting sequence of main cuts, the main cutting sequence comprising at least a first main section with a first main section angle of the saw arm and a first diameter of the saw blade used, followed by a second main section with a second main section angle of the saw arm and a first diameter of the saw blade used.

The known method for controlling a wall sawing system has the disadvantage that no special method for controlling the wall saw is provided for the machining of hard materials. When machining hard materials, polishing of the cutting segments may occur during the pivoting movement of the saw blade into the workpiece. By polishing the cutting segments, the life of the cutting segments and the machining speed of the saw blade are reduced.

DESCRIPTION OF THE INVENTION The object of the present invention is to develop a method for controlling a wall sawing system which enables the machining of hard materials and in which the service life and the machining speed of the saw blade are optimized.

This object is achieved according to the invention in the method mentioned at the outset for controlling a wall saw system by the features of the independent claim. Advantageous developments are specified in the dependent claims.

According to the invention it is provided that the pivoting movement of the saw arm from the first main cutting angle is carried out in a new pivot angle in at least two steps with at least one Zwischenwinkei, wherein between the Schwenkbewegun- conditions of the saw arm in the Zwischenwinkei each carried out a free cutting of the saw blade.

Saw blades for wall saws are constructed in two parts from a base body and cutting segments on the circumference of the body. The cutting segments consist of a matrix material in which diamond particles are embedded. To expose the diamond particles during machining, a minimum surface pressure is required. If the minimum surface pressure is not reached, the diamond particles are not exposed during machining with the saw blade and there is a risk of polishing the cutting segments, which reduces the service life of the cutting segments and the machining speed of the saw blade. The minimum surface pressure of the cutting segments corresponds to a critical arc length of the saw blade, which must not be exceeded. The value for the The critical arc length of a saw blade depends on several parameters, including the specification of the saw blade, the material of the workpiece to be machined and the power and torque of the drive motor for the saw blade.

The division of the pivoting movement in at least two steps reduces the risk that a polishing of the saw blade occurs. A smaller swing angle results in reducing the arc length of the saw blade engaged with the workpiece or the number of cutting segments engaged with the workpiece. The free cutting of the saw blade, which takes place between the pivoting movements of the saw arm, results in the further reduction of the arc length of the saw blade engaging the workpiece.

Preferably, the pivoting movement of the saw arm is carried out from the first main cutting angle in the new pivot angle in n steps with n-1 intermediate angles, wherein between the pivoting movements of the saw arm in the intermediate angle in each case a free cutting of the saw blade. The number of steps depends, among other things, on the specification of the saw blade, the hardness of the material and the performance and the

Torque of the drive motor for the saw blade off. The intermediate angles can be determined by the operator or the control unit of the wall sawing system determines the intermediate angles depending on different boundary conditions. For the method according to the invention, the intermediate angles represent an input quantity which is used to control the wall saw.

Preferably, prior to starting the machining controlled by the control unit, a saw arm length of the saw arm, which is defined as the distance between the swivel axis of the saw arm and the axis of rotation of the saw blade, and a distance between the swivel axis and the top of the work piece are set. For a controlled processing of a separating cut, the control unit must be aware of various parameters. These include the Sägearmlänge, which represents a fixed device-specific size of the wall saw, and the vertical distance between the pivot axis and the surface of the workpiece, which also depends on the geometry of the wall saw and the geometry of the guide rail used. Particularly preferably, before the start of the controlled processing, a first width is additionally defined for a blade guard used in the first main section, and a second width for a blade guard used in the second main section, wherein the first and second widths each consist of a first distance of the axis of rotation to the first blade guard edge and a second distance of the axis of rotation to the second blade guard edge are put together. If an endpoint is an obstacle, the position control of the Saw head over the, the obstacle facing, blade protection edge of the used blade guard. In asymmetric biatting, the first and second distances of the axis of rotation from the blade guard edges are different, whereas in the case of symmetrical blade guard, the first and second pitches of the blade guard edges are equal to half the width of the blade guard.

In a first preferred embodiment of the method according to the invention, the pivoting movement from the first main cutting angle to the new main cutting angle at the first end point and the saw head is positioned in the jth step, j = 1 to n-1, that after the pivoting movement of the saw arm in the j -ten intermediate angle! a first boundary of the wall saw facing the first end coincides with the first end point, wherein the first boundary of the wall saw is formed by a, the first end point facing first upper exit point of the saw blade used at the top of the workpiece when the first end point represents a free end point without hindrance, by a first saw blade edge of the saw blade used facing the first end point, when the first end point represents an obstacle and the machining takes place without blade protection, and by a, the first end point facing first blade guard edge of the used Leaf protection, if the first endpoint is an obstacle and processing is done with blade protection.

Each step includes the steps of positioning the saw head, pivoting the saw arm into the intermediate angle, and moving the saw head to free the saw blade. After the pivoting movement of the saw arm into the intermediate angle, the first boundary coincides with the first end point. With a free end point without obstruction, the position control is performed on the first upper Austnttspunkt the saw blade at the top of the workpiece. If the first endpoint is an obstacle, the first edge of the saw blade (machining without blade protection) or the first blade guard edge (machining with blade guard) are used for position control.

After the pivoting movement of the saw arm to the jth intermediate angle with j = 1 to n-1, the first upper break point coincides with the first end point when the pivot axis is a distance from the first end point of v '[h (± ß _{! Rj} ). (D - h (± β _{1,, j} ))] - δ sin (± β _{1,, j} ), where h (± β _{1,, j} ) = D / 2 - Δ - δ. cos (± ß _{1, j} ) denotes the penetration depth of the saw blade used into the workpiece at the jth intermediate angle, the first saw blade edge of the saw blade used coincides with the first end point when the pivot axis is a distance from the first end point of D / 2-8 Sin (± ß _{1,, j} ), and the first blade protection edge of the sheet protection used coincides with the first end point when the

Pivoting axis has a distance to the first end point of B _2a - δ sin (± ß _{1, j} ). After the pivoting movement, the saw head in the j-th step, j = 1 to n-1 with the, under the j-th intermediate angle, inclined saw arm by a path length of · ν '[η ₂ ' (D - h ₂ )] - 5 'sin (± α ₂ ), where h ₂ = · h (± α ₂ , D) = D / 2 - Δ - δ cos (± α ₂ ) the penetration depth of the saw blade used into the workpiece at the second main cutting angle! designated. By the advancing movement of the saw head, the saw blade is cut free and the standing in engagement with the workpiece part of the saw blade is reduced.

After the η-1-th step, the saw head is positioned so that, after the pivoting movement of the saw arm into the new main cutting angle, the first boundary of the wall saw facing the first end point coincides with the first end point. After the pivotal movement of the saw arm into the second main cutting angle, the first upper exit point coincides with the first end point when the pivot axis is a distance from the first end point of V [h ₂ ^* (D-h ₂ )] -δ ^. sin (± oc ₂ ), where h (± α ₂ ) = D / 2 - Δ - δ cos (± α ₂ ) denotes the penetration depth of the saw blade used in the workpiece at the second main cutting angle with the second diameter, the first saw blade edge of the used saw blade coincides with the first end point, when the pivot axis is a distance from the first end point of D / 2 - δ ^. sin (± u ₂ ), and the first blade guard edge of the blade guard used coincides with the first end point when the pivot axis is spaced from the first end point of B _a - δ - sin (± α ₂ ).

In a second preferred embodiment of the method according to the invention, the pivoting movement takes place from the first main section angle! in the new main cutting angle at the second end point and the saw head is in the j-th intermediate section, j = 1 to n-1 positioned so that after the pivoting movement of the saw arm in the j-th intermediate angle, the second end point facing the second boundary of the wall saw coincides with the second end point, wherein the second boundary of the wall saw is formed by a, the second end point facing, the second upper exit point of the saw blade used at the top of the workpiece, when the second end point represents a free end point without obstruction, by one, the second End point facing, second saw blade edge of the saw blade used when the second endpoint is an obstacle and the processing is done without blade protection, and by a second end point facing the second blade guard of the blade guard used when the second endpoint is an obstacle and the processing with blade guard he follows.

Each step includes the steps of positioning the saw head, pivoting the saw arm into the intermediate angle, and moving the saw head to free the saw blade. After pivotal movement of the saw arm to the jth intermediate angle with j = 1 to n-1, the second upper exit point coincides with the second end point when the pivot axis is a distance from the second end point of V [h (± β _2, j) ^. (D - h (± β _2ij ))] + δ · sin (± β _{2 | j} ), where h (± β _2ij ) = D / 2 - Δ - δ · cos (± β _{2, j} ) the penetration depth the second saw blade edge of the saw blade used coincides with the second end point when the pivot axis has a distance to the second end point of D / 2 + δ sin (± ß _2j ), and the second blade guard edge of the blade guard used coincides with the second end point when the pivot axis has a distance to the second end point of B _b + δ sin (± ß _{2, j} ) up.

After the pivotal movement, the saw head is in the j-th step, j = 1 to n-1 with the, under the j-th intermediate angle, inclined saw arm by a path length of V [h ₂ (D - h ₂ )] - δ ^' sin (± α ₂ ) method, where h ₂ = h (± α ₂ , D) - D / 2 - Δ - δ cos (± α ₂ ) denotes the penetration depth of the saw blade used in the workpiece at the second Hauptschnittwlnkei. By the advancing movement of the saw head, the saw blade is cut free and the standing in engagement with the workpiece part of the saw blade is reduced.

The saw head is positioned after the n-1-th step so that after the pivoting movement of the saw arm in the new main section angle coincides, the second end point facing the second boundary of the wall saw with the second end point. After the swiveling movement of the saw arm into the second main cutting angle! the second upper exit point coincides with the second end point when the pivot axis is at a distance from the second end point of V [h ₂ * (D-h ₂ )] + δ * sin (± α ₂ ), where h (+ α ₂ ) - D / 2 - Δ - δ cos (± α ₂ ) denotes the penetration depth of the saw blade used into the workpiece at the second main cutting angle, the second saw blade edge of the saw blade used coincides with the second end point when the pivot axis is a distance from the second end point of D / 2 + δ sin (± α ₂ ), and the second blade guard edge of the blade guard used coincides with the second end point when the pivot axis is spaced from the second end point of B _b + δ sin (± α ₂ ).

The first and second main cuts are made with a saw blade and a blade guard. Alternatively, the first main section is performed by a first saw blade having a first blade diameter and a first blade guard having a first blade guard width, and the second major section is performed by a second blade having a second blade diameter and a second batten guard having a second blade guard width. embodiments

Embodiments of the invention are described below with reference to the drawing. This is not necessarily to scale the embodiments, but the drawing, where appropriate for explanation, executed in a schematic and / or slightly distorted form. With regard to additions to the teachings directly recognizable from the drawing reference is made to the relevant prior art. It should be noted that various modifications and changes may be made in the form and detail of an embodiment without departing from the general idea of the invention. The features of the invention disclosed in the description, the drawing and the claims may be essential both individually and in any combination for the development of the invention. In addition, all combinations of at least two of the features disclosed in the description, the drawings and / or the claims fall within the scope of the invention. The general idea of the invention is not limited to the exact form or detail of the preferred embodiment shown and described below or limited to an article that would be limited in comparison with the subject matter claimed in the claims. For given design ranges, values lying within the specified limits should also be disclosed as limit values and be arbitrarily usable and claimable. For simplicity, the same reference numerals are used below for identical or similar parts or parts with identical or similar function.

Show it:

FIG. 1 a wall saw system with a guide rail and a wall saw;

FIGS. 2A, B, the processing of a separation cut between a first and second free end point without obstacle; FIGS. 3A, B, the processing of a separating cut between a first and second

Obstacle with a saw blade that is not surrounded by a blade guard;

FIGS. 4A, B, the processing of a separating cut between a first and second

Obstacle with a saw blade surrounded by a blade guard;

FIGS. 5A-K show the wall sawing system of FIG. 1 when creating a separation cut between a first endpoint representing an obstacle and a second free one

Endpoint without obstacle FIG. 1 shows a wall sawing system 10 with a guide rail 11, a tool device 12 displaceably arranged on the guide rail 11, and a remote control 13. The tool device is designed as a wall saw 12 and comprises a machining unit 14 and a motorized feed unit 15. The machining unit is a saw head 14 formed and includes a trained as a saw blade machining tool 16 which is fixed to a saw arm 17 and is driven by a drive motor 18 about an axis of rotation 19.

To protect the operator, the saw blade 18 is surrounded by a blade guard 21 which is secured by a blade guard on the saw arm 17. The saw arm 17 is formed by a pivot motor 22 about a pivot axis 23 pivotally. The swivel angle α of the saw arm 17 determines, with a saw blade diameter D of the saw blade 16, how deep the saw blade 16 dips into a workpiece 24 to be machined. The drive motor 18 and the pivot motor 22 are arranged in a device housing 25. The motor-driven feed unit 15 comprises a guide carriage 26 and a feed motor 27, which is likewise arranged in the device housing 25 in the exemplary embodiment. The saw head 14 is mounted on the Führungsschiitten 26 and slidably formed via the feed motor 27 along the guide rail 1 1 in a feed direction 28, in the device housing 25 is in addition to the motors 19, 22, 27, a Kontroileinheit 29 for controlling the saw head 14 and the motor feed unit 15 arranged. For monitoring the wall sawing system 10 and the machining process, a sensor device is provided with a plurality of sensor elements. A first sensor element 32 is designed as a swivel angle sensor and a second sensor element 33 as a displacement sensor. The swivel angle sensor 32 measures the current pivoting angle! the saw arm 17 and the displacement sensor 33 measures the current position of the saw head 14 on the guide rail 1 1, the measured variables are transmitted from the swivel angle sensor 32 and displacement sensor 33 to the control unit 29 and used to control the wall saw 12.

The remote control 13 comprises a device housing 35, an input device 36, a display device 37 and a control unit 38, which is arranged in the interior of the device housing 35. The control unit 38 converts the inputs of the input device 36 into control commands and data which are transmitted to the wall saw 12 via a first communication link. The first communication connection is designed as a wireless and wireless communication connection 41 or as a communication cable 42. The wireless and wireless communication connection is formed in the embodiment as a radio link 41, which is formed between a first radio unit 43 on the remote control 13 and a second radio unit 44 on the power tool 12. Alternatively, the wired and wireless loose communication connection 41 in the form of an infrared, Bluetooth, Wi-Fi or Wi-Fi connection be formed.

FIGS. 2A, B show the guide rail 1 1 and the wall saw 12 of the wall sawing system 10 of FIG. 1 when creating a separating cut 51 in the workpiece 24 of the workpiece thickness d. The separating cut 51 has an end depth T and extends in the feed direction 28 between a first end point Ei and a second end point E ₂ . As the X direction, a direction parallel to the feed direction 28 is defined, wherein the positive X direction is directed from the first end point E, to the second end point E ₂ , and as the Y direction is a direction perpendicular to the X direction in the depth of the workpiece 24 defined. The end point of a separation cut can be defined as a free end point without hindrance or as an obstacle. Both endpoints can be defined as free endpoints without obstacles, both endpoints as obstacles or one endpoint as a free endpoint and the other endpoint as an obstacle. At a free endpoint without obstacle, an overlap may be allowed. Due to the overlapping, the cutting depth at the end point reaches the final depth T of the separating cut. In the embodiment of FIGS. 2A, B form the end points E ₁ , E ₂ free end points without obstruction, wherein at the free first end point E, an overlapping is not allowed and at the second end point E _2, an overlapping is done.

FIG. 2A shows the saw head 14 in a mounting position X ₀ and the saw arm 17 in a basic position of 0 °. The saw head 14 is positioned by the operator by means of the guide carriage 26 in the mounting position X ₀ on the guide rail 1 1. The mounting position X _{0 of} the saw head 14 is between the first and second end point E ₁ , E ₂ and is determined by the position of the pivot axis 23 in the feed direction 28. The position of the

Pivot axis 23 is particularly suitable as a reference position X _Ref for the position monitoring of the saw head 14 and the control of the wall saw 12, since the X position of the pivot axis 23 remains unchanged even during the pivoting movement of the saw arm 17. Alternatively, another X position on the saw head 14 can be set as the reference position, in which case the distance in the X direction to the pivot axis 23 must additionally be known.

The X-Pcsitionen the first and second end point Ε,, E, are set in the embodiment by the entry of part lengths. The distance between the mounting position X ₀ and the first end point E ₁ determines a first part length Li and the distance between the mounting position X ₀ and the second end point E ₂ a second part length L ₂ . Alternatively, the X positions of the end points Ε ·, E _{2 can be} defined by entering a partial length (L ₁ or L ₂ ) and a total length L as the distance between the end points E, E ₂ . The separating cut 51 is created in several partial sections until the desired final depth T is reached. The partial sections between the first and second end points E ₁ , E ₂ are defined as main sections and the cutting sequence of the main sections as the main section sequence. At the end points of the separating cut, additional corner processing can be carried out, which in the case of an obstacle is referred to as obstacle processing and in the case of a free end point with overlapping as overcut processing.

The main cutting sequence can be determined by the operator or the control unit of the VVandsägeing system determines the main cutting sequence depending on several boundary conditions. Usually, the first main section, which is also referred to as a precut, is executed with a reduced depth of cut and a reduced power of the drive motor in order to prevent polishing of the saw blade. The other main cuts are usually made with the same depth of cut, but can also have different cutting depths. The boundary conditions usually defined by an operator include the depth of cut of the precut, the power of the precut, and the maximum depth of cut of the other major sections. From these constraints, the control unit can determine the main cutting sequence.

The main sections of a separating cut are made with a saw blade diameter or with two or more saw blade diameters. If multiple saw blades are used, machining usually begins with the smallest saw blade diameter. To mount the saw blade 16 on the saw arm 17, the saw blade 16 in the

Basic position of the saw arm 17 may be arranged above the workpiece 24. Whether this boundary condition is fulfilled depends on two device-specific variables of the VVandsägesystems 10, on the one hand by a vertical distance Δ between the pivot axis 23 of the saw arm 17 and a top 53 of the workpiece 24 and on the other by a Sägersmasse δ of the saw arm 17, which is defined as the distance between the axis of rotation 19 of the saw blade 16 and the pivot axis 23 of the saw arm 17. If the sum of these two device-specific sizes is greater than half the saw blade diameter D / 2, the saw blade 16 is arranged in the basic position above the workpiece 24. The saw arm length 8 is a fixed device-specific size of the wall saw 12, whereas the vertical distance Δ between the pivot axis 23 and the surface 53 in addition to the geometry of the wall saw 12 also depends on the geometry of the guide rail 11 used.

The saw blade 16 is mounted on a flange on the saw arm 17 and is driven by the drive motor 18 about the axis of rotation 19 in the sawing operation. In the basic position of the saw arm 17, which in FIG. 2A, the pivoting angle is 0 ° and the axis of rotation 19 The saw blade 16 is moved in the depth direction 52 above the pivot axis 23. The saw blade 16 is moved by a pivoting movement of the saw arm 17 about the pivot axis 23 from the basic position at 0 ° in the workpiece 24. During the pivoting movement of the saw arm 17, the saw blade 16 is driven by the drive motor 18 about the axis of rotation 19.

To protect the operator, the saw blade 16 should be surrounded by the blade guard 21 during operation. The wall saw 12 is operated with blade guard 21 or without blade guard 21. For processing the separating cut in the region of the end points E ₁ , E ₂ , a disassembly of the blade guard 21 may be provided, for example. If different saw blade diameters are used to machine the cutting cut, various blade protectors with appropriate blade guard widths are usually used.

FIG. FIG. 2B shows the saw arm 17, which is inclined in a negative direction of rotation 54 at a negative swivel angle -α. The saw arm 17 is adjustable in the negative direction of rotation 54 between pivot angles of 0 ° to -180 ° and adjustable in a direction opposite to the negative direction of rotation 54, positive direction of rotation 55 between pivot angles of 0 ° to + 80 °. The in FIG. 2B arrangement of the saw arm 17 is referred to as a pulling arrangement when the saw head 14 is moved in a positive feed direction 56. If the saw head 14 is moved in a direction opposite to the positive feed direction 56, negative feed direction 57, the arrangement of the saw arm 17 is referred to as an abutting arrangement.

With a swivel angle of ± 180 °, the maximum penetration depth of the saw blade 16 into the workpiece 24 is achieved. By the pivoting movement of the saw arm 17 to the

Swivel axis 23, the position of the rotation axis 19 is moved in the X direction and in the Y direction. In this case, the displacement of the axis of rotation 19 of the Sägearmlänge δ and the pivot angle α of the saw arm 17 is dependent. The displacement δ _χ in the X direction is 5 ^. sin (± a) and the displacement path δ _y in the Y direction is δ ^' cos (± a).

The saw blade 1 6 generates in the workpiece 24 a cutting wedge in the form of a circle segment with a height h and a width b. The height h of the circle segment corresponds to the penetration depth of the saw blade 16 into the workpiece 24. For the penetration depth h, the relationship D / 2 = h + Δ + δ applies ^. cos (a), where D is the saw blade diameter, h is the penetration depth of the saw blade 16, Δ is the vertical distance between the pivot axis 23 and the top 53 of the workpiece 24, δ is the saw arm length and α is the first pivot angle, and for the width b is the Connection b ² - D / 2 · 8h - 4h ² = 4Dh - 4h ² - 4h (D - h), where- at h the penetration depth of the saw blade 16 in the workpiece 24 and D denote the saw blade diameter.

The control of the wall saw 12 during the separating cut depends on whether the end points are defined as obstacles, and on an obstacle whether the processing is performed with blade guard 21 or without blade guard 21. In a free end point without hindrance, the control of the wall saw 12 in the process according to the invention via upper exit points of the saw blade 16 at the top 53 of the workpiece 24. The upper exit points of the saw blade 16 can be from the reference position X _Ref the pivot axis 23 in X- Direction, calculate the displacement δ _{x of} the rotation axis 19 in the X direction and the width b. An upper exit point facing the first endpoint E is referred to as a first upper exit point 58 and an upper exit point facing the second endpoint E ₂ as a second upper exit point 59. For the first upper exit point 58, X (58) ~ X _Ref + δ _x - b / 2 and for the second upper exit point 59, X (59) = X _Ref + δ "+ b / 2 with b = V [h ^' (D - h)] and h = h (a, D ). If the end points E ,, E ₂ are defined as obstacles, crossing the end points E ₁ , Ej with the wall saw 12 is not possible. In this case, the control of the wall saw 12 in the method according to the invention on the reference position X _Ref the pivot axis 23 and the boundary of the wall saw 12. There is a distinction between a processing without blade guard 21 and a processing with blade guard 21. FIGS. 3A, B show the wall sawing system 10 in creating a separation cut between the first end point E, and the second end point E ₂ , which are defined as obstacles, wherein the processing is performed without blade guard 21. During processing without blade guard 21, a first saw blade edge 61, which faces the first end point E, and a second saw blade edge 62, which faces the second end point E _z , form the boundary of the wall saw 12.

The X positions of the first and second saw blade edges 61, 62 in the X direction can be calculated from the reference position X _{Ref of} the pivot axis 23, the displacement path δ _{χ of} the rotation axis 19 and the saw blade diameter D. FIG. 3A shows the wall saw 12 with the saw arm 17 tilted in the negative rotational direction 54 at a negative swivel angle -a (0 ° to -180 °). For the first saw blade edge 61, X (61) = X _Ref + δ · sin (-a) - D / 2 and for the second saw blade edge 62, X (52) = X _Ref + 5 - sin (-a) + D / 2. FIG. 3B shows the wall saw 12 with the saw arm 17 tilted in the positive direction of rotation 55 at a positive pivoting angle α (0 ° to + 180 °). For the first saw blade edge 61, X (61) = X _rel + δ ^' sin (a ) - D / 2 and for the second saw blade edge 62, X (62) = X _Ref + δ ^' sin (a) + D / 2. FIGS. 4A, B show the wall sawing system 10 in the process of obtaining a separating cut between the first end point E, and the second end point E ₂ , which are defined as obstacles, with the blister guard 21 being processed. When processing without blade guard 21 form a first blade protection edge 71, which faces the first end point E., And a second blade protection edge 72, which faces the second end point E ₂ , the boundary of the wall saw 12,

The X positions of the first and second blade protection edges 71, 72 in the X direction can be calculated from the reference position X _{Ref of} the pivot axis 23, the displacement path δ _{χ of} the rotation axis 19 and the blade guard width B. FIG. 4A shows the wall saw 12 with the saw arm 17 tilted at a negative swivel angle -a (0 ° to -180 °) and the blade guard 21 mounted blade guard 21. With asymmetrical blade protection, the clearances become before the controlled machining starts the rotation axis 19 to the blade guard edges 71, 72 determined, wherein the distance to the first blade protection edge 71 as a first distance B _a and the distance to the second blade protection edge 72 as a second distance B _{b are} designated.

For the first blade protection edge 71, X (71) = X _Ref + δ sin (a) -Ba _, and for the second blade protection edge 72 X (72) = X _{Rs (} + δ sin (ex) + B _b ) Fig. 43 shows the wall saw 12 with the saw arm 17 inclined at a positive swing angle α (0 ° to + 180 °) and the blade guard 21 mounted on the blade guard width B. For the first blade guard edge 71, X (71) = X _Ref + δ ^'sin (a) - B and _a second sheet for the protective edge 72, where X (72) = X _ref + δ' sin (a) + B _b.

FIGS. FIGS. 2A, B show a separation section between two end points E ₁ , E ₂ , which are defined as free end points without an obstacle, and FIG. 3A, B and 4A, B show a separating section between two end points E ₁ , E ₂ , which are defined as obstacles. In practice, also cuts are possible in which one endpoint is defined as an obstacle and the other endpoint represents a free endpoint without obstruction, the control of the wall saw at the free end point on the upper exit point of the saw blade and obstacle on the saw blade edge {processing without blade guard 21) or the blade guard edge (processing with blade guard 21).

The first upper exit point 58, the first saw blade edge 61 and the first blade guard edge 71 are grouped together under the term "first boundary" of the wall saw 12 and the second upper exit point 59, the second saw blade edge 62 and the second blade guard edge 72 are termed "second Limitation ".

FIGS. 5A-K show the wall saw system 10 of FIG. 1 with the guide rail 11 and the wall saw 12 when creating a separating cut of the final depth T in the workpiece 24 between a first endpoint Ei, which represents an obstacle, and a second endpoint E ₂ , which represents a free endpoint without hindrance.

The processing of the separating cut is carried out with the aid of the method according to the invention for controlling a wall sawing system. The separating cut is made in a main cutting sequence of several main cuts until the desired final depth T is reached. The main cutting sequence comprises a first main section with a first main cutting angle α _{1 of} the saw arm 17, a first diameter D ₁ and a first penetration depth h _{t of} the saw blade used, a second main section with a second main cutting angle α _{2 of} the saw arm 17, a second diameter D ₂ and a second penetration depth h _{2 of} the saw blade used and a third main section having a third main cutting angle α _{3 of} the saw arm 17, a third diameter D ₃ and a third penetration depth h _{3 of} the saw blade used.

The first, second and third main sections are performed by the saw blade 16 with the saw blade diameter D and the blade guard 21 with the blade guard width B. The diameters D,, D _z , D _{3 of} the main sections coincide with the saw blade diameter D, and the widths B, B, B ₂ , B ₃ of the main sections coincide with the blade guard width B.

The main sections of a separating cut are advantageously carried out either with a pulling saw arm 17 arranged or the saw arm 17 is arranged alternately pulling and pushing. The pulling arrangement of the saw arm 17 allows stable guiding of the saw blade during machining and a narrow cutting gap. A separating cut, in which the saw arm 17 is alternately pulled and pushed, has the advantage that the auxiliary times necessary for positioning the saw head 14 and pivoting the saw arm 17 are reduced. In the embodiment, the saw head 14 is moved in the first main section and third main section with the pulling saw arm 17 arranged in the positive feed direction 56; When lying between the second main section of the saw head 14 is moved with the jerky arranged saw arm 17 in the negative feed direction 57. The saw arm 17 is arranged in the three main sections each in the negative direction of rotation 54.

The editing of the separation cut begins at the first endpoint E _:. After the start of the method according to the invention, the saw head 14 is positioned at a start position X _start , in which the pivot axis 23 is at a distance of V [hi ^* (D ₁ -h ₁ ] -δ-sin (-oci) to the first end point E , where h, = h (-α ₁ , D ₁ ) = 0 ^ 2 -Δ-B ^' cos (-α ₁ ) the penetration depth of the saw blade used into the workpiece 24 at the negative first main cutting angle -α ₁ with the first Diameter D ₁ denoted. Here corresponds to the first diameter D ₁ for the first main section the saw blade diameter D. In the start position X _start the saw arm 17 from the basic position at 0 ° in the negative direction of rotation 54 in the negative first main section angle! -α ₁ , panned. After the pivoting movement into the negative first main section angle -α ₁ , the first blade protection edge 71 of the blade guard 21 adjoins the obstacle at the first end point E ₁ . Subsequently, the saw head 14 is moved in the positive feed direction 56 with the saw arm 17 inclined at the negative first main cutting angle -a <and the rotating saw blade 16 (FIG. 5A). During the feed movement, the position of the saw head 14 is regularly measured by the displacement sensor 33.

The feed movement of the saw head 14 is stopped, if the pivot axis 23 has egg NEN distance from the second end point E of _2, where h ₁ -

h (-α ₁ D ₁₎ = D _1/2 - Δ - cos δ (-oci) -et- the depth of penetration of the saw blade used in the workpiece 24 at first major negative cutting angle, with the first diameter D _1, of the D Sägebiattdurchmesser corresponds, designated. In this position, the second upper exit point 59 of the saw blade 16 facing the second end point E ₂ coincides with the second end point E ₂ .

The pivoting movement from the negative first main cutting angle -α ₁ into the negative second main cutting angle -α ₂ takes place in two steps with an intermediate angle -β _{2 1} . At the intermediate angle, the first index indicates whether the pivoting movement occurs at the first or second endpoint E-, E ₂ , with the index "1" for the first endpoint E _; and the index "2" stands for the second endpoint E ₂ . The second index indicates the step and varies from 1 to n-1, n> 2. After the pivotal movement of the saw arm 17 into the intermediate angle _-β 2i ₁ , the saw blade 16 is cut free.

The saw head 14 is positioned in the feed direction 28 so that the pivot axis 23 a distance from the second end point E _z of V [h (-ß _2,1 ) ^' (D - h (-ß _2,1 ))] + δ ^' sin (-βn), where h (-β _2,1 ) = D / 2 -Δ-δ ^' cos (-β _2,1 ) denotes the penetration depth of the saw blade used into the workpiece 24 at the intermediate angle -β _2,1 (FIG.5B). In this position, the saw arm 17 is pivoted from the negative first main cutting angle -α ₁ to the intermediate angle -β _2,1 (FIG. 5C). In the positioning in FIG. 5C, the distance is adjusted so that the second end point E ₂ facing the second upper exit point 59 of the saw mate 16 after the pivotal movement of the saw arm 17 in the intermediate angle -ß _2.1 coincides with the second end point E ₂ .

For free cutting of the saw blade 16, the saw head 14 is displaced in the negative feed direction 57 by a path length of V [h ₂ ^' (D ₂ -h ₂ )], where h ₂ -h (-α ₂ , D ₂ ) ~ D ₂ / 2 - Δ - δ cos (-α ₂ ) denotes the penetration depth of the saw blade into the workpiece 24 at the negative second main cutting angle -α ₂ with the second diameter D ₂ corresponding to the saw blade diameter D (FIG. 5D). The saw head 14 is positioned in the feed direction 28 such that the pivot axis 23 is at a distance of V [h ₃ (D ₂ -h ₂ )] + δ sin (-α ₂ ) from the second end point E ₂ . In this position, the saw arm 17 from the intermediate angle -β _{2 | 1} in the negative second main section angle! -α ₂ pivoted (FIG 5E). When positioning the distance is set so that, the second end point E ₂ facing, second upper exit point 59 of the saw blade 16 -α in the negative second main cutting angle by the pivotal movement of the saw arm 17 together ₂ with the second end point E ₂ menfällt.

The saw head 14 is in the negative feed direction 57 to the first end point E, to be moved, wherein the position of the saw head 14 is measured during the advancing movement of the displacement sensor 33 regularly. The advancing movement of the saw head 14 is stopped when the pivot axis 23 is at a distance of B _2/2 -5 sin (-α ₂ ) from the first end point ET and the first blade protection edge 71 of the blade guard 21 against the obstacle at the first end point E, adjacent (Figure 5F).

The pivoting movement from the negative second main cutting angle -α ₂ into the negative third main cutting angle -α ₃ takes place in two steps with an intermediate angle ~ γ _2.1 . In the intermediate angle, the first index indicates whether the pivoting movement takes place at the first or _second end point E ₁ , E ₂ , where the index "1" stands for the first end point E, and the index "2" stands for the second end point E ₂ . The second index identifies the step and varies from 1 to n-1, n> 2.

Before the pivoting movement of the saw arm 17 into the intermediate angle -γ _2,1 , the saw head 14 is positioned. Since the positioning at the obstacle takes place at E ₁ and the intermediate angle -γ _{2,1 is} less than -90 °, it is not possible to position the saw head 14 so that the second blade guard edge 72 after the pivoting movement in the intermediate angle -γ _2.1 to the obstacle E, adjacent. The positioning of the saw head 14 takes place by means of the critical angle a _crit of -90 ° and the saw arm 17 is subsequently pivoted into the intermediate angle -β ₂₁ (FIG. 5G). The critical angle of -90 ° must be taken into account, since the first end point E, during pivoting movement must not be exceeded. The pivot axis 23 has at the critical angle a _crit of -90 ° a distance of B (2) / 2 - δ sin (-90 °) = B (2) / 2 + δ to the first end point E, on. After the pivoting movement of the saw arm 17 in the intermediate angle -γ _2.1 , the saw blade 16 is cut free. For this purpose, the saw head 14 with the, under the intermediate angle -γ _2.1> inclined saw arm 17 and the rotating saw blade 16 in the positive feed direction 56 to a path length of V [h ₃ (D ₃ - h ₃₎ j method (FIG 5H.), where h ₃ - h (- α ₃ D _3.) - D3 / 2 - δ - (cos δ -α ₃ ) - DV2 - Δ + δ the penetration depth of the saw blade 16 in the

Workpiece 24 at the negative third main cutting angle -α ₃ with the third diameter D ₃ , which corresponds to the saw blade diameter D denotes. After the free cutting, the saw head 14 is posifioniert by means of the critical angle α _crit of -90 ° and the saw arm 17 then pivots from the intermediate angle -γ _2.1 in the negative third main section angle -α ₃ (Figure 51).

Since the third main section represents the last main section of the main cutting sequence, a corner processing of the first end point E, takes place before the processing of the last main section. For this purpose, the saw head 14 is moved in the negative feed direction 57 with the saw arm inclined at -α ₃ until the first blade guard edge 71 of the blade guard 21 adjoins the obstacle at the first end point ET (FIG. The corner processing of the first end point E _t can be improved if the blade guard 21 is dismantled and the corner processing takes place without blade protection. Without blade protection of the saw head 14 is moved with the under -α ₃ inclined saw arm 17 in the negative feed direction 57 until the first saw blade edge 61 of the saw blade 16 coincides with the first end point egg. After the corner processing of the first end point Ei, the third main section with the, under the negative third main cutting angle -α ₃ inclined, saw arm 17 in the positive

Feed direction 56 executed (FIG 5K). The advancing movement of the saw head 14 is stopped when the pivot axis 23 is at a distance of V [h ₃ (D ₃ -h ₃ )] + δ sin (180 ^D ) --- i [h ₃ (D ₃ -h ₃ )] has second end point E ₂ , wherein h ₃ ~ h (-α ₃ , D ₃ ) = D3 / 2 - Δ - δ cos (- 180 °) = Dy'2 - Δ + δ the penetration depth of the saw blade in the workpiece 24 at negative third main cutting angle -α ₃ with the third diameter D ₃ , which corresponds to the saw blade diameter D designated. If the second end point E _2, an overcut is allowed is based on the third main cutting a corner processing of the second end point E. ₂

Claims

claims

1 . Method for controlling a wall sawing system (10) comprising a guide rail (1 1) and a wall saw (12) with a saw head (14), a motorized feed unit (15) which moves the saw head (14) parallel to a feed direction (28) along the Guide rail (11) moves, at least one saw blade (16) which is attached to a, about a pivot axis (23) pivotable, saw arm (17) of the saw head (14) and driven about a rotation axis (19), and at least one, the Sawblade (16) surrounding detachable blade guard (21) when firsting a separating cut (51) of the final depth (T) in a workpiece (24) of the workpiece thickness (d) between a first end point (E _; ) and a second end point (E ₂ ) , With:

^At least the blade diameter (D) of the at least one saw blade (16), the positions of the first and second end points (E _1, E ₂ ) in the feed direction (before starting of a control unit (29) of the wall saw system (10) 28), the final depth (T) of the separating cut (51) and a main cutting sequence of m main cuts with m> 2, the main cutting sequence comprising at least a first main cut with a first main cutting angle (α ₁ ) of the saw arm (17) and a first diameter ( D ₁ ) of the saw blade used and a following second main section having a second main cutting angle (α ₂ ) of the saw arm (17) and a second diameter (D ₂ ) of the saw blade used,

• during the processing controlled by the control unit (29)

- the first main section with, under the positive or negative first

Main cutting angle (± α ₁ ), inclined saw arm (17) performed and

- The second main section with, under the positive or negative second main cutting angle (± α ₂ ), inclined saw arm (17) carried out, characterized in that the pivoting movement of the saw arm (17) from the first main cutting angle (± α ₁ ) in a new major cutting angle! (± α ₁ , ± α ₂ ) is performed in at least two steps with at least one intermediate angle (± ßi, ± ß ₂ ), wherein between the pivoting movements of the saw arm (17) in the at least one intermediate angle (± ß ₁ , ± ß ₂ ) in each case a free cutting of the saw blade (16).

2. The method according to claim 1, characterized in that the pivoting movement of the saw arm (17) from the first main section angle! (± a ₁ ) into the new main cutting angle (± α ₁ , ± α ₂ ) in n steps with n-1 intermediate _angles (± β _{1, j} , ± β _2ij ), j = 1 to n-1 is carried out, wherein between the pivoting movements of the saw arm (17) in the intermediate angle (± ß _{1, j} , ± ß _{2, j} ) respectively a free cutting of the saw blade (16),

3. The method according to any one of claims 1 to 2, characterized in that prior to the start of the control unit (29) controlled machining in addition a Sägearm- length (δ) of the saw arm (17), as the distance between the pivot axis (23) the saw arm (17) and the axis of rotation (19) of the saw blade (16) is defined, and a distance (Δ) between the pivot axis (23) and a top surface (53) of the workpiece (24) are fixed.

4. The method according to claim 3, characterized in that prior to the start of the controlled processing additionally a first width (B ₁ ) for a, used in the first main section, blade protection and a second width (B ₂ ) for one, the second main section , the first and second widths (B, B, B ₂ ) respectively from a first distance (B _{1 a} , B _2a ) of the axis of rotation (19) to the first blade guard edge (71) of the blade guard and a second distance ( B _1b , B _2b ) of the axis of rotation (19) to the second blade protection edge (72) of the blade guard are composed.

5. The method according to any one of claims 3 to 4, characterized in that the

Pivoting movement from the first main cutting angle (± oii) to the new main cutting angle (± α ₁ , ± α ₂ ) at the first end point (E- ₁ ) and the saw head (14) in the j-th step, j = 1 to n- 1 is positioned such that, after the pivoting movement of the saw arm (17) into the j-th intermediate angle (± ß _{1, j} ), a first boundary (58, 61, 71) of the wall saw (12) facing the first end point (Ei) coincides with the first end point (Et), wherein the first boundary (58, 61, 71) of the wall saw (12) by a, the first end point (E ^ facing, the first upper exit point (58) of the saw blade used at the top (53 ) of the workpiece (24) is formed, when the first end point (E- ₁ ) represents a free end point without hindrance, by a, the first end point (E- ₁ ) facing first saw blade edge (61) of the saw blade used when the first End point (E- ₁ ) is an obstacle and the processing is done without blade protection, and by one, the first En dpunkt (E- ₁ ) facing, the first blade protection edge (71) of the blade guard used when the first end point (E- ₁ ) is an obstacle and the processing is done with blade guard.

6. The method according to claim 5, characterized in that after the pivoting movement of the saw arm (17) in the j-th intermediate angle (± ß _{1, j} ) with j = 1 to n-1, the first upper exit point (58) with the first End point (E,) coincides when the pivot axis (23) is a distance from the first end point (E _t ) of V [h (± ß _{1, j} ) (D - h (± ß _{1 J} ))] - δ sin (± ß _{1 ii} ) where h (± β _1j ) = D / 2 - Δ - δ ^' cos (± β _1j ) the penetration depth of the saw blade used into the workpiece (24) at the j th intermediate _angle ! (± _SSI,,) denotes the first blade edge (61) of the saw blade used with the first end point (E _t) coincides, when the pivot axis (23) spaced from the first end point (Ei) of D / 2 - δ sin (± ß ,, _j ), and the first Blattschutzkanie (71) of the blade guard used coincides with the first end point (Ei) when the pivot axis (23) a distance from the first end point (Ε ·,) of B _a - δ sin (± ß _{1, j} ).

7. The method according to claim 6, characterized in that the saw head (14) in the j-th step with j - 1 to n-1 with the, under the j-th intermediate angle! (± ß _1J ), inclined saw arm (17) is moved by a path length of V [h ₂ ^' (D - h ₂ )] - δ ^' sin (± α ₂ ), where h ₂ = h (± α ₂ , D) - D / 2 - δ - cos δ (± _«2) the depth of penetration of the saw blade used (in the workpiece 24) at the second main cutting angle (± α _2), respectively.

8. The method according to claim 7, characterized in that the saw head (14) after the η-1-th step is positioned so that after the pivotal movement of the saw arm (17) in the new main cutting angle! (± oti, ± α ₂ ) the, the first end point (E <) facing the first boundary (58, 61, 71) of the wall saw (12) coincides with the first end point (E,).

9. The method according to claim 8, characterized in that after the pivoting movement of the saw arm (17) in the second main section angle! (± α ₂ ) the first upper exit point (58) coincides with the first end point (E) when the pivot axis (23) is at a distance from the first end point (Ei) of V [h ₂ ^* (D - h ₂ )] - δ sin (± α ₂ ), where h (± α ₂ ) - D / 2 - Δ - δ ^■ cos (± α ₂ ) the penetration depth of the saw blade used in the workpiece (24) at the second main cutting angle (± α ₂ ) with the second diameter (D ₂₎ indicates, the first blade edge (61) of the saw blade used with the first end point (e,), coincides if the pivot axis (23) _t a distance from the first end point (e) of D _2/2 - ö sin (± α ₂ ), and the first Blattschutzkanie (71) of the blade guard used coincides with the first end point (Ε-ι) when the pivot axis (23) is a distance from the first end point (E _t ) of B _2a - 6 sin (± α ₂ j has.

10. The method according to any one of claims 3 to 4, characterized in that the

Pivoting movement from the first main cutting angle (± ot-,) in the new main cutting angle (± oii, ± α ₂ ) at the second end point (E ₂ ) and the saw head (14) in the j-th intermediate section, j = 1 to n-1 so is positioned after the pivoting movement of the saw arms (17) in the j-th intermediate angle (± ß ₂ , _j ) one, the second end point (E ₂ ) facing the second boundary (59, 62, 72) of the wall saw (12) coincides with the second end point (E ₂ ) in that the second boundary (59, 62, 72) of the wall saw (12) is formed on the upper side (53) of the workpiece (24) by a second upper exit point (59) of the saw blade used facing the second end point (E ₂ ) is, if the second end point (E ₂ ) represents a free end point without obstruction, by a second end point (E ₂ ) facing the second saw blade edge (62) of the saw blade used, when the second end point (E ₂ ) is an obstacle, and the processing takes place without blade protection, and by a, the second end point (E ₂ ) facing the second blade guard edge (72) of the blade guard used when the second end point (E ₂ ) is an obstacle and the processing is done with blade guard.

1 1. A method according to claim 10, characterized in that after the pivoting movement of the saw arm (17) in the j th Zwischenwinkei (± ß _{2, j} ) with j = 1 to n-1, the second upper exit point (59) with the second end point (E ₂ ) coincides when the pivot axis (23) a distance from the second end point (E ₂ ) of ^' (D - h (± ß _2j ))] + δ ^' sin (± ß _2ii ), where h (± ß _2J ) = D / 2 - Δ - δ cos (± ß _2ij ) is the penetration depth of the saw blade used in the workpiece (24) at the j-th intermediate _angle (± ß _2ij ), the second saw blade _edge (62) of the saw blade used coincides with the second end point (E ₂ ), when the pivot axis (23) spaced from the second end point (E ₂ ) of D / 2 + δ ^' sin (± β _2ij ), and the second blade _{guard edge} (72) of the blade _guard used coincides with the second end point (E ₂ ) when the pivot axis (23) is spaced from the second end point (E? ) of B _s + o sin (± β _{2, j} ).

12. The method according to claim 1 1, characterized in that the saw head (14) in the j-th step, j = 1 to n-1 with the, under the j-th intermediate _angle (± ß _2ii ), inclined saw arm

(17) by a path length of V [h ₂ '(D-h ₂ ) 3-S ^' sin (± α ₂ ), where h ₂ = h (± α ₂ , D) = D / 2-Δ - δ cos (± α _2), the penetration depth of the saw blade used in the workpiece (24) at the second main cutting angle (± α _2), respectively.

13. The method according to claim 12, characterized in that the saw head (14) after the η-1-th step is positioned so that after the pivotal movement of the saw arm (17) in the new main cutting angle (± α _1> ± α ₂ ) the, the second end point (e ₂₎ facing second boundary (59, 62, 72) of the wall saw (12) with the second end point (e ₂₎ coincide.

14. The method according to claim 13, characterized in that after the pivotal movement of the saw arm (17) in the second main section angle (± α ₂ ), the second upper exit point (59) coincides with the second end point (E ₂ ) when the pivot axis (23 ) has a distance to the second end point (E ₂ ) of V [h ₂ (D - h ₂ )] + 8 sin (± α ₂ ), where h (± oc ₂ ) = D / 2 - Δ - δ ^' cos ( ± α ₂ ) denotes the penetration depth of the saw blade used into the workpiece (24) at the second main cutting angle (± α ₂ ), the second saw blade edge (62) of the saw blade used coincides with the second end point (E ₂ ) when the pivot axis (23) has a distance to the second end point (E ₂ ) of D / 2 + δ sin (± cx ₂ ), and the second blade guard edge (72) of the blade guard used coincides with the second end point (E _? ) when the pivot axis (23) Distance from the second end point (E ₂ ) of B _2b + δ ^· sin (± α ₂ ).