Patent Publication Number: US-2020298335-A1

Title: Laser machining method for cutting workpiece

Description:
BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates to a laser machining method for cutting a workpiece. 
     2. Description of the Related Art 
     A laser machining method is known in which a workpiece is cut while an optical axis of the laser beam being shifted relative to an exit port of a nozzle through which an assist gas is emitted (e.g., JP 6116757 B). 
     On both sides of a cutting spot of the workpiece, cutting quality of each side of the workpiece required (a dimension of dross, roughness of a cut surface, a taper of a kerf, etc.) differs each other in some cases. Specifically, although high cutting quality is required on one side of the cutting spot of the workpiece, cutting quality equivalent to that on the one side is not required on the other side of the cutting portion in some cases. In such a case, there is a demand for a technique able to effectively satisfy the cutting quality required on one side of the cutting spot of the workpiece. 
     SUMMARY OF THE INVENTION 
     In an aspect of the present disclosure, a laser machining method of cutting a workpiece using a machining head configured to emit a laser beam and an assist gas coaxially and non-coaxially includes preparing a machining program that specifies, on the workpiece, a cutting line, and a first region and a second region on both sides of the cutting line, cutting quality requirements of which are different from each other; and maintaining a center axis of the assist gas to be shifted from an optical axis of the laser beam toward the first region in response to the difference between the cutting quality requirements, during cutting between the first region and the second region along the cutting line in accordance with the machining program. 
     According to the present disclosure, when two regions having different cutting quality requirements are specified on both sides of a cutting spot of a workpiece, it is possible to effectively satisfy the cutting quality requirement for one of the regions. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a diagram of a laser machine according to an embodiment. 
         FIG. 2  is a block diagram of the laser machine illustrated in  FIG. 1 . 
         FIG. 3  is a diagram of a moving device according to an embodiment. 
         FIG. 4  illustrates a state in which the moving device illustrated in  FIG. 3  shifts a center axis of an assist gas from an optical axis of a laser beam. 
         FIG. 5  is a diagram of a moving device according to another embodiment. 
         FIG. 6  is a diagram of a moving device according to still another embodiment. 
         FIG. 7  illustrates a state in which the moving device illustrated in  FIG. 6  shifts a center axis of an assist gas from an optical axis of a laser beam. 
         FIG. 8  is a diagram of a moving device according to further another embodiment. 
         FIG. 9  illustrates a state in which the moving device illustrated in  FIG. 8  shifts a center axis of an assist gas from an optical axis of a laser beam. 
         FIG. 10  is a diagram of a moving device according to still another embodiment. 
         FIG. 11  illustrates a state in which the moving device illustrated in  FIG. 10  shifts a center axis of an assist gas from an optical axis of a laser beam. 
         FIG. 12  is a diagram of a moving device according to still another embodiment. 
         FIG. 13  illustrates an example of a workpiece to be cut. 
         FIG. 14  illustrates a state in which a workpiece is cut while an assist gas and a laser beam being emitted coaxially. 
         FIG. 15  illustrates a state in which a workpiece is cut while an assist gas and a laser beam being emitted non-coaxially. 
         FIG. 16  also illustrates a state in which a workpiece is cut while an assist gas and a laser beam being emitted non-coaxially. 
         FIG. 17  is a diagram of a laser machine according to another embodiment. 
         FIG. 18  is a block diagram of the laser machine illustrated in  FIG. 17 . 
         FIG. 19  is a diagram of a laser machine according to still another embodiment. 
         FIG. 20  is a block diagram of the laser machine illustrated in  FIG. 19 . 
         FIG. 21  is a flowchart illustrating an example of an operation flow of the laser machine illustrated in  FIG. 19 . 
         FIG. 22  is a diagram of a laser machine according to yet another embodiment. 
         FIG. 23  is a block diagram of the laser machine illustrated in  FIG. 22 . 
         FIG. 24  is a flowchart illustrating an example of an operation flow of the laser machine illustrated in  FIG. 22 . 
         FIG. 25  is a diagram of a laser machine according to further another embodiment. 
         FIG. 26  is a block diagram of the laser machine illustrated in  FIG. 25 . 
         FIG. 27  is a block diagram of a machine learning apparatus according to an embodiment. 
         FIG. 28  is a diagram for explaining trial laser machining with respect to a trial workpiece. 
         FIG. 29  illustrates an aspect of dross generated in a workpiece by trial laser machining. 
         FIG. 30  is a block diagram of a machine learning apparatus according to another embodiment. 
         FIG. 31  is a flowchart illustrating an example of a learning flow carried out by the machine learning apparatus illustrated in  FIG. 30 . 
         FIG. 32  schematically illustrates a neuron model. 
         FIG. 33  schematically illustrates a multi-layer neural network model. 
         FIG. 34  is a block diagram of a machine learning apparatus according to still another embodiment. 
         FIG. 35  illustrates a mode in which the learning apparatus illustrated in  FIG. 34  is mounted in the laser machine illustrated in  FIG. 1 . 
         FIG. 36  is a block diagram of the laser machine illustrated in  FIG. 35 . 
         FIG. 37  illustrates an example of a workpiece in which an additional cutting line is specified. 
         FIG. 38  is a flowchart illustrating another example of an operation flow of the laser machine illustrated in  FIG. 19 . 
     
    
    
     DETAILED DESCRIPTION 
     Embodiments of the present disclosure will now be described in detail with reference to the drawings. Note that, in the various embodiments described below, similar components are denoted by the same reference numerals, and redundant description thereof will be omitted. Further, in the following description, an orthogonal coordinate system in the drawings is used as a reference of directions, and the x-axis positive direction is referred to as the rightward direction, the y-axis positive direction is referred to as the frontward direction, and the z-axis positive direction is referred to as the upward direction, for that sake of convenience. 
     Referring to  FIG. 1  and  FIG. 2 , a laser machine  10  according to an embodiment will be described. The laser machine  10  includes a control device  12 , a laser oscillator  14 , a machining head  16 , an assist gas supply device  18 , a moving mechanism  20 , and a moving device  22 . The control device  12  includes e.g. a processor  13  (CPU, GPU, etc.) and a storage  15  (ROM, RAM, etc.), and controls each component of the laser machine  10  directly or indirectly. The processor  13  and the storage  15  are communicably connected to each other via a bus  17 . 
     The laser oscillator  14  performs laser oscillation inside thereof in accordance with a command from the control device  12 , and emits a laser beam to the outside. The laser oscillator  14  may be of any type, such as a CO 2  laser oscillator, a solid-state laser (YAG laser) oscillator, or a fiber laser oscillator. 
     The machining head  16  includes a head main body  24 , optical elements  26 , a lens driver  28 , and a nozzle  30 . The head main body  24  is hollow, and an optical fiber  32  is connected to a proximal end of the head main body  24 . The laser beam emitted from the laser oscillator  14  propagates through the optical fiber  32 , and enters into the head main body  24 . 
     The optical elements  26  include e.g. a collimating lens or a focus lens, and constitute an optical system of the machining head  16 . The optical elements  26  collimate or focus the laser beam entering into the head main body  24 , and guide it to a workpiece W. The optical elements  26  are housed in the head main body  24  so as to be movable in a direction of an optical axis A 1  of the laser beam. The lens driver  28  moves at least one optical element  26  in the direction of the optical axis A 1 . By the lens driver  28  adjusting the position of the optical element  26  in the direction of the optical axis A 1 , it is possible to control a focus position in the optical axis direction of the laser beam emitted from the nozzle  30 . 
     The nozzle  30  is hollow, and provided at a distal end of the head main body  24 . The nozzle  30  has a truncated-conical outer shape in which a cross-sectional area orthogonal to the optical axis A 1  decreases from the proximal end thereof toward the distal end thereof, and includes a circular-shaped emission port  34  at the distal end thereof. A hollow chamber  36  is formed inside the nozzle  30  and the head main body  24 . The laser beam propagating from the optical elements  26  passes through the chamber  36  and is emitted to the outside through the emission port  34 . 
     The assist gas supply device  18  supplies an assist gas to the chamber  36  formed inside the head main body  24  and the nozzle  30 , through a gas supply tube  35 . The assist gas is e.g. nitrogen or air. The assist gas supplied to the chamber  36  is emitted through the emission port  34  as a jet B, together with the laser beam. 
     The nozzle  30  is configured to emit the assist gas and the laser beam coaxially and non-coaxially with each other, as described later. In  FIG. 1 , the assist gas jet B is schematically illustrated by dotted lines. When the nozzle  30  emits the assist gas and the laser beam coaxially, the optical axis A 1  of the laser beam and a center axis A 2  of the assist gas are parallel to the z-axis. The z-axis direction is parallel to a vertical direction, for example. 
     The moving mechanism  20  moves the machining head  16  and the workpiece W relative to each other. Specifically, the moving mechanism  20  includes a work table  38 , an x-axis moving mechanism  40 , a y-axis moving mechanism  42 , and a z-axis moving mechanism  44 . The workpiece W is set on the work table  38 . The x-axis moving mechanism  40  includes e.g. a servomotor (not illustrated) and a ball screw mechanism having a ball screw extending in the x-axis direction (not illustrated). The x-axis moving mechanism  40  moves the work table  38  in the x-axis direction in accordance with a command from the control device  12 . 
     The y-axis moving mechanism  42  includes e.g. a servomotor (not illustrated) and a ball screw mechanism having a ball screw extending in the y-axis direction (not illustrated). The y-axis moving mechanism  42  moves the work table  38  in the y-axis direction in accordance with a command from the control device  12 . The z-axis moving mechanism  44  includes e.g. a servomotor (not illustrated) and a ball screw mechanism having a ball screw extending in the z-axis direction (not illustrated). The z-axis moving mechanism  44  moves the machining head  16  in the z-axis direction. 
     In accordance with a command from the control device  12 , the moving device  22  moves the optical axis A 1  of the laser beam and the center axis A 2  of the assist gas B relative to each other, by varying at least one of the optical axis arrangement of the optical system in the machining head  16 , the position of the nozzle  30 , and the emission mode of the assist gas. There are various embodiments of the moving device  22 . Hereinafter, the various embodiments of the moving device  22  will be described with reference to  FIG. 3  to  FIG. 12 . 
     A moving device  22  illustrated in  FIG. 3  includes a nozzle moving mechanism  45 . In the embodiment illustrated in  FIG. 3 , the nozzle  30  is provided at the head main body  24  so as to be movable along an x-y plane (i.e., a plane orthogonal to an optical axis A 1 ) relative to the head main body  24 . For example, an elastic material (e.g., annular rubber)  43  is interposed between the nozzle  30  and the head main body  24 , such that the nozzle  30  can be supported by the elastic material  43  so as to be movable along the x-y plane relative to the head main body  24 . 
     The nozzle moving mechanism  45  includes a plurality of drivers  46 . For example, a total of four drivers  46  are disposed around the optical axis A 1  at substantially equal intervals (i.e., interval of 90 degree). Each driver  46  is a servomotor or a piezoelectric element, etc., and includes a drive shaft  46   a , the tip of which is coupled to the nozzle  30 . In accordance with a command from the control device  12 , the drivers  46  advance and retract their drive shafts  46   a  in cooperation with each other so as to drive the nozzle  30  along the x-y plane relative to the head main body  24 . 
     For example, as illustrated in  FIG. 4 , of the two drivers  46  aligned in the x-axis direction, the driver  46  located on the right side advances the drive shaft  46   a  thereof leftward, in synchronization with which the driver  46  located on the left side retracts the drive shaft  46   a  thereof leftward. Whereby, the nozzle  30  is moved leftward relative to the head main body  24 . As a result, the center axis A 2  of the assist gas emitted from the emission port  34  of the nozzle  30  is shifted leftward from the optical axis A 1  of the laser beam. 
     Similarly, of the two drivers  46  aligned in the y-axis direction, the driver  46  located on the front side retracts the drive shaft  46   a  thereof forward, in synchronization with which the driver  46  located on the rear side advances the drive shaft  46   a  thereof forward. Whereby, the nozzle  30  is moved forward relative to the head main body  24 . The processor  13  of the control device  12  controls the advancing and retracting direction and the movement amount of the drive shaft  46   a  of each driver  46 , whereby moving the nozzle  30  in the x-axis and y-axis directions (i.e., along the x-y plane) relative to the head main body  24 . 
     A moving device  22  illustrated in  FIG. 5  includes a flow-rate adjustment mechanism  47 . The flow-rate adjustment mechanism  47  is configured to shift the center axis A 2  of the assist gas B emitted through the emission port  34  from the optical axis A 1  of the laser beam, by varying the flow rate of the assist gas supplied to the chamber  36  along the circumferential direction around the optical axis A 1 . 
     Specifically, the machining head  16  includes a plurality of discharge ports  48  disposed to be aligned in the circumferential direction around the optical axis A 1 , wherein each discharge port  48  is opened to the chamber  36 . The assist gas supplied from the assist gas supply device  18  is discharged into the chamber  36  through each discharge port  48 . 
     The flow-rate adjustment mechanism  47  includes a plurality of movable shutters  50  configured to block the discharge ports  48 , respectively, so as to change the opening areas thereof; and drivers  52  configured to drive the respective movable shutters  50 . The driver  52  includes e.g. a servomotor, and changes the opening area of the discharge port  48  by moving the movable shutter  50  in response a command from the control device  12 , thereby adjusting the flow rate of the assist gas introduced from each discharge port  48  into the chamber  36 . 
     For example, as illustrated in  FIG. 5 , the flow-rate adjustment mechanism  47  blocks by the movable shutter  50  a part of the left discharge port  48  of the two discharge ports  48  disposed to face each other in the x-axis direction, so as to adjust the flow rate of the assist gas discharged therefrom to a flow rate Q 1 . 
     On the other hand, the flow-rate adjustment mechanism  47  fully opens the movable shutter  50  of the right discharge port  48  of the two discharge ports  48  disposed to face each other in the x-axis direction, so as to adjust the flow rate of the assist gas discharged therefrom to a flow rate Q 2  (&gt;Q 1 ). By adjusting the flow rates Q 1  and Q 2  of the assist gas in this manner, the center axis A 2  of the assist gas emitted through the emission port  34  may be shifted leftward from the optical axis A 1  of the laser beam. 
     Similarly, the flow-rate adjustment mechanism  47  blocks by the movable shutter  50  a part of the rear discharge port  48  of the two discharge ports  48  disposed to face each other in the y-axis direction, so as to adjust the flow rate of the assist gas discharged therefrom to a flow rate Q 3 . On the other hand, the flow-rate adjustment mechanism  47  fully opens the movable shutter  50  of the front discharge port  48  so as to adjust the flow rate of the assist gas discharged therefrom to a flow rate Q 4  (&gt;Q 3 ). 
     By adjusting the flow rates Q 3  and Q 4  of the assist gas in this manner, it is possible to shift the center axis A 2  of the assist gas emitted from the emission port  34  rearward from the optical axis A 1  of the laser beam. Thus, the flow-rate adjustment mechanism  47  varies the emission mode of the assist gas by varying the flow rate Q of the assist gas supplied into the chamber  36  in the circumferential direction around the optical axis A 1 , whereby shifting the center axis A 2  of the assist gas from the optical axis A 1  of the laser beam. 
     The moving device  22  illustrated in  FIG. 6  includes an optical-fiber moving mechanism  56 . In the embodiment illustrated in  FIG. 6 , the optical fiber  32  is connected to a proximal end  24   a  of the head main body  24  so as to be movable along the x-y plane. The optical-fiber moving mechanism  56  includes e.g. a servomotor or a piezoelectric element, and moves the optical fiber  32  relative to the proximal end  24   a . As a result, the position (or angle) of the laser beam entering into the head main body  24  from the optical fiber  32  is changed, whereby optical axis arrangement of the laser beam is varied. 
     For example, as illustrated in  FIG. 7 , the optical-fiber moving mechanism  56  moves the optical fiber  32  to the left from the position illustrated in  FIG. 6  relative to the proximal end  24   a . As a result, the laser beam entering into the head main body  24  from the optical fiber  32  is shifted leftward, whereby the optical axis A 1  of the laser beam emitted through the emission port  34  may be shifted to the left from the position in  FIG. 6 . Thus, it is possible to shift the center axis A 2  of the assist gas from the optical axis A 1  of the laser beam. 
     The moving device  22  illustrated in  FIG. 8  includes an optical-element moving mechanism  58 . Specifically, the optical-element moving mechanism  58  includes e.g. a servomotor or a piezoelectric element, and is disposed inside the head main body  24  to move optical elements  26  (e.g., focus lenses) along the x-y plane. Along with the movement of the optical elements  26 , the optical axis of the laser beam guided by the optical elements  26  is also moved along the x-y plane, whereby varying the optical axis arrangement of the laser beam. 
     For example, as illustrated in  FIG. 9 , the optical-element moving mechanism  58  moves the lowest optical element  26  (focus lens) of the plurality of optical elements  26  to the left from the position illustrated in  FIG. 8 . As a result, the optical axis arrangement of the laser beam is varied, whereby the optical axis A 1  of the laser beam emitted through the emission port  34  may be shifted to the left from the position illustrated in  FIG. 7 . Thus, it is possible to shift the center axis A 2  of the assist gas from the optical axis A 1  of the laser beam. 
     The optical-element moving mechanism  58  may vary the optical axis arrangement of the laser beam by moving any one of the plurality of optical elements  26 , or by moving two or more optical elements  26 . Further, the lens driver  28  may function as the optical-element moving mechanism  58  to move each of the optical elements  26  in the optical axis A 1  direction, along with moving at least one optical element  26  along the x-y plane, in order to vary the optical axis arrangement of the laser beam. 
     The moving device  22  illustrated in  FIG. 10  includes optical-element moving mechanisms  60 A and  60 B. In the embodiment illustrated in  FIG. 10 , optical elements  62 A and  62 B are further provided inside the head main body  24 . The optical elements  62 A and  62 B constitute the optical system of the machining head  16 , together with optical elements  26 . 
     The optical element  62 A is a transparent flat plate member able to guide a laser beam. The optical element  62 A is disposed to be inclined relative to the optical axis (i.e., z-axis direction) of the laser beam incident thereon, and supported inside the head main body  24  so as to be rotatable about the optical axis. Similar to the optical element  62 A, the optical element  62 B is a transparent flat plate member able to guide a laser beam, disposed to be inclined relative to the optical axis of the laser beam incident on the optical element  62 A, and supported inside the head main body  24  so as to be rotatable about the optical axis. The optical elements  62 A and  62 B are arranged separate from each other in the z-axis direction, and are rotatable independently of each another. 
     The optical-element moving mechanism  60 A includes e.g. a servomotor, and is disposed inside the head main body  24  to rotate the optical element  62 A. The optical-element moving mechanism  60 B includes e.g. a servomotor, and is disposed inside the head main body  24  to rotate the optical element  62 B. The optical-element moving mechanisms  60 A and  60 B rotate the optical elements  62 A and  62 B, respectively, thereby varying the optical axial arrangement of the laser beam emitted through the emission port  34 . 
     For example, when the optical-element moving mechanism  60 B rotates the optical element  62 B from the position illustrated in  FIG. 10  to the position illustrated in  FIG. 11 , the propagation direction of the laser beam incident on the optical element  62 B is varied. 
     As a result, the optical axis arrangement of the laser beam is varied, and the optical axis A 1  of the laser beam emitted through the emission port  34  may be shifted to the left from the position illustrated in  FIG. 10 . In this way, the optical-element moving mechanisms  60 A and  60 B vary the optical axis arrangement of the laser beam by varying the rotation angles of the optical elements  62 A and  62 B, respectively, thereby shifting the center axis A 2  from the optical axis A 1 . 
     The moving device  22  illustrated in  FIG. 12  includes a beam-coupling adjustment mechanism  64 . In the embodiment illustrated in  FIG. 12 , a plurality of laser beams Le enter the head main body  24 . For example, the plurality of laser beams Le enter the head main body  24  in such arrangement that the beams are aligned in the circumferential direction around the center axis of the emission port  34  (i.e., the center axis A 2  of the assist gas) at substantially equal intervals. 
     As an example, the laser oscillator  14  emits the plurality of laser beams Le, and the emitted laser beams Le enter the head main body  24  through a plurality of optical fibers  32 . In this case, the laser oscillator  14  may include a plurality of laser oscillators, each of which emits a laser beam Le. Alternatively, the laser oscillator  14  may emit a laser beam, and the emitted laser beam may be divided into the plurality of laser beams Le by a beam-divider (not illustrated), wherein the divided beams Le may enter the head main body  24 . 
     A beam-coupling section  66  is further provided inside the head main body  24 . The beam-coupling section  66  constitutes the optical system of the machining head  16 , together with optical elements  26 . The beam-coupling section  66  couples the plurality of laser beams Le having entered the head body  24 , and guides the mixed beams to the optical elements  26  as a single laser beam. 
     The beam-coupling adjustment mechanism  64  adjusts the distribution of the laser beams Le entering the beam-coupling section  66 . For example, the beam-coupling adjustment mechanism  64  is configured to adjust the distribution of the plurality of laser beams Le entering the beam-coupling section  66  by blocking at least one of the plurality of laser beams Le by a mirror (a total-reflection mirror or a partial-reflection mirror). 
     When the distribution of the laser beams Le is adjusted in this manner, the coupling mode of the plurality of laser beams Le in the beam-coupling section  66  becomes non-uniform, and the optical axis A 1  of the laser beam emitted through the emission port  34  is displaced along the x-y plane. In this way, the beam-coupling adjustment mechanism  64  adjusts the distribution of the laser beams Le entering the beam-coupling section  66  to make the coupling mode in the beam-coupling section  66  be non-uniform, thereby varying the optical axis arrangement of the laser beam. 
     The moving device  22  may include at least two of the nozzle moving mechanism  45 , the flow-rate adjustment mechanism  47 , the optical-fiber moving mechanism  56 , the optical-element moving mechanism  58 , the optical-element moving mechanism  60 , and the beam-coupling adjustment mechanism  64 . For example, the moving device  22  may include the nozzle moving mechanism  45  and the optical-element moving mechanism  58  to vary the position of the nozzle  30 , along with varying the optical axis arrangement of the laser beam. 
     Next, functions of the laser machine  10  will be described. The laser machine  10  cuts a workpiece W as illustrated in  FIG. 13 , for example, in accordance with a machining program  72 . The machining program  72  is prepared in advance by an operator, and stored in the storage  15 . In the machining program  72 , a cutting line l on the workpiece W, and a product region E 1  and a waste region E 2  on both sides of the cutting line l, which are separated by the cutting line l, are specified. 
     The product region E 1  is a portion of the workpiece W that is used as a product, while the waste region E 2  is a portion that is not used as a product. In an example illustrated in  FIG. 13 , the cutting line l includes a plurality of continuous cutting lines l 1 , l 2 , l 3 , l 4 , l 5 , l 6  and l 7 . The cutting line l 1  linearly extends forward from a point P 1 , which is a start point of machining, to a point P 2 . The cutting line l 2  is continuously connected with the cutting line l 1  in a straight line, and linearly extends forward from the point P 2  to a point P 3 . 
     The cutting line l 3  extends in a curved manner in a right-forward direction from the point P 3  to a point P 4 . The cutting line l 4  linearly extends rightward from the point P 4  to a point P 5 . The cutting line l 5  linearly extends in a right-rear direction from the point P 5  to a point P 6 . The cutting line l 6  extends in a curved manner in a left-rear direction from the point P 6  to a point P 7 . The cutting line l 7  linearly extends leftward from the point P 7  to the point P 2 . 
     Thus, in this embodiment, the cutting lines l 1 , l 2 , l 4 , l 5  and l 7  are straight lines, while the cutting lines l 3  and l 6  are curved (e.g., arc-shaped). The laser machine  10  cuts the workpiece W along the cutting lines l 1 , l 2 , l 3 , l 4 , l 5 , l 6  and l 7  between the product region E 1  and the waste region E 2  in arrow directions in  FIG. 13 , by the laser beam emitted through the nozzle  30 . 
     In this regard, the cutting quality requirement for the product region E 1  may be different from that for the waste region E 2  may be different from each other. The cutting quality requirement includes e.g. requirements for a dimension of the dross generated at the cutting spot of the workpiece W, roughness of the cut surface of the workpiece W, and a taper angle of the kerf formed between the product region E 1  and the waste region E 2  when the workpiece W is cut between the product region E 1  and the waste region E 2  along the cutting line l. 
     As an example, if the cutting quality requirement is for the dimension of the dross, the dimension of the dross formed at the product region E 1 , which is used as a product, is required to be as small as possible, while the dimension of the dross formed at the waste region E 2 , which is not used as a product, may be allowed to be relatively large, as the cutting quality requirement. 
     As another example, if the cutting quality requirement is for the cut surface roughness, the cut surface roughness of the product region E 1  is required to be as small as possible, while the cut surface roughness of the waste region E 2  may be allowed to be relatively large, as the cutting quality requirement. As yet another example, if the cutting quality requirement is for the taper angle of the kerf, the taper angle of the product region E 1  is required to be substantially 0°, while the taper angle of the waste region E 2  may be allowed to be relatively large, as the cutting quality requirement. 
     The inventor of the present invention have focused on a fact that, during cutting along a cutting line between two regions, if the center axis A 2  of the assist gas is shifted from the optical axis A 1  of the laser beam toward one of two regions, a difference in cutting quality between the two regions occurs, and have found that it is possible to effectively satisfy the cutting quality of the product region E 1  by maintaining the center axis A 2  to be shifted from the optical axis A 1  toward the product region E 1  or the waste region E 2  during the cutting along the cutting line l between the product region E 1  and the waste region E 2 . 
     Hereinafter, with reference to  FIG. 14  to  FIG. 16 , examples for shifting the center axis A 2  of the assist gas B from the optical axis A 1  of the laser beam L will be described.  FIG. 14  illustrates an example in which the assist gas B and the laser beam L are emitted coaxially to cut the cutting line l 1 . As illustrated in  FIG. 13 , regions on both sides of the cutting line l 1  are the waste region E 2 . 
     Therefore, the cutting quality requirements are the same on both the sides of the cutting line l 1 . Accordingly, during cutting the cutting line l 1 , the laser machine  10  coaxially emits the laser beam L and the assist gas through the nozzle  30  to cut the workpiece W by the laser beam L. As a result, a kerf K is formed in the workpiece W, and the workpiece W is cut along the cutting line l 1 . 
     On the other hand, when the workpiece W is cut along the cutting lines l 2 , l 3 , l 4 , l 5 , l 6  and l 7 , a region on one side and a region on the other side of these cutting lines l 2 , l 3 , l 4 , l 5 , l 6 , and l 7  are the product region E 1  and the waste regions E 2 , the cutting quality requirements of which are different. In the present embodiment, the laser machine  10  maintains the center axis A 2  to be shifted from the optical axis A 1  toward the product region E 1  or the waste region E 2  in response to the difference in the cutting quality requirements for the product region E 1  and the waste region E 2 , during the cutting along the cutting lines l 2 , l 3 , l 4 , l 5 , l 6  and l 7  between the product region E 1  and the waste region E 2 . 
     For example, in an example illustrated in  FIG. 15 , the laser machine  10  cuts the workpiece W along the cutting line l 2  between the product region E 1  and the waste region E 2  by the laser beam L. In this example, the laser machine  10  maintains the center axis A 2  of the assist gas B to be shifted from the optical axis A 1  of the laser beam L toward the product region E 1  by a shift amount δ, during the cutting of the cutting line l 2 . 
     When the center axis A 2  is shifted in this manner, the rate of the assist gas B blown onto the product region E 1  at the cutting point of the workpiece W may be greater than the rate of the assist gas B blown onto the waste region E 2 . Accordingly, even when a supply pressure SP of the assist gas to the nozzle  30 , which is defined as a machining condition, is set to be lower than a machining condition for when the assist gas B and the laser beam L are emitted coaxially (hereinafter, referred to as “normal operation”), it is possible to make a flow speed of the assist gas B blown onto the product region E 1  at the cutting spot to be sufficient. 
     As a result, even when the machining condition (e.g., the supply pressure SP) is set to be lower than that for the normal operation, a molten material of the workpiece W caused by the laser beam L may be blown off by the assist gas B blown onto the product region E 1  at a sufficient flow speed, whereby it is possible to make the dimension of the dross formed on a back surface (i.e., a surface on the lower side) of the product region E 1  to be a value which can satisfy the cutting quality requirement. 
     On the other hand, in an example illustrated in  FIG. 16 , the laser machine  10  maintains the center axis A 2  of the assist gas B to be shifted from the optical axis A 1  of the laser beam L toward the waste region  5   2  by a shift amount δ during the cutting along the cutting line l 2  between the product region E 1  and the waste region  5   2 . The inventor of the present invention have discovered that the roughness of the cut surface when the workpiece is cut by the laser beam becomes larger (i.e., coarser) in some cases as the flow speed of the assist gas B blown onto the cutting spot is larger during the cutting. This suggests that the roughness of the cut surface may become smaller (smoother) as the flow speed of the assist gas B blown onto the cutting spot is smaller. 
     When the center axis A 2  of the assist gas B is shifted toward the waste region  5   2  as illustrated in  FIG. 16 , the rate of the assist gas B blown onto the product region E 1  at the cutting spot becomes small, which may reduce the flow speed of the assist gas B blown onto the product region E 1  at the cutting spot. Accordingly, if the roughness of the cut surface of the product region E 1  is required to be small as the cutting quality requirement, it is possible to make the roughness of the cut surface of the product region E 1  to be a value satisfying the cutting quality requirement, by shifting the center axis A 2  toward the waste region E 2  as illustrated in  FIG. 16 . 
     The control of shifting the center axis A 2  from the optical axis A 1  toward the product region E 1  or the waste region E 2  as described above is also applicable to cutting along the cutting lines l 3 , l 4 , l 5 , l 6  and l 7  between the product region E 1  and the waste region E 2 . In this manner, the laser machine  10  maintains a state in which the center axis A 2  is shifted from the optical axis A 1  toward the product region E 1  or the waste region E 2  in response to the difference in the cutting quality requirements, during cutting along the cutting lines l 2 , l 3 , l 4 , l 5 , l 6  and l 7  between the product region E 1  and the waste region E 2 . 
     Referring again to  FIG. 1  and  FIG. 2 , in the present embodiment, the storage  15  stores a data table  70 . In the data table  70 , data of the machining conditions for cutting the workpiece W using the machining head  16 , and shift amounts δ by which the center axis A 2  of the assist gas B is shifted from the optical axis A 1  of the laser beam L are stored in association with each other. 
     An example of the data table  70  is described in Table 1 below. 
     
       
         
           
               
               
             
               
                 TABLE 1 
               
             
            
               
                   
               
               
                 Machining Condition 
                   
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                   
                   
                   
                   
                   
                   
                 Output 
                   
               
               
                 Workpiece 
                 Workpiece 
                 Machining 
                 Nozzle 
                 Supply 
                 Focus 
                 Characteristic 
                 Shift 
               
               
                 Material 
                 Thickness 
                 Speed 
                 Diameter 
                 Pressure 
                 Position 
                 Value 
                 Amount 
               
               
                   
               
               
                 Material 1 
                 t 1   
                 v 1   
                 ϕ 1   
                 SP 1   
                 z 1   
                 OP 1   
                 δ 1   
               
               
                 Material 2 
                 t 2   
                 v 2   
                 ϕ 2   
                 SP 2   
                 z 2   
                 OP 2   
                 δ 2   
               
               
                 Material 3 
                 t 3   
                 v 3   
                 ϕ 3   
                 SP 3   
                 z 3   
                 OP 3   
                 δ 3   
               
               
                 . 
                 . 
                 . 
                 . 
                 . 
                 . 
                 . 
                 . 
               
               
                 . 
                 . 
                 . 
                 . 
                 . 
                 . 
                 . 
                 . 
               
               
                 . 
                 . 
                 . 
                 . 
                 . 
                 . 
                 . 
                 . 
               
               
                 Material n 
                 t n   
                 v n   
                 ϕ n   
                 SP n   
                 z n   
                 OP n   
                 δ n   
               
               
                   
               
            
           
         
       
     
     As illustrated in Table 1, in the data table  70 , the machining condition data includes a material of the workpiece W to be machined, a thickness t of the workpiece W, a machining speed v at which the workpiece W is cut, a nozzle diameter ϕ of the machining head  16 , a supply pressure SP of the assist gas, a focus position z of the laser beam, and an output characteristic value OP of the laser beam. 
     The material of the workpiece is e.g. stainless steel (SUS301, SUS304, etc.), nickel, copper, etc. The thickness t of the workpiece W is a thickness in the z-axis direction (or the direction of the optical axis A 1  of the laser beam L to be radiated) when the workpiece W is set on the work table  38 . The machining speed v is a speed of the laser beam L relative to the workpiece W when cutting the workpiece W, and may be an average speed, a maximum speed, or a lowest speed. The nozzle diameter ϕ is a diameter (or radius) of the emission port  34  of the nozzle  30 . 
     The supply pressure SP is a pressure of the assist gas supplied from the assist gas supply device  18  into the chamber  36  of the machining head  16 . The focus position z of the laser beam L is a focus position of the laser beam L focused by the optical element (focus lens)  26 , and is represented as a z-axis coordinate. The output characteristic value OP of the laser beam L includes e.g. laser power of the laser beam L or a laser power command value transmitted to the laser oscillator  14 ; or a frequency or a duty ratio when the laser oscillator  14  emits a PW (pulse oscillation) laser beam. 
     In the data table  70 , the shift amounts δ are stored in association with the various machining conditions. Note that, two different data tables  70 A and  70 B may be prepared for a case in which the center axis A 2  is to be shifted from the optical axis A 1  toward the product region e 1  (e.g., a case in which the cutting quality requirement is a dimension of the dross), and for a case in which the center axis A 2  is to be shifted from the optical axis A 1  toward the waste region E 2  (e.g., when the cutting quality requirement is roughness of the cut surface), respectively. 
     The shift amounts δ stored in the data table  70  are obtained as optimal values able to satisfy the cutting quality requirement (dross dimension, cut surface roughness, etc.) of the product region E 1  when laser machining is performed under the corresponding machining conditions. The machining conditions and the shift amounts δ in the data table  70  may be obtained by an experimental (empirical rule) or a simulation technique, or by machine learning described later. 
     By referring to the data table  70 , the optimal shift amount δ, which is able to satisfy the cutting quality requirement under the corresponding machining conditions, can be uniquely determined, when the machining conditions are determined. For example, if an operator inputs, as the machining conditions, the material of the workpiece W as “material 2” and the thickness t thereof as “t 2 ”, the processor  13  determines other machining conditions such that the machining speed v is “v 2 ”, the nozzle diameter ϕ is “ϕ 2 ”, the supply pressure SP is “SP 2 ”, the focus position z is “z 2 ” and the output characteristic value is “OP 2 ”, and automatically determines the shift amount δ as “δ 2 ”. 
     Next, the details of the laser machining according to the present embodiment will be described. As a preparation process for the laser machining, for example, the processor  13  receives input of information on the cutting quality requirement. As the information on the cutting quality requirements, the operator inputs information such as the dimension of the dross or the roughness of the cut surface, and then the processor  13  determines, from the input information on the cutting quality requirements, the direction in which the center axis A 2  is to be shifted (i.e., the direction toward the product region E 1  or the direction toward the waste region E 2 ). Alternatively, the operator may directly input to the control device  12  the direction in which the axis A 2  is to be shifted. 
     Further, the processor  13  receives the machining condition (e.g., the material and the thickness t of the workpiece) from the operator. Then, the processor  13  determines the shift amount δ by applying the input machining condition to the data table  70  corresponding to the input cutting quality requirement (i.e., the direction in which the center axis A 2  is to be shifted). Hereinafter, a case is described in which the received cutting quality requirement is for the dross dimension, and the center axis A 2  of the assist gas B is to be shifted from the optical axis A 1  toward the product region E 1  during cutting between the product region E 1  and the waste region E 2 . 
     The processor  13  of the control device  12  performs laser machining to cut the workpiece W, in accordance with the machining program  72  in which the determined machining condition and shift amount δ are defined. Specifically, the processor  13  operates the moving mechanism  20  to arrange the machining head  16  with respect to the workpiece W such that the optical axis A 1  of the laser beam L intersects the point P 1  ( FIG. 13 ). 
     Subsequently, the processor  13  sends a command to the assist gas supply device  18  so as to start the supply of the assist gas to the nozzle  30 , and also sends a command to the laser oscillator  14  so as to emit the laser beam from the laser oscillator  14 . As a result, the laser beam L and the assist gas B are emitted from the emission port  34  of the nozzle  30 , and piercing is performed on the point P 1  by the laser beam L, whereby a through hole is formed at the point P 1 . When the piercing is performed, the moving device  22  arranges the laser beam L and the assist gas B coaxially with each other. 
     Next, the processor  13  operates the moving mechanism  20  to move the laser beam L forward with respect to the workpiece W, and cuts the workpiece W along the cutting line l 1  from the point P 1  to the point P 2 . In the machining program  72 , regions on both sides of the cutting line l 1  from the point P 1  to the point P 2  (third and fourth regions) are both specified as the waste region E 2 . Accordingly, because the cutting quality requirements are not different in the regions on both sides of the cutting line l 1 , the processor  13  maintains the laser beam L and the assist gas B in a coaxial state while cutting the workpiece W along the cutting line l 1 . 
     When the laser beam L reaches the point P 2  (or immediately before reaching there), the processor  13  operates the moving device  22  so as to shift the center axis A 2  from the optical axis A 1  toward the product region E 1  in accordance with the shift amount δ. As a result, the center axis A 2  of the assist gas B is shifted from the optical axis A 1  by the shift amount δ toward the product region E 1 , as illustrated in  FIG. 15 . 
     Then, the processor  13  operates the moving mechanism  20  to linearly move the laser beam L forward with respect to the workpiece W while maintaining the center axis A 2  to be shifted from the optical axis A 1 , and cuts the workpiece W by the laser beam L along the cutting line l 2  between the product region E 1  and the waste region E 2  from the point P 2  to the point P 3 . 
     Next, the processor  13  moves the laser beam L in a curved manner in the right-forward direction with respect to the workpiece W, and cuts the workpiece W along the cutting line l 3  from the point P 3  to the point P 4 . Next, the processor  13  linearly moves the laser beam L to the right with respect to the workpiece W from the point P 4  to the point P 5 , and cuts the workpiece W along the cutting line l 4 , and subsequently, moves the laser beam L linearly in the right-rear direction with respect to the workpiece W from the point P 5  to the point P 6 , and cuts the workpiece W along the cutting line l 5 . 
     Next, the processor  13  moves the laser beam L in a curved manner in the left-rear direction with respect to the workpiece W, and cuts the workpiece W along the cutting line l 6  from the point P 6  to the point P 7 , and subsequently, moves the laser beam to the left with respect to the workpiece W from the point P 7  to the point P 2 , and cuts the workpiece W along the cutting line l 7 . As a result, the product region E 1  of the workpiece W is cut off from the waste region E 2 . 
     The processor  13  maintains the state in which the center axis A 2  of the assist gas B is shifted from the optical axis A 1  toward the product region E 1  during the cutting along the cutting lines l 2 , l 3 , l 4 , l 5 , l 6  and l 7  between the product region E 1  and the waste region E 2 . For example, the processor  13  controls the moving device  22  so as to shift the center axis A 2  toward the product region E 1  in a direction orthogonal to the machining direction (i.e., the direction in which the laser beam L moves relative to the workpiece W) and parallel to the x-y plane. 
     Note that, if the received cutting quality requirement is for the roughness of the cut surface, the processor  13  may control the moving device  22  so as to shift the center axis A 2  of the assist gas B from the optical axis A 1  toward the waste region E 2  during the cutting along the cutting lines l 2 , l 3 , l 4 , l 5 , l 6  and l 7  between the product region E 1  and the waste region E 2 , in the present embodiment. 
     As discussed above, in the present embodiment, the control device  12  maintains the center axis A 2  to be shifted from the optical axis A 1  toward the product region E 1  or the waste region E 2  in response to the difference in the cutting quality requirements (dross dimension, or cut surface roughness), during the cutting along the cutting lines l 2 , l 3 , l 4 , l 5 , l 6  and l 7  between the product region E 1  and the waste region E 2 . According to this configuration, if the product region E 1  and the waste region E 2  having different cutting quality requirements are specified on both sides of the cutting spot (kerf K) on the workpiece W, it is possible to effectively satisfy the cutting quality requirement of the product region E 1 . 
     Further, in a case in which the cutting quality requirement is for the dross dimension for example, even when the supply pressure SP of the assist gas as the machining condition is set to be lower as described above, the flow speed of the assist gas B blown onto the product region E 1  at the cutting spot may be sufficient, and thus it is possible to make the dimension of the dross formed at the cutting spot of the product region E 1  to be a value that satisfies the cutting quality requirement. Therefore, it is possible to satisfy the cutting quality requirement of the product region E 1  along with setting the machining condition to be low. 
     Note that, in the embodiment described above, the laser beam L and the assist gas are coaxially emitted through the nozzle  30  while the control device  12  cuts the cutting line l 1 . However, the control device  12  may shift the center axis A 2  from the optical axis A 1  toward the product region E 1  or the waste region E 2  at the time of piercing or immediately after the piercing, and may maintain the state in which the center axis A 2  is shifted from the optical axis A 1  during the cutting of the cutting line l 1 . 
     Next, a laser machine  80  according to another embodiment will be described with reference to  FIG. 17  and  FIG. 18 . The laser machine  80  differs from the above-mentioned laser machine  10  in that the laser machine  80  further includes a program creation device  82 . The program creation device  82  is e.g. a computer such as a CAD and CAM, and includes a processor, a storage, an input device (a keyboard, mouse, touch panel, etc.), and a display (an LCD, organic EL, etc. Not illustrated). 
     An operator manipulates the input device to create drawing data of a workpiece to be machined while viewing the display of the program creation device  82 . Hereinafter, a case is described in which the operator creates drawing data of the workpiece W illustrated in  FIG. 13  using the program creation device  82 . 
     The operator manipulates the input device of the program creation device  82  to specify the cutting line l, the product region E 1 , and the waste region E 2  based on image information of the workpiece W, while viewing an image of the created drawing data of the workpiece W. Based on image information of the cutting line l, product region E 1 , and waste region E 2 , which have been specified by the operator, the processor of the program creation device  82  automatically determines a machining speed v when cutting between the product region E 1  and the waste region E 2  along the cutting line l. 
     As an example, the processor of the program creation device  82  determines the machining speed v so as to change the machining speed v depending on a shape of the trajectory of the cutting line l. For example, if the cutting speeds v when cutting between the product region E 1  and the waste region E 2  along the cutting lines l 1 , l 2 , l 3 , l 4 , l 5 , l 6  and l 7  are defined as cutting speeds v 11 , v 12 , v 13 , v 14 , v 15 , v 16 , and v 17 , respectively, the cutting speeds v 11 , v 12 , v 14 , v 15  and v 17  when cutting along the linear cutting lines l 1 , l 2 , l 4 , l 5  and l 7  are set to a predetermined speed v H . 
     On the other hand, the processor of the program creation device  82  sets the cutting speeds v 13  and v 16  when cutting along the curved cut lines l 3  and l 6  to a speed v L  smaller than the speed V H  (i.e., v L &lt;v H ). In this manner, the processor of the program creation device  82  sets the machining speed v so as to change the machining speed v in response to the trajectory-shape of the cutting line l. 
     Note that the cutting speeds v 11 , v 12 , v 14 , v 15  and v 17  may be set to be greater than the cutting speeds v 13  and v 16 , and to be different from each other. The cutting speeds via and v 16  may also be set to be different from each another. Instead of manually specifying the cutting line l, the product region E 1  and the waste region E 2  by the operator, the processor of the program creation device  82  may automatically specify the cutting line l, the product region E 1 , and the waste region E 2  based on the drawing data of the workpiece W created by the operator. 
     Next, the operator manipulates the input device of the program creation device  82  to input the data of respective machining conditions. Specifically, the operator inputs the material of the workpiece W, the thickness t of the workpiece W, the nozzle diameter ϕ of the machining head  16 , the supply pressure SP of the assist gas, the focus position z of the laser beam, and the output characteristic value OP of the laser beam, among the above-discussed machining conditions. 
     On the other hand, the cutting speed v is determined in response to the cutting line l. Subsequently, the operator manually sets the shift amount δ such that it changes in accordance with the determined machining speed v. At this time, the operator can select the shift amount δ suitable for the machining speed v, with reference to the data table  70  stored in the storage  15 . 
     More specifically, the shift amount δ may be determined to be smaller as the machining speed v is larger. In this case, the shift amount δ when cutting between the product region E 1  and the waste region E 2  along the cutting lines l 1 , l 2 , l 4 , l 5  and l 7  at the cutting speed v H  is set to δ H , while the shift amount δ when cutting between the product region E 1  and the waste region E 2  along the cutting lines l 3  and l 6  at the cutting speed v L  may be set to δ L  greater than δ H  (i.e., δ L -δ H ). 
     Instead of manually setting the shift amount δ by the operator, the processor of the program creation device  82  may automatically set the shift amounts δ H  and δ L  in accordance with the cutting speeds v H  and v L . In this case, the processor may refer to the data table  70  and read out the optimal shift amounts δ H  and δ L  from the data table  70  from the determined cutting speeds v H  and v L , and the data of the machining conditions other than the machining speed v. 
     In this way, a machining program  84  ( FIG. 18 ) is created by the program creation device  82 . In this machining program  84 , the cutting line l, the product region E 1 , and the waste region E 2  are specified on the workpiece W, and the material and thickness t of the workpiece W, the nozzle diameter ϕ, the supply pressure SP, the focus position z, and the output characteristic value OP of the laser beam L, as well as the machining speeds v H  and v L  determined in response to the cutting line l, are defined as the machining conditions. Furthermore, in the machining program  84 , the shift amount δ that is set in accordance with the machining speeds v H  and v L  is also defined. The machining program  84  created by the program creation device  82  is stored in the storage  15  of the control device  12 . 
     When the workpiece W is cut along the cutting line l in accordance with the machining program  84  as mentioned above, the processor  13  changes the positional relationship between the center axis A 2  of the assist gas B and the optical axis A 1  of the laser beam L in response to the machining speed v, during cutting between the product region E 1  and the waste region E 2  along the cutting line l. 
     Specifically, the processor  13  operates the moving device  22  so as to maintain the center axis A 2  to be shifted from the optical axis A 1  toward the product region E 1  (or the waste region E 2 ) by the shift amount δ H  during cutting along the cutting lines l 1 , l 2 , l 4 , l 5  and l 7 , while changing the shift amount δ so as to maintain the center axis A 2  to be shifted from the optical axis A 1  toward the product region E 1  (or the waste region E 2 ) by the shift amount δ L  (&gt;δ H ) during cutting along the cutting lines l 3  and l 6 . 
     Note that, when executing the machining program to cut the workpiece W, the processor  13  may acquire the machining speed v (i.e., movement speed of the laser beam L relative to the workpiece W) and control the shift amount δ by changing the positional relationship between the center axis A 2  and the optical axis A 1  in accordance with the acquired machining speed v. 
     The machining speed v can be obtained from the feedback transmitted from the servomotor of the moving mechanism  20  (e.g., a rotation speed transmitted from an encoder configured to detect the rotation speed of the servomotor). In this case, the encoder provided in the servomotor of the moving mechanism  20  constitutes a machining speed acquisition section configured to acquire the machining speed v. 
     As an example, the processor  13  may control the shift amount δ to δL if the machining speed v acquired during cutting of the workpiece is smaller than a first threshold value v th1  (i.e., v&lt;v th1 ), while setting the shift amount δ to δ H  (&lt;δ L ) if the machining speed v is greater than the first threshold value v th1  (v≥v th1 ). 
     The processor  13  may set a total of “n” threshold values (n is an integer of 2 or greater) from the first threshold value v th1  to an n-th threshold value v th(n)  for the machining speed v, and control the shift amount δ in multiple stages depending on the magnitude of the machining speed v such that the shift amount δ is smaller as the machining speed v is larger. Moreover, the processor  13  may acquire acceleration instead of the machining speed v. 
     As described above, in the present embodiment, the operator or the program creation device  82  determines the machining speeds v H  and v L  based on the image information of the workpiece W, and the control device  12  changes the positional relationship between the center axis A 2  and the optical axis A 1  in response to the determined machining speeds v H  and v L  during cutting along the cutting line l. 
     If the workpiece W is cut at a higher machining speed v, a width w in the direction orthogonal to the machining direction of the kerf K formed between the product region E 1  and the waste region E 2  may be smaller than that in a case where the cutting is performed at a lower machining speed v. If the kerf-width w is small in this way, it is possible to satisfy the cutting quality requirement of the product region E 1  even when the shift amount δ of the center axis A 2  is set to be small. According to the present embodiment, since the positional relationship between the central axis A 2  and the optical axis A 1  is finely controlled in accordance with the machining speeds v a  and v L  during the laser machining, it is possible to more effectively satisfy the cutting quality requirement of the product region E 1 . 
     In addition, in the present embodiment, the processor of the program creation device  82  automatically determines the machining speeds v H  and v L  based on the image information of the workpiece W. According to this configuration, it is possible to simplify the work for preparing the machining program  84 . Further, in the present embodiment, if the processor of the program creation device  82  automatically sets the shift amounts δ H  and δ L  in accordance with the cutting speeds v H  and v L , the work for preparing the machining program  84  can be further simplified. 
     Next, a laser machine  90  according to still another embodiment will be described with reference to  FIG. 19  and  FIG. 20 . The laser machine  90  differs from the above-described laser machine  10  in that the laser machine  90  further includes a temperature sensor  92 . The temperature sensor  92  detects a temperature T of the workpiece W while the workpiece W is cut by the laser beam L. As an example, the temperature sensor  92  detects a temperature T 1  of a front surface (or upper surface) of the product region E 1  on one side of the formed kerf K, during the cutting of the workpiece W. 
     As another example, the temperature sensor  92  detects the temperature T 1  on the front surface of the product region E 1  on one side of the formed kerf K and the temperature T 2  on a front surface of the waste region E 2  on the other side of the kerf K, during the cutting of the workpiece W. In this case, one temperature sensor  92  may detect the temperatures T 1  and T 2  on both sides of the kerf K, or the temperature sensor  92  may include a first temperature sensor  92 A configured to detect the temperature T 1  of the product region E 1  and a second temperature sensor  92 B configured to detect the temperature T 2  of the waste region E 2 . 
     The temperature sensor  92  detects the temperature T of the workpiece W at a position near an optical axis A 1  on rear side of the movement direction of the laser beam L relative to the workpiece W. In other words, the temperature sensor  92  detects the temperature T of the workpiece W on one side (or both sides) of the kerf K immediately after the formation of the kerf K by the laser beam L. 
     The control device  12  controls the moving device  22  so as to change the positional relationship between the 0 center axis A 2  of the assist gas and the optical axis A 1  of the laser beam L in response to the temperature T detected by the temperature sensor  92 , during cutting between the product region E 1  and the waste region E 2  along the cutting line l. Such control is described below. 
     Since the temperature of the dross generated by laser machining is high, if the dross of a large dimension is generated on a rear surface of the product region E 1  or the waste region E 2 , the heat of the dross is conducted from the rear surface to the front surface, whereby the temperature on the front surface increases compared to a case where no dross is generated. Thus, the temperature T of the product region E 1  and the waste region E 2  during laser machining is considered to correlate with the cutting quality (dross dimension). 
     In the present embodiment, the control device  12  changes the shift amount δ of the center axis A 2  from the optical axis A 1  in accordance with the temperature detected by the temperature sensor  92  during cutting the workpiece W along the cutting line l. Hereinafter, an operation flow of the laser machine  90  will be described with reference to  FIG. 21 . 
     The processor  13  of the control device  12  carries out the flow illustrated in  FIG. 21  in accordance with a machining program  94  stored in the storage  15 . Accordingly, various commands for carrying out the flow illustrated in  FIG. 21  are defined in the machining program  94 . The flow illustrated in  FIG. 21  is started when the processor  13  receives a laser-machining-start command from an operator, a host controller, or the machining program  94 . 
     In step S 1 , the processor  13  starts laser machining. Specifically, similarly to the above-described embodiment, the processor  13  performs piercing by the laser beam L at the point P 1 , and then controls the moving mechanism  20  so as to move the laser beam L relative to the workpiece W to cut the workpiece W between the product region E 1  and the waste region E 2  along the cutting lines l 1 , l 2 , l 3 , l 4 , l 5 , l 6  and l 7 . Upon the piercing and during cutting the waste region E 2  along the cutting line l 1 , the processor  13  coaxially emits the assist gas B and the laser beam. 
     During cutting between the product region E 1  and the waste region E 2  along the cutting lines l 2 , l 3 , l 4 , l 5 , l 6  and l 7 , the processor  13  operates the moving device  22  so as to maintain the center axis A 2  of the assist gas B to be shifted from the optical axis A 1  of the laser beam L toward the product region E 1 . Here, the processor  13  shifts the center axis A 2  from the optical axis A 1  by an initial shift amount δ 0  when the laser beam L reaches the point P 2  which is a starting point of the cutting line l 2 . 
     This initial shift amount δ 0  may be determined from the data table  70 . For example, when the operator determines the machining conditions (e.g., the material and the thickness t of the workpiece W) prior to laser machining, the processor  13  may read out from the data table  70  the shift amount δ corresponding to the determined machining conditions, and determine it as the initial shift amount δ 0 . 
     In step S 2 , the processor  13  starts the detection of the temperature T by the temperature sensor  92 . As an example, if the temperature sensor  92  detects, as the temperature T, the temperature T 1  on the front surface of the product region E 1 , the processor  13  consecutively (e.g., periodically) acquires, from the temperature sensor  92 , the temperature T 1  detected by the temperature sensor  92  during the cutting of the workpiece W. 
     As another example, if the temperature sensor  92  detects, as the temperature T, the temperature T 1  on the front surface of the product region E 1  and the temperature T 2  on the front surface of the waste region E 2 , the processor  13  consecutively (e.g., periodically) acquires, from the temperature sensor  92 , the temperatures T 1  and T 2  detected by the temperature sensor  92  during the cutting of the workpiece W by the laser beam L. 
     In step S 3 , the processor  13  determines whether or not the temperature T most-recently acquired from the temperature sensor  92  is equal to or greater than the first threshold value T th1 . As an example, if the temperature T 1  is acquired from the temperature sensor  92 , the processor  13  determines whether or not the most-recently acquired temperature T 1  is equal to or greater than a first threshold value T th1_1  (T 1 ≥Tth 1_1 ). The first threshold T th1_1  is predetermined for the temperature T 1  and stored in the storage  15 . 
     As another example, if the temperatures T 1  and T 2  are acquired from the temperature sensor  92 , the processor  13  calculates a temperature difference TA between the most-recently acquired temperatures T 1  and T 2  (i.e., T Δ =T 1 −T 2 ), and determines whether or not the temperature difference T Δ  is equal to or greater than a first threshold value T th1_2  (T Δ ≥T th1_2 ). The first threshold T th1_2  is predetermined for the temperature difference TA and stored in the storage  15 . 
     Alternatively, the processor  13  calculates a temperature ratio R T  of the temperature T 1  and the temperature T 2  that are most-recently acquired (i.e., R T =T 1 /T 2 ), and determines whether or not the temperature ratio R T  is equal to or greater than a first threshold value T th1_3  (R T ≥T th1_3 ). The first threshold T th1_3  is predetermined for the temperature ratio R T  and stored in the storage  15 . 
     In this regard, the temperature T 1  directly indicates the temperature on the front surface of the product region E 1 , and the temperature difference T Δ  and the temperature ratio R T  indicate the temperature on the front surface of the product region E 1  as a relative value with respect to the temperature on the front surface of the waste region E 2 . Accordingly, any of the temperatures T 1 , T Δ , and R T  may be considered to correlate with cutting quality (dross dimension) of the product region E 1 . 
     When the processor  13  determines that the temperature T (T 1 , T Δ , or R T ) is equal to or greater than the first threshold value T th1  (T th1_1 , T th1_2 , or T th1_3 ) (i.e., determines YES), it proceeds to step S 5 . On the other hand, when the processor  13  determines that the temperature T is smaller than the first threshold value T th1  (i.e., determines NO), it proceeds to step S 4 . 
     In step S 4 , the processor  13  controls the moving device  22  such that the shift amount δ of the center axis A 2  from the optical axis A 1  is equal to the initial shift amount δ 0 . Due to this, the center axis A 2  is maintained to be shifted from the optical axis A 1  toward the product region E 1  by the initial shift amount δ 0 . 
     In step S 5 , the processor  13  outputs a first alarm. For example, the processor  13  generates an audio or image signal indicative of “There is possibility that cutting quality requirement (dross dimension) of product region is not satisfied”, and outputs it through a speaker or display (not illustrated) provided at the control device  12 . 
     In step S 6 , the processor  13  determines whether or not the temperature T most-recently acquired from the temperature sensor  92  is equal to or greater than a second threshold value T th2  (&gt;T th1 ). As an example, if the temperature T 1  is acquired from the temperature sensor  92 , the processor  13  determines whether the most-recently acquired temperature T 1  is equal to or greater than a second threshold value T th2_1  (i.e., T 1 ≥T th2_1 ). The second threshold value T th2_1  is predetermined for the temperature T 1  as a value greater than the first threshold value T th1_1  (i.e., T th2_1 &gt;T th1_1 ), and is stored in the storage  15 . 
     As another example, if the temperatures T 1  and T 2  are acquired from the temperature sensor  92 , the processor  13  determines whether the most-recently calculated temperature difference T Δ  (=T 1 −T 2 ) is equal to or greater than a second threshold value T th2_2  (T Δ ≥T th2_2 ). The second threshold value T th2_2  is predetermined for the temperature difference T Δ  as a value greater than the first threshold value T th1_2  (i.e., T th2_2 &gt;T th1_2 ), and is stored in the storage  15 . 
     Alternatively, the processor  13  determines whether the most-recently calculated temperature ratio R T  is equal to or greater than a second threshold value T th2_3  (R T ≥T th2_3 ). The second threshold value T th2_3  is predetermined for the temperature ratio R T  as a value greater than the first threshold value T th1_3  (i.e., T th2_3 &gt;T th1_3 ), and is stored in the storage  15 . 
     When the processor  13  determines that the temperature T (T 1 , T Δ , or R T ) is equal to or greater than the second threshold value T th2  (T th2_1 , T th2_2 , or T th2_3 ) (i.e., determines YES), it proceeds to step S 8 . On the other hand, when the processor  13  determines that the temperature T is smaller than the second threshold value T th2  (i.e., determines NO), it proceeds to step S 4 . 
     In step S 7 , the processor  13  controls the moving device  22  such that the shift amount δ of the center axis A 2  from the optical axis A 1  is equal to a first shift amount δ 1 . The first shift amount δ 1  is predetermined as a value greater than the initial shift amount δ 0  (i.e., δ 1 &gt;δ 0 ). Due to this, the center axis A 2  is maintained to be shifted from the optical axis A 1  toward the product region E 1  by the first shift amount δ 1 . 
     In step S 8 , the processor  13  determines whether or not the temperature T most-recently acquired from the temperature sensor  92  is equal to or greater than a third threshold value T th3  (&gt;T th2 ). As an example, if the temperature T 1  is acquired from the temperature sensor  92 , the processor  13  determines whether the most-recently acquired temperature T 1  is equal to or greater than a third threshold value T th3_1  (i.e., T 1 ≥T th3_1 ). The third threshold value T th3_1  is predetermined for the temperature T 1  as a value greater than the second threshold value T th2_1  (i.e. T th3_1 &gt;T th2_1 ) and is stored in the storage  15 . 
     As another example, if the temperatures T 1  and T 2  are acquired from the temperature sensor  92 , the processor  13  determines whether the most-recently calculated temperature difference T Δ  (=T 1 −T 2 ) is equal to or greater than a third threshold value T th3_2  (i.e., T Δ ≥T th3_2 ). The third threshold value T th3_2  is predetermined for the temperature difference T Δ  as a value greater than the second threshold value T th2_2  (i.e., T th3_2 &gt;T th2_2  and is stored in the storage  15 . 
     Alternatively, the processor  13  determines whether the most-recently calculated temperature ratio R T  is equal to or greater than a third threshold value T th3_3  (i.e., R T ≥T th3_3 ). The third threshold value T th3_3  is predetermined for the temperature ratio R T  as a value greater than the second threshold value T th2_3  (i.e., T th3_3 &gt;T th3_3 ), and is stored in the storage  15 . 
     When the processor  13  determines that the temperature T (T 1 , T Δ , or R T ) is equal to or greater than the third threshold value T th3  (T th3_1 , T th3_2 , or T th3_3 ) (i.e., determines YES), it proceeds to step S 10 . On the other hand, when the processor  13  determines that the temperature T is smaller than the third threshold value T th3  (i.e., determines NO), it proceeds to step S 9 . 
     In step S 9 , the processor  13  controls the moving device  22  such that the shift amount δ of the center axis A 2  from the optical axis A 1  is equal to a second shift amount δ 2 . The second shift amount δ 2  is predetermined as a value greater than the first shift amount δ 1  (i.e., δ 2 &gt;δ 1 ). Due to this, the center axis A 2  is maintained to be shifted from the optical axis A 1  toward the product region E 1  by the second shift amount δ 2 . 
     On the other hand, when it is determined YES in step S 8 , in step S 10 , the processor  13  controls the moving device  22  such that the shift amount δ of the center axis A 2  from the optical axis A 1  is equal to a third shift amount δ 3 . The third shift amount δ 3  is predetermined as a value greater than the second shift amount δ 2  (i.e., δ 3 &gt;δ 2 ). 
     Due to this, the center axis A 2  is maintained to be shifted from the optical axis A 1  toward the product region E 1  by the third shift amount δ 3 . The first shift amount δ 1 , the second shift amount δ 2 , and the third shift amount δ 3  described above may be obtained as parameters correlated with the temperature T and cutting quality (dross dimension), using e.g. an experimental or simulation technique. 
     An additional data table, in which the first shift amount δ 3 , second shift amount δ 2  and third shift amount δ 3 ; and the temperature T (T 1 , T Δ , R T ) are stored in association with each other, may be created to be separate from the data table  70  (or to be incorporated in the data table  70 ), and the processor  13  may refer to the additional data table to determine the shift amount δ in response to the detected temperature T. 
     In step S 11 , the processor  13  determines whether the laser machining is completed. For example, the processor  13  determines whether the laser beam L reaches the point P 2  which is an end point of the cutting line l 7 , from a command included in the machining program  94  or from the feedback of the servomotors of the moving mechanism  20 . The processor  13  determines YES when the laser beam L reaches the point P 2  of the cutting line l 7 , and ends the flow illustrated in  FIG. 21 . On the other hand, the processor  13  determines NO when the laser beam L does not reach the point P 2  of the cutting line l 7 , and returns to step S 3 . 
     As discussed above, in the present embodiment, the processor  13  changes the positional relationship between the center axis A 2  and the optical axis A 1  in response to the temperature T (T 1 , T Δ , R T ) correlated with the cutting quality (dross dimension) of the product region E 1 , during cutting along the cutting lines l 2 , l 3 , l 4 , l 5 , l 6  and l 7  between the product region E 1  and the waste region E 2 . 
     More specifically, the processor  13  changes the shift amount δ in response to the magnitude of the temperature T, so as to be the initial shift amount δ 0  if T&lt;T th1  is satisfied, to be the first shift amount δ 0  if T th1 ≤T&lt;T th2  is satisfied, to be the second shift amount δ 2  if T th2 ≤T&lt;T th3  is satisfied, and to be the third shift amount δ 3  if T th3 ≤T is satisfied. 
     According to this configuration, the shift amount δ of the center axis A 2  toward the product region E 1  can be greater as the probability that the dimension of the dross generated on the product region E 1  gets large is greater (i.e., the temperature T is higher), whereby it is possible to increase the rate of the assist gas B blown onto the product region E 1 . As a result, the dimension of the dross generated on the product region E 1  can be reduced by controlling the shift amount δ. 
     Further, since the above-described temperature difference T Δ  and temperature ratio R T  relatively indicate the temperature on the front surface of the product region E 1  as comparison with the temperature on the front surface of the waste region E 2 , even when the temperature of the product region E 1  gets significantly high by the laser beam L, the influence of the temperature rise by the laser beam L can be eliminated, and the dimension of the dross formed at the product region E 1  can be precisely and quantitatively evaluated by the temperature difference T Δ  and the temperature ratio R T . 
     In the present embodiment, the processor  13  maintains the state in which the center axis A 2  is shifted from the optical axis A 1  toward the product region E 1  during laser machining. However, the processor  13  may maintain a state in which the center axis A 2  is shifted from the optical axis A 1  toward the waste region E 2  during laser machining. Depending on the machining condition (e.g., supply pressure SP), the flow speed of the assist gas in the kerf K may increase to reduce the dross dimension when the center axis A 2  is shifted toward the waste region E 2 . 
     Next, a laser machine  100  according to still another embodiment will be described with reference to  FIG. 22  and  FIG. 23 . The laser machine  100  differs from the above-described laser machine  10  in that the laser machine  100  further includes a dimension measuring instrument  102 . The dimension measuring instrument  102  includes e.g. an optical displacement meter, a camera, or a vision sensor, and measures the width w of the kerf K formed between the product region E 1  and the waste region E 2  during cutting the workpiece W by the laser beam L. 
     The control device  12  changes the positional relationship between the center axis A 2  of the assist gas and the optical axis A 1  of the laser beam L in response to the kerf-width w measured by the dimension measuring instrument  102 , during cutting between the product region E 1  and the waste region E 2  along the cutting line l. In this regard, if the kerf-width w is small, even when the shift amount δ of the center axis A 2  from the optical axis A 1  is reduced, it is possible to satisfy the cutting quality requirement (dross dimension, cut surface roughness, etc.) of the product region E 1 . 
     Accordingly, in the present embodiment, the control device  12  changes the shift amount δ of the center axis A 2  from the optical axis A 1  in response to the kerf-width w measured by the dimension measuring instrument  102 , during cutting between the product region E 1  and the waste region E 2  along the cutting line l. Below, an operation flow of the laser machine  100  will be described with reference to  FIG. 24 . Note that, in  FIG. 24 , processes similar as those in the flow illustrated in  FIG. 21  is assigned the same step numbers, and redundant descriptions thereof will be omitted. 
     The processor  13  of the control device  12  carries out the flow illustrated in  FIG. 24  in accordance with a machining program  104  stored in the storage  15 . Accordingly, various commands for carrying out the flow illustrated in  FIG. 24  are defined in the machining program  104 . The flow illustrated in  FIG. 24  is started when the processor  13  receives a laser-machining-start command from an operator, a host controller, or the machining program  104 . 
     In step S 1 , the processor  13  starts laser machining, and shifts the center axis A 2  of the assist gas B from the optical axis A 1  of the laser beam L toward the product region E 1  (or the waste region E 2 ) by the initial shift amount δ 0  when the laser beam L reaches the point P 2  which is the starting point of the cutting line l 2 . 
     In step S 21 , the processor  13  starts measurement of the kerf-width w by the dimension measuring instrument  102 . Specifically, the processor  13  consecutively (e.g., periodically) acquires from the dimension measuring instrument  102  the kerf-width w measured by the dimension measuring instrument  102  during cutting the workpiece W. 
     In step S 22 , the processor  13  determines whether or not the kerf-width w most-recently acquired from the dimension measuring instrument  102  is equal to or greater than a first threshold value w th1 . The first threshold value w th1  is predetermined for the kerf-width w, and is stored in the storage  15 . When the processor  13  determines that the kerf-width w is equal to or greater than the first threshold value w th1  (i.e., determines YES), it proceeds to step S 23 . On the other hand, when the processor  13  determines that the kerf-width w is smaller than the first threshold value w th1  (i.e., determines NO), it proceeds to step S 4 . 
     In step S 23 , the processor  13  determines whether or not the kerf-width w most-recently acquired from the dimension measuring instrument  102  is equal to or greater than a second threshold value w th2 . The second threshold value w th2  is predetermined for the kerf-width w as a value greater than the first threshold value w th1  (i.e., w th2 &gt;w th1 ), and is stored in the storage  15 . When the processor  13  determines that the kerf-width w is equal to or greater than the second threshold value w th2  (i.e., determines YES), it proceeds to step S 25 . On the other hand, when the processor  13  determines that the kerf-width w is smaller than the second threshold value w th2  (i.e., determines NO), it proceeds to step S 24 . 
     In step S 24 , the processor  13  controls the moving device  22  such that the shift amount δ of the center axis A 2  from the optical axis A 1  is equal to a first shift amount δ 4 . The first shift amount δ 4  is predetermined as a value greater than the initial shift amount δ 0  (i.e. δ 4 &gt;δ 0 ). Due to this, the center axis A 2  is maintained to be shifted from the optical axis A 1  toward the product region E 1  (or the waste region E 1 ) by the first shift amount δ 4 . 
     In step S 25 , the processor  13  determines whether or not the kerf-width w most-recently acquired from the dimension measuring instrument  102  is equal to or greater than a third threshold value w th3 . The third threshold value w th3  is predetermined for the kerf-width w as a value greater than the second threshold value w th2  (i.e., w th3 &gt;w th2 ), and is stored in the storage  15 . When the processor  13  determines that the kerf-width w is equal to or greater than the third threshold value w th3  (i.e., determines YES), it proceeds to step S 27 . On the other hand, when the processor  13  determines that the kerf-width w is smaller than the third threshold value w th3  (i.e., determines NO), it proceeds to step S 26 . 
     In step S 26 , the processor  13  controls the moving device  22  such that the shift amount δ of the center axis A 2  from the optical axis A 1  is equal to a second shift amount δ 5 . The second shift amount δ 5  is predetermined as a value greater than the first shift amount δ 4  (i.e., δ 5 &gt;δ 4 ). Due to this, the center axis A 2  is maintained to be shifted from the optical axis A 1  toward the product region E 1  (or the waste region E 1 ) by the second shift amount δ 5 . 
     When it is determined YES in step S 25 , in step S 27 , the processor  13  controls the moving device  22  such that the shift amount δ of the center axis A 2  from the optical axis A 1  is equal to a third shift amount δ 6 . The third shift amount δ 6  is predetermined as a value greater than the second shift amount δ 5  (i.e., δ 6 &gt;δ 5 ). 
     Due to this, the center axis A 2  is maintained to be shifted from the optical axis A 1  toward the product region E 1  (or the waste region E 1 ) by the third shift amount δ 6 . The first shift amount δ 4 , the second shift amount δ 5 , and the third shift amount δ 6  described above may be obtained as parameters correlated with the kerf-width w and the cutting quality (dross dimension, cut surface roughness, etc.), by e.g. an experimental or simulation technique. 
     Further, an additional data table, in which the first shift amount δ 4 , second shift amount δ 5  and third shift amount δ 6 ; and the kerf-width w are stored in association with each other, may be created to be separate from the data table  70  (or to be incorporated in the data table  70 ), and the processor  13  may refer to the additional data table to determine the shift amount δ in response to the measured kerf-width w. 
     As discussed above, in the present embodiment, the processor  13  changes the positional relationship between the center axis A 2  and the optical axis A 1  in response to the kerf-width w during cutting along the cutting lines l 2 , l 3 , l 4 , l 5 , l 6  and l 7  between the product region E 1  and the waste region E 2 . More specifically, the processor  13  changes the shift amount δ in response to the magnitude of the kerf-width w, so as to be the initial shift amount δ 0  if w&lt;w th1  is satisfied, to be the first shift amount δ 4  if w th1 ≤w&lt;w th2  is satisfied, to be the second shift amount δ 5  if w th2 ≤w&lt;w th3  is satisfied, and to be the third shift amount δ 6  if w th3 &lt;w is satisfied. 
     As the kerf-width w gets larger, it may be necessary to increase the shift amount δ of the center axis A 2  in order to increase the rate of the assist gas B blown onto the cutting spot of the product region E 1 . According to the present embodiment, the positional relationship between the center axis A 2  and the optical axis A 1  is changed in response to the kerf-width w, whereby it is possible to finely adjust the rate of the assist gas B blown onto the product region E 1 . As a result, the cutting quality requirement (dross dimension) of the product region E 1  can be more effectively satisfied. 
     In the above laser machines  80 ,  90 , and  100 , the processor  13  determines the shift amount δ, by which the center axis A 2  is shifted from the optical axis A 1 , in response to the machining speed v, the temperature T, and the kerf-width w. However, the processor  13  may determine the shift amount δ in response to a requirement to be achieved in the cutting process of the workpiece W. 
     As an example, the operator selects a high-speed cutting, a high-precision cutting, or a gas-saving cutting, as the requirement to be achieved. If the requirement of the high-speed cutting is selected, the processor  13  performs laser machining in a high-speed mode in which the machining speed v is controlled to be faster than that in the normal machining condition defined in the data table  70 . For example, the processor  13  sets the shift amount δ to be smaller than the normal shift amount defined in the data table  70  when performing the laser machining in the high-speed mode. 
     If the requirement of the high-precision cutting is selected, the processor  13  sets the machining speed v to be slower than that in the normal machining condition defined in the data table  70 , and performs the laser machining in a high-precision mode in which the processor  13  controls the moving mechanism  20  precisely such that the laser beam L accurately passes on the cutting line l. For example, the processor  13  sets the shift amount δ to be larger than the normal shift amount defined in the data table  70  when performing the laser machining in the high-precision mode. 
     If the requirement of the gas-saving cutting is selected, the processor  13  performs the laser machining in a gas-saving mode in which the supply pressure SP is set to be lower than that in the normal machining condition defined in the data table  70 . For example, the processor  13  sets the shift amount δ to be larger than the normal shift amount defined in the data table  70  when performing the laser machining in the gas-saving mode. In this manner, by determining the shift amount δ in response to the requirement to be achieved in the cutting process of the workpiece W, it is possible to effectively satisfy the cutting quality requirement of the product region E 1 , as well as the above-mentioned requirement to be achieved. 
     Next, a laser machine  110  according to still another embodiment will be described with reference to  FIG. 25  and  FIG. 26 . The laser machine  110  differs from the above-described laser machine  10  in that the laser machine  110  further includes a position detector  112 . The position detector  112  checks the positional relationship between the optical axis A 1  of the laser beam L and the center axis A 2  of the assist gas B emitted through the nozzle  30 , before or during laser machining. 
     As an example, the position detector  112  includes e.g. a camera, a vision sensor, or a beam profiler (e.g., of a knife-edge type), and is disposed on the optical axis A 1  of the laser beam L. In this case, the position detector  112  directly detects the laser beam L emitted through the nozzle  30 , and also detects the center point of the emission port  34  of the nozzle  30 . The position detector  112  can detect the positional relationship between the optical axis A 1  and the center axis A 2  (e.g., coordinates of the x-y plane) based on the detected data of the laser beam L and the exit port center point. 
     For example, the position detector  112  detects the positional relationship between the optical axis A 1  and the central axis A 2  when the moving device  22  shifts the state of the optical axis A 1  and the center axis A 2  from the coaxial arrangement to the non-coaxial arrangement, in response to a predetermined command value from the control device  12 , prior to laser machining. Using the data of the thus-detected positional relationship, an operator can calibrate correlation between the command value from the control device  12  and the shift amount δ. As a result, the processor  13  can operate the moving device  22  so as to precisely shift the center axis A 2  from the optical axis A 1  in the target direction by the target shift amount δ, during the laser machining. 
     As another example, if the moving device  22  includes the servomotor, the position detector  112  includes an encoder configured to detect the rotation angle of the servomotor of the moving device  22 . The rotation angle of the servomotor is information indicating the positional relationship between the optical axis A 1  and the center axis A 2  (coordinates of the x-y plane). The processor  13  of the control device  12  may acquire the rotation angle from the position detector  112 , and check the positional relationship between the optical axis A 1  and the center axis A 2  from the acquired rotation angle. In this example, the position detector  112  can detect the positional relationship between the optical axis A 1  and the center axis A 2  during the laser machining. 
     For example, if the position detector  112  including the encoder is applied to the above-described laser machine  80 ,  90 , or  110 , the processor  13  may check the position of the center axis A 2  relative to the optical axis A 1  based on the rotation angle acquired from the position detector  112 , when changing the positional relationship between the center axis A 2  and the optical axis A 1  in response to the machining speed v, the temperature T, or the kerf-width w. Thus, during the laser machining, the processor  13  can accurately control the shift amount δ of the center axis A 2  in response to the machining speed v, the temperature T, or the kerf-width w, along with checking the position of the center axis A 2  relative to the optical axis A 1 . 
     Next, a machine learning apparatus  120  according to an embodiment will be described with reference to  FIG. 27 . The machine learning apparatus  120  is for learning the shift amount δ when the laser beam L and the assist gas B emitted through the nozzle  30  are shifted from a coaxial state to a non-coaxial state. The machine learning apparatus  120  may be constituted of a computer including a processor and a storage, or software such as a learning algorithm. For example, the machine learning apparatus  120  may be used to create the data table  70  described above. 
     In order to learn the shift amount δ, in the present embodiment, the laser machine  10  repeatedly performs trial laser machining to cut a trial workpiece W T  in accordance with a trial machining program  121 . An example of the trial work W T  is illustrated in  FIG. 28 . The workpiece W T  is a rectangular flat plate member. In the trial machining program  121 , a plurality of cutting lines l T1 , l T2 , l T3 , and l T4  are specified on the workpiece W T . In the trial laser machining, the laser machine  10  sequentially cuts the workpiece W T  forward from a rear end to a front end along the cutting lines l T1 , l T2 , l T3 , and l T4  in accordance with the trial machining program  121 , under optionally set machining conditions (a material and a thickness t of the workpiece W, a machining speed v, a nozzle diameter ϕ, a supply pressure SP, a focus position z, and an output characteristic value OP of the laser beam L). 
     During the cutting of the cutting lines l T1 , l T2 , l T3  and l T4 , the laser machine  10  emits the laser beam L and the assist gas B through the nozzle  30 , and maintains the center axis A 2  of the assist gas B to be shifted from the optical axis A 1  of the laser beam L in an optional direction by an optional shift amount δ. The laser machine  10  randomly changes the shift amount δ and the shift direction of the center axis A 2  every time one cutting line l T1 , l T2 , l T3  or l T4  is cut. The trial laser machining as discussed above is repeatedly performed on a plurality of workpieces W T . 
     After cutting the workpiece W T  along one cutting line l T1 , l T2 , l T3  or l T4 , a measuring section  125  measures the dimension of the dross generated at a cutting spot of the workpiece W T .  FIG. 29  illustrates an example of the dross generated on a rear surface of the workpiece W T , as a result of the trial laser machining. In the example illustrated in  FIG. 29 , as a result of the trial laser machining, the kerf K is formed at the cutting spot of the workpiece W T , wherein the dross D 1  is generated on the left side of the kerf K, while the dross D 2  is generated on the right side of the kerf K. 
     A dimension F 1  of the dross D 1  includes e.g. a height H 1  of the dross D 1  in the z-axis direction, or an area (maximum occupancy area) G 1  in the x-y plane of the dross D 1 . Similarly, a dimension F 2  of the dross D 2  includes e.g. a height H 2  of the dross D 2  in the z-axis direction, or an area (maximum occupancy area) G 2  in the x-y plane of the dross D 2 . The measuring section  125  includes e.g. a dimension measurement gauge, a camera, or a vision sensor, and measures the dimensions F 1  and F 2  of the dross D 1  and D 2 , respectively. 
     As illustrated in  FIG. 27 , the machine learning apparatus  120  includes a state-observation section  122  and a learning section  124 . The state-observation section  122  observes machining condition data included in the machining program  121  given to the laser machine  10  for performing the trial laser machining, and measurement data of the dimension F 1 , F 2  of the dross D 1 , D 2  generated when the machining program  121  is executed, as a state variable SV representing the current state of the environment in which the workpiece W T  is cut. 
     The measurement data includes the individual dimensions F 1  and F 2  of the dross D 1  and D 2  on both sides of the cutting spot (or the kerf K) of the workpiece W T , or a dimension difference ΔF (=|F 2 −F 1 |) between the dross D 1  and D 2 . The machining condition data includes e.g. at least one of the material and thickness t of the workpiece W T , the machining speed v, the nozzle diameter ϕ, the supply pressure SP, the focus position z, and the output characteristic value OP of the laser beam L. The learning section  124  learns the shift amount δ in association with the cutting quality of the workpiece W T , using the state variables SV (i.e., the machining condition data, and the measurement data F 1 , F 2 , ΔF). In the present embodiment, the cutting quality is the dross dimension. 
     The learning section  124  learns the shift amount δ of the center axis A 2  from the optical axis A 1  in accordance with any learning algorithm generally referred to as machine learning. The learning section  124  is able to iteratively perform learning based on a data set including the state variables SV obtained by repeatedly performing the trial laser machining. 
     By repeating such a learning cycle, the learning section  124  is able to automatically identify a feature implying a correlation between the cutting quality (dross dimension=measurement data F 1 , F 2 , ΔF) and the shift amount δ. At the beginning of the learning algorithm, the correlation between the shift amount δ and the measurement data F 1 , F 2 , ΔF is substantially unknown, however, as the learning is advanced, the learning section  124  gradually identifies the feature and consequently interprets the correlation. 
     When the correlation between the shift amount δ and the measurement data F 1 , F 2 , ΔF is interpreted to a level reliable to some extent, learning results iteratively outputted by the learning section  124  can be used to select an action (i.e., decision-making) of how much the center axis A 2  should be shifted to meet the cutting quality requirement when the workpiece W T  of the current state is cut. 
     That is, as the learning algorithm is advanced, the learning section  124  is able to make the shift amount δ to gradually approach an optimal solution, wherein the shift amount δ represents the correlation between the current state of the workpiece W T  and the action of how much the center axis A 2  should be shifted to meet the cutting quality requirement when the workpiece W T  of the current state is cut. The cutting quality requirement in this case is that any one of the dimensions F 1  and F 2  becomes zero (or a value close to zero), for example. 
     As described above, in the machine learning apparatus  120 , the learning section  124  learns the shift amount δ of the center axis A 2  from the optical axis A 1  in accordance with the machine learning algorithm, using the state variables SV (the machining condition data, and the dimensions F 1  and F 2 ) observed by the state-observation section  122 . According to the machine learning apparatus  120 , by using the learning result of the learning section  124 , it is possible to automatically and accurately obtain the shift amount δ. 
     When the shift amount δ can be automatically obtained, it is possible to quickly determine the shift amount δ necessary for satisfying the cutting quality requirement from the machining condition data. Accordingly, the work for determining the shift amount δ under various machining conditions can be significantly simplified. In addition, since the shift amount δ is learned based on a vast data set, the optimal shift amount δ for satisfying the cutting quality requirement (dross dimension) can be acquired with high precision. 
     In the machine learning apparatus  120 , the learning algorithm executed by the learning section  124  is not limited, and any learning algorithm known as machine learning, such as supervised learning, unsupervised learning, reinforcement learning, or a neural network, may be employed. 
       FIG. 30  shows an embodiment of the machine learning apparatus  120  illustrated in  FIG. 1 , and illustrates a configuration including a learning section  124  configured to perform reinforcement learning as an example of the learning algorithm. The reinforcement learning is a technique to iterative, in a trial and error manner, a cycle in which the current state (i.e., input) of an environment where a learning object is present is observed and a predetermined action (i.e., output) is carried out in the current state, and a certain reward for this action is given, and whereby learning a scheme (in the present embodiment, shift amount δ) that maximizes the total sum of the rewards, as an optimal solution. 
     In the machine learning apparatus  120  illustrated  FIG. 30 , the learning section  124  includes a reward calculator  126  configured to obtain a reward R associated with the dimensions F 1 , F 2 , ΔF of the dross D 1 , D 2 , and a function-update section  128  configured to update a function EQ representing a value of the shift amount δ using the reward R. The learning section  124  learns the shift amount δ by the function-update section  128  repeating the update of the function EQ. 
     An example of the reinforcement learning algorithm executed by the learning section  124  will be described below. The algorithm according to this example is known as Q-learning, which is a technique in which a state “s” of an action subject and an action “a” selectable by the action subject in the state s are taken as independent variables, and a function EQ (s, a) representing an action value is learned when the action a is selected in the state s. 
     To select the action a that makes the value function EQ highest in the state s brings an optimal solution. Q-learning is started in a state where the correlation between the state s and the action a is unknown, trials and errors to select various actions in arbitrary state s are repeated, whereby the value function EQ is iteratively updated to approach an optimal solution. When an environment (i.e., state s) changes as a result of selecting the action a in the state s, a reward r (i.e., weighting of the action a) in response to the environment change is obtained, and the value function EQ can be approach the optimal solution in a relatively short time by guiding the learning to select the action a to obtain a higher reward r. 
     An update formula for the value function EQ can be generally expressed as Formula (1) given below. 
     
       
         
           
             
               
                 
                   
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     In Formula (1), s t  and a t  are a state and an action at time t, respectively, and the state is changed to s t+1  by action a t . Here, r t+1  is a reward obtained by changing the state from st to s t+1 . The term of max Q means Q when the action a is taken to obtain (or to be considered to obtain at time t) a maximum value Q at time t+1. Further, α and γ are a learning coefficient and a discount rate, respectively, and are optionally set as 0&lt;α≤1 and 0&lt;γ≤1. 
     When the learning section  124  performs Q learning, the state variable SV observed by the state-observation section  122  corresponds to the state s of the update formula, and the action (i.e., shift amount δ) of how much the center axis A 2  should be shifted from the optical axis A 1  when cutting the workpiece W T  in the current state corresponds to the action a of the update formula. The reward R obtained by the reward calculator  126  corresponds to the reward r of the update formula. Therefore, the function-update section  128  repeatedly updates the function EQ representing the value of the shift amount δ when cutting the workpiece W T  in the current state, by Q learning using the reward R. 
     As an example, the reward calculator  126  obtains different rewards R depending on the dimension difference ΔF (=|F 2 −F 1 |) between the dross D 1  and D 2  on both sides of the cutting spot (or kerf K) of the workpiece W T . For example, the reward R obtained by the reward calculator  126  is a positive (plus) reward R when the dimension difference ΔF occurs between the dimension F 1  of the dross D 1  and the dimension F 2  of the dross D 2 , while it is a negative (minus) reward R when the dimension difference ΔF does not occur. The absolute values of the positive and negative rewards R may be the same or may be different from each other. 
     The reward calculator  126  may give the reward R whose absolute value becomes larger as the dimension difference ΔF is larger. For example, the reward R=+1 may be given in a case of 0&lt;ΔF≤ΔF th1 , the reward R=+2 may be given in a case of ΔF th1 &lt;ΔF≤Δ Fth2 , and the reward R=+5 may be given in a case of ΔF th2 &lt;ΔF. By obtaining the reward R weighted by the conditions in this manner, Q-learning can be convergent to the optimal solution in a relatively short time. 
     As another example, the reward calculator  126  obtains different rewards R depending on individual dimensions F 1  and F 2  of the dross D 1  and D 2  on both sides of the cutting spot (or kerf K) of the workpiece W T . For example, the reward R obtained by the reward calculator  126  is a positive reward R when one of the dimensions F 1  and F 2  is smaller than the threshold value F th1 , while the other one of the dimensions F 1  and F 2  is greater than the threshold value F th2 . The threshold values F th1  and F th2  may be defined as the same value (F th1 =F th2 ) or different values from each other (e.g., F th1 &lt;F th2 ). 
     On the other hand, the reward R obtained by the reward calculator  126  is a negative reward R when the dimensions F 1  and F 2  are substantially the same. Alternatively, in a case where the threshold value F th1  is smaller than threshold value F th2 , the reward R obtained by the reward calculator  126  is a negative reward R when the dimensions F 1  and F 2  satisfy F th1 &lt;F 1 &lt;F th2  and F th1 &lt;F 2 &lt;F th2 . 
     The reward calculator  126  may obtain different rewards R depending on a difference in machining condition data, in addition to the dimensions F 1  and F 2 , or the dimension difference ΔF. For example, the reward calculator  126  gives a positive reward R when the dimension difference ΔF occurs and the supply pressure SP in the machining condition data is smaller than a reference value SP R . The reference value SP R  may be predetermined by the operator from the past heuristics, for example. 
     The function-update section  128  may have an action value table in which the state variables SV and the reward R are compiled in association with an action value (e.g., a numeric value) represented by the function EQ. In this case, the act of the function-update section  128  to update the function EQ is synonymous with the act of the function-update section  128  to update the action value table. 
     Since the correlation between the current state of the environment and the shift amount δ is unknown at the beginning of Q learning, various state variables SV and rewards R are prepared in the action value table in association with randomly defined the action values (function EQ). When acquiring the dimensions F 1  and F 2 , or the dimension difference ΔF, the reward calculator  126  can immediately calculate the reward R corresponding to the acquired information, and then the calculated value of the reward R is written into the action value table. 
     As Q learning is advanced using the reward R corresponding to the dross dimension (F 1 , F 2 , ΔF), the learning is guided to select an action (i.e., shift amount δ) able to obtain a higher reward R. Then, in response to the state of the environment (i.e., state variables SV) caused to change as a result of carrying out the selected action in the current state, the action value (function EQ) regarding the action carried out in the current state is rewritten and the action value table is updated. 
     By repeating this update, the action value (function EQ) represented in the action value table is rewritten to be larger as the action (shift amount δ) is more appropriate. In this manner, the correlation between the current state of the environment (dross dimension of F 1 , F 2 , Δf) and the corresponding action (shift amount δ), which was unknown at first, becomes gradually apparent. 
     Next, an example of a flow of Q learning performed by the learning section  124  will be further described with reference to  FIG. 31 . In this flow, the learning section  124  performs Q learning using the reward R in response to the dimension difference ΔF and the machining condition data. In step S 31 , the function-update section  128  randomly selects the shift amount δ as an action to be carried out in the current state indicated by the state variables SV having been observed by the state-observation section  122 , with reference to the action value table at this time. 
     In step S 32 , the function-update section  128  acquires the dimension difference ΔF as the state variable SV in the current state observed by the state-observation section  122 . Specifically, the laser machine  10  performs trial laser machining in accordance with the shift amount δ selected in step S 1  under optional machining conditions. The state-observation section  122  observes, as the state variables SV, the machining condition data when the trial laser machining is performed, and the dimension difference ΔF obtained as a result of the trial laser machining. The function-update section  128  acquires the state variables SV observed by the state-observation section  122 . 
     In step S 33 , the function-update section  128  determines whether or not the dimensional difference ΔF acquired in step S 32  is greater than zero. When the dimension difference ΔF is greater than zero, the function-update section  128  determines YES, and proceeds to step S 34 . On the other hand, when the dimension difference ΔF is zero, the function-update section  128  determines NO, and proceeds to step S 35 . Note that the function-update section  128  may determine YES if the dimension difference ΔF is greater than a threshold value ΔF th0  (&gt;0) predetermined as a value close to zero. 
     In step S 34 , the reward calculator  126  obtains a positive reward R. At this time, the reward calculator  126  may obtain the reward R such that the larger the dimension difference ΔF is, the larger the absolute value of the reward R is, as described above. The reward calculator  126  applies the obtained positive reward R to the update formula of the function EQ. By giving the reward R in response to the dimension difference ΔF in this manner, the learning by the learning section  124  is guided to select an action in which the dimension difference ΔF increases (in other words, one of the dimensions F 1  and F 2  becomes smaller than the other). 
     On the other hand, when it is determined NO in step S 33 , in step S 35 , the reward calculator  126  obtains a negative reward R, and applies it to the update formula of the function EQ. Note that, in this step S 35 , the reward calculator  126  may apply the reward R=0 to the update formula of the function EQ, instead of giving the negative reward R. 
     In step S 36 , the function-update section  128  determines whether there is a difference in the machining condition data obtained in step S 32 , for which a positive reward R it to be given. For example, the function-update section  128  determines whether or not the supply pressure SP in the machining condition data is smaller than the reference value SP R , and determines YES when the supply pressure SP is smaller than the reference value SP R . 
     Alternatively, the function-update section  128  may determine whether or not the machining speed v in the machining condition data is greater than a reference value v R , and may determine YES when the machining speed v is greater than the reference value v R . When the function-update section  128  determines YES, it proceeds to step S 37 . On the other hand, when the function-update section  128  determines NO, it proceeds to step S 38 . 
     In step S 37 , the reward calculator  126  obtains a positive reward R. The reward R that is to be obtained at this time may be predetermined by the operator as a value corresponding to the machining condition data, the difference of which has been determined in above step S 36 . For example, if the difference in the supply pressure SP as the machining condition data is determined in step S 36 , the reward calculator  126  gives a positive reward R in response to the supply pressure SP. By giving the reward R in response to the supply pressure SP in this manner, the learning by the learning section  124  is guided to select an action to reduce the supply pressure SP (i.e., the consumption of the assist gas). 
     On the other hand, if the difference in the machining speed v as the machining condition data is determined in step S 36 , the reward calculator  126  gives a positive reward R in response to the machining speed v. By giving the reward R in response to the machining speed v in this manner, the learning by the learning section  124  is guided to select an action to increase the machining speed v (i.e., to reduce a cycle time). The reward calculator  126  applies the obtained positive reward R to the update formula of the function EQ. 
     In step S 38 , the function-update section  128  updates the action value table, using the state variables SV in the current state, the reward R, and the action value (the function EQ after being updated). In this manner, the learning section  124  iteratively updates the action value table by repeating steps S 31  to S 38 , so as to advance the learning of the shift amount δ. 
     When advancing the above-described reinforcement learning, a neural network may be used, instead of Q learning.  FIG. 32  schematically illustrates a neuron model.  FIG. 33  schematically illustrates a three-layer neural network model constituted by combining the neurons illustrated in  FIG. 32 . The neural network may be constituted by, for example, a processor, a storage device, and the like imitating a neuron model. 
     The neuron illustrated in  FIG. 32  outputs a result “o” with respect to a plurality of inputs “i” (inputs i 1  to i 3  as an example in the drawing). Each individual input i (i 1 , i 2 , or i 3 ) is multiplied by a weight w (w 1 , w 2 , or w 3 ). The relationship between the input i and the result o may be represented by Formula (2) given below. Any of the input i, result o, and weight w is a vector. In Formula (2), θ is a bias, and f k  is an activation function. 
         y=f   k (Σ i=1   n   x   i   w   i −θ)  (2)
 
     In the three-layer neural network illustrated in  FIG. 33 , a plurality of inputs i (inputs i 1  to i 3 , as an example in the drawing) are inputted from the left side, and a plurality of results o (results of to o 3 , as an example in the drawing) are outputted from the right side. In the illustrated example, each of the inputs i 1 , i 2 , and i 3  is multiplied by the corresponding weight (collectively represented as W 1 ), and any of the individual inputs i 1 , i 2 , and i 3  is inputted to three neurons N 11 , N 12 , and N 13 . 
     In  FIG. 33 , each output of the neurons N 11  to N 13  is collectively represented as H 1 . H 1  may be regarded as feature vectors achieved by extracting feature amounts of input vectors. In the illustrated example, each individual feature vector H 1  is multiplied by the corresponding weight (collectively represented as W 2 ), and any of the individual feature vectors H 1  is inputted to two neurons N 21  and N 22 . The feature vectors H 1  represent features between the weight W 1  and the weight W 2 . 
     In  FIG. 33 , each output of the neurons N 21  to N 22  is collectively represented as H 2 . H 2  may be regarded as feature vectors achieved by extracting feature amounts of the feature vectors H 1 . In the illustrated example, each individual feature vector H 2  is multiplied by the corresponding weight (collectively represented as W 3 ), and any of the individual feature vectors H 2  is inputted to three neurons N 31 , N 32 , and N 33 . The feature vectors H 2  represent features between the weight W 2  and the weight W 3 . Lastly, the neurons N 31  to N 33  output the results o 1  to o 3 , respectively. 
     In the machine learning apparatus  120 , it is possible to output the shift amount δ (result o) by the learning section  124  carrying out the arithmetic operation of the multi-layer structure according to the above-described neural network while taking the state variables SV as the input i. There are a learning mode and a value prediction mode in the operation mode of the neural network. For example, the weight W may be learned in the learning mode by using a learning data set, and a value judgment may be made in the value prediction mode by using the learned weight W. In the value prediction mode, detection, classification, reasoning, or the like may also be performed. 
     The above-mentioned configuration of the machine learning apparatus  120  may be described as a machine learning method (or software) executed by a processor of a computer. This machine learning method comprises, by the processor, observing the machining condition data included in the machining program  121  given to the laser machine  10 , and the measurement data of the dimensions F 1 , F 2 , ΔF of the dross D 1 , D 2  generated at the cutting spot (or kerf K) of the workpiece W T  when executing the machining program  121 , as the state variables SV representing the current state of the environment where the workpiece W T  is cut; and learning the shift amount δ in association with the cutting quality (dross dimension) of the workpiece W T  using the state variables SV. 
       FIG. 34  illustrates a machine learning apparatus  130  according to another embodiment. The machine learning apparatus  130  differs from the above-described machine learning apparatus  120  in that the machine learning apparatus  130  further includes a decision-making section  132 . The decision-making section  132  outputs a command value Cδ of the shift amount δ to be commanded to the laser machine  10 , based on the learning result by the learning section  124 . 
     When the decision-making section  132  outputs the shift amount δ, the state of an environment  134  (dross dimension F 1 , F 2 , ΔF) changes accordingly. A state-observation section  122  observes state variables SV, wherein the dross dimension F 1 , F 2 , ΔF generated when the machining program  121  is executed in accordance with the command value Cδ outputted by the decision-making section  132  is observed as the measurement data for the next learning cycle. 
     The learning section  124  learns the shift amount δ by updating e.g. the value function EQ (i.e., an action value table) using the changed state variables SV. The decision-making section  132  outputs the command value Cδ in response to the state variables SV, under the learned shift amount δ. By repeating this cycle, the machine learning apparatus  130  advances the learning of the shift amount δ, and gradually improves reliability of the shift amount δ. 
     The machine learning apparatus  130  can bring about an effect similar to the above-described machine learning device  120 . In particular, the machine learning apparatus  130  can change the state of the environment  134  by the output of the decision-making section  132 . On the other hand, in the machine learning apparatus  130 , a function corresponding to the decision-making section for reflecting the learning result of the learning section  124  in the environment may be achieved by an external device (e.g., the control device  12 ). 
     As a modification of the above-described machine learning apparatus  120  or  130 , the state-observation section  122  may further observe, as the state variable SV, measurement data of the kerf-width w on the rear surface of the workpiece W T . The kerf-width w in the rear surface may be measured by e.g. the dimension measuring instrument  102  described above. The learning section  124  may learn the shift amount δ, further using the kerf-width w as the state variable. 
     For example, in the machine learning apparatus  120  illustrated in  FIG. 30 , the reward calculator  126  may obtain a negative reward R when the kerf-width w is zero (or equal to or smaller than a threshold value close to zero). If the kerf-width w in the rear surface of the workpiece W T  is zero when performing the trial laser machining, the laser beam L does not penetrate the workpiece W T . In this case, the dross D 1  and D 2  are not formed actually. By making the reward R be negative in this case, it is possible to guide the learning by the learning section  124  to select an action for preventing the kerf-width w in the rear surface from being zero. 
     The above-described machine learning apparatus  120  or  130  may be installed in the laser machine  10 . With reference to  FIG. 35  and  FIG. 36 , a laser machine  10 ′, in which the machine learning apparatus  130  is installed, will be described below. The laser machine  10 ′ further includes the above-described measuring section  125 , and performs the trial laser machining on the trial workpiece W T  set on the work table  38 . 
     As illustrated in  FIG. 36 , the processor  13  functions as the machine learning apparatus  130  (i.e., the state-observation section  122 , learning section  124 , and decision-making section  132 ). The measuring section  125  measures the dimensions F 1  and F 2  of the dross D 1  and D 2 , and the control device  12  acquires the measurement data F 1 , F 2 , ΔF from the data transmitted from the measuring section  125 . 
     The processor  13  acquires machining condition data (the material and thickness t of the workpiece W T , the machining speed v, the nozzle diameter ϕ, the supply pressure SP, the focus position z, and the output characteristic value of the laser beam L) included in the machining program  121  for performing the trial laser machining. The machining condition data may be inputted by an operator via the input device (the keyboard, mouse, touch panel, etc. Not illustrated) provided at the control device  12 , for example. In this manner, the processor  13  functions as a state-data acquisition section  136  configured to acquire the machining condition data and measurement data. 
     According to the present embodiment, the control device  12  of the laser machine  10 ′ includes the machine learning apparatus  130 , which makes it possible to automatically and precisely obtain the shift amount δ optimal for the cutting quality (dross dimension) using the learning result of the learning section  124  when the trial laser machining is repeatedly performed. 
     Note that, in the machining program  72 ,  84 ,  94 , or  104 , an additional cutting line traversing the product region E 1  may be specified on the workpiece W. Such a modification of the workpiece W is illustrated in  FIG. 37 . In a workpiece W′ illustrated in  FIG. 37 , a cutting line l 8  extending linearly from a point P 8  to a point P 9  is further specified, in addition to cutting lines l 1  to l 7 . In this case, in the machining program  72 ,  84 ,  94 , or  104 , regions on both sides of the cutting line l 8  are both specified as the product region E 1 . 
     For example, the control device  12  of the laser machine  10 ,  80 ,  90 ,  100  or  110  cuts the workpiece W along the cutting line l 8  between the left side region (third region) and the right side region (fourth region) of the product region E 1 , after cutting the workpiece W along the cutting lines l 1  to l 7 . Since the cutting quality requirements do not differ between the regions on both sides of the cutting line l 8 , the processor  13  maintains a state in which the laser beam L and the assist gas B are coaxial during the cutting of the product region E 1  along the cutting line l 8 . 
     The flow illustrated in  FIG. 21  is described as an example of the operation of the laser machine  90  described above. However, another example of the operation flow of the laser machine  90  is also conceivable. Hereinafter, with reference to  FIG. 38 , another example of the operation flow of the laser machine  90  will be described. In the flow illustrated in  FIG. 38 , processes similar to those of the flow illustrated in  FIG. 21  are assigned the same step number, and redundant descriptions thereof will be omitted. 
     In the flow illustrated in  FIG. 38 , the processor  13  of the laser machine  90  increases the shift amount δ in stepwise manner so as to make the temperature T (T 1 , T Δ , or R T ) to fall within a range equal to or smaller than the first threshold value T th1  (T th1_1 , T th1_2 , or T th1_3 ). Specifically, after step S 7 , the processor  13  repeats a loop of steps S 3  and S 11  until it determines YES in step S 3  or S 11 , so as to maintain the shift amount δ to the first shift amount δ 1 . On the other hand, when it is determined YES in step S 3  carried out immediately after step S 7 , in step S 9 , the processor  13  increases the shift amount δ from the first shift amount δ 1  to the second shift amount δ 2 . 
     After step S 9 , the processor  13  repeats a loop of steps S 3  and S 11  until it determines YES in step S 3  or S 11 , so as to maintain the shift amount δ to the second shift amount δ 2 . On the other hand, when it is determined YES in step S 3  carried out immediately after step S 9 , in step S 10 , the processor  13  increases the shift amount δ from the second shift amount δ 2  to the third shift amount  63 . 
     After step S 10 , the processor  13  repeats a loop of steps S 3  and S 11  until it determines YES in step S 3  or S 11 , so as to maintain the shift amount δ to the third shift amount δ 3 . On the other hand, when the processor  13  determines YES in step S 3  carried out immediately after step S 10 , it proceeds to step S 41 . 
     In step S 41 , the processor  13  outputs a second alarm. For example, the processor  13  generates an audio or image signal indicative of “Although shift amount of center axis of assist gas is maximum, there is possibility that cutting quality requirement (dross dimension) of product region is not satisfied”, and outputs the generated signal through the speaker or display (not illustrated) provided at the control device  12 . Subsequently, the processor  13  continues the laser machining while maintaining the shift amount δ to the third shift amount δ 2  until it determines YES in step S 11 . 
     Thus, according to the flow illustrated in  FIG. 38 , the processor  13  increases the shift amount δ of the center axis A 2  toward the product region E 1  in a stepwise manner in response to the temperature T, so as to make the temperature T (T i , T Δ , or R T ) to fall within the range equal to or smaller than the first threshold value T th1  (T th1_1 , T th1_2 , or T th1_3 ). According to this configuration, it is possible to control the dimension of the dross generated in the product region E 1  so as to meet the cutting quality requirement. 
     Note that the width w of the kerf K described above correlates with the output characteristic value OP of the laser beam. Specifically, the larger the laser power of the laser beam L radiated onto the workpiece W is, the larger the width w of the kerf K generated may be. Accordingly, the processor  13  may control the shift amount δ in response to the output characteristic value OP of the laser beam. 
     For example, in the flow illustrated in  FIG. 24 , the output characteristic value OP of the laser beam may be acquired instead of the width w of the kerf K, and the positional relationship between the center axis A 2  and the optical axis A 1  may be changed in response to the acquired output characteristic value OP to control the shift amount δ. In this case, the processor  13  starts to obtain the output characteristic value OP in step S 21 . If the output characteristic value OP is the laser power of the laser beam L for example, the laser machine  100  includes a laser power measuring instrument instead of (or in addition to) the dimension measuring instrument  102 , wherein the processor  13  may acquire the laser power as the output characteristic value OP from the laser power measuring instrument. 
     Alternatively, if the output characteristic value OP is the laser power command value, or the frequency or duty ratio of the PW laser beam, such a parameter is defined in the machining program or stored in the storage  15  as a setting value. Accordingly, the processor  13  is able to acquire, from the machining program or the storage  15 , the data of the laser power command value, or the frequency or duty ratio of the PW laser beam. 
     In step S 22 , the processor  13  determines whether or not the output characteristic value OP most-recently acquired is equal to or greater than a first threshold value OP th1 . The processor  13  determines YES when the output characteristic value OP is equal to or greater than the first threshold value OP th1 , and proceeds to step S 23 . On the other hand, the processor  13  determines NO when the output characteristic value OP is smaller than the first threshold value OP th1 , and proceeds to step S 4 . 
     In step S 23 , the processor  13  determines whether or not the output characteristic value OP most-recently acquired is equal to or greater than a second threshold value OP th2  (&gt;OP th1 ). The processor  13  determines YES when the output characteristic value OP is equal to or greater than the second threshold value OP th2 , and proceeds to step S 25 . On the other hand, the processor  13  determines NO when the output characteristic value OP is smaller than the second threshold value OP th2 , and proceeds to step S 24 . 
     In step S 25 , the processor  13  determines whether or not the output characteristic value OP most-recently acquired is equal to or greater than a third threshold value OP th3  (&gt;OP th2 ). The processor  13  determines YES when the output characteristic value OP is equal to or greater than the third threshold value OP th3 , and proceeds to step S 27 . On the other hand, the processor  13  determines NO when the output characteristic value OP is smaller than the third threshold value OP th3 , and proceeds to step S 26 . 
     In this way, the processor  13  changes the positional relationship between the center axis A 2  and the optical axis A 1  in response to the output characteristic value OP during cutting between the product region E 1  and the waste region E 2 . Specifically, the processor  13  changes the shift amount δ in response to the magnitude of the output characteristic value OP, so as to be the initial shift amount δ 0  if OP&lt;OP th1  is satisfied, to be the first shift amount δ 4  if OP th1 ≤OP&lt;OP th2  is satisfied, to be the second shift amount δ 5  if OP th2 &lt;OP&lt;OP th3  is satisfied, and to be the third shift amount δ 6  if OP th3 ≤OP is satisfied. 
     According to this configuration, the positional relationship between the center axis A 2  and the optical axis A 1  is changed in response to the change in the kerf-width w which occurs depending on the output characteristic value OP, whereby it is possible to finely adjust the rate of the assist gas B blown onto the product region E 1 . As a result, the cutting quality requirement (dross dimension) of the product region E 1  can be more effectively satisfied. 
     Note that the storage  15  is not limited to one that is built in the control device  12 , but it may be a memory unit (e.g., a hard disk or EEPROM) externally connected to the control device  12 , or may be built in an external apparatus (e.g., a server) connected to the control device  12  via a communication network. 
     Further, the above-described optical fiber  32  may be omitted, and the laser beam emitted from the laser oscillator  14  may be reflected by a mirror to be guided to the machining head  16 , for example. Further, the moving mechanism  20  is not limited to the above-described configuration. For example, the moving mechanism  20  may be configured so as to move the machining head  16  (or a work table) in the x-axis, y-axis, and z-axis directions. 
     Furthermore, the workpiece W is not limited to the example illustrated in  FIG. 13 . For example, in the workpiece W, the cutting line l 3  or l 6  may be a bent line bent to form an acute, right or obtuse angle. In this case, the cutting speeds v 13  and v 16  when cutting the workpiece W along the bent cutting lines l 3  and l 6  are set to the speed v L  slower than the speed v H , similarly to the above-described embodiments. 
     Although the present disclosure is described above through the embodiments, the embodiments described above are not intended to limit the claimed invention.