Computer-aided monitoring procedure and monitoring system
The computer-assisted monitoring method for laser processing machines addresses the inadequacies of conventional methods by providing continuous production records, determining event locations, and outputting detailed monitoring reports, thereby facilitating rapid and targeted fault correction and reducing downtime.
Patent Information
- Application Number
- DE102023134072
- Authority / Receiving Office
- DE · DE
- Patent Type
- Applications
- Current Assignee / Owner
- Filing Date
- 2023-12-06
- Publication Date
- 2025-06-12
AI Technical Summary
Conventional methods for monitoring laser processing machines are inadequate for rapid fault detection and targeted correction, often resulting in repeated downtime due to undetermined causes of errors.
A computer-assisted monitoring method that continuously provides production records from laser processing machines, compares them with predetermined monitoring events, determines the event location, and outputs a monitoring report with visual information about the fault event and its cause.
Enables rapid and targeted detection and correction of defects, minimizing downtime and maintenance effort by providing operators with clear visual information about the error and its cause.
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Abstract
Description
BACKGROUND OF THE INVENTIONThe invention relates to a computer-assisted monitoring method for a production process with a laser processing machine. The invention also relates to a monitoring system.Such methods are used for monitoring manufacturing processes in order to detect errors occurring during manufacturing more quickly and to avoid financial damage due to downtime of the laser processing machine and damage to the laser processing machine due to mismachined and / or collisions.Conventional methods detect deviations in the manufacturing sequence of the laser processing machine and typically output an error message indicating the deviation. However, the error message is usually output in text form, as a result of which no further information about the error itself or the cause of the error can be communicated to an operator. The error message therefore usually relates to the error result, for example the collision between the laser processing machine and a workpiece, but not to the cause, here the collision.As a result, often only the fault result can be corrected, so that a renewed occurrence of the fault cannot be ruled out. This results in repeated downtime at the laser processing machine due to the same cause of failure. If the operator is stopped in order to locate the cause of the fault message on the laser processing machine, this leads to considerable maintenance effort and longer downtime on the laser processing machine.Furthermore, manufacturing processes are increasingly being carried out in an automated manner by laser processing machines, and the laser processing machines are often controlled and maintained by remote access. As a result, the direct visual access to the laser processing machine and the possible fault is restricted or not possible at all, as a result of which the cause of the fault is even more difficult to determine.WO 2020 / 078683 A1 discloses a method for visualizing process information during the production of sheet metal components. The method is used to support the sorting process, wherein recorded workpiece image data of manufactured workpieces are visually output together with associated manufacturing process information in order to facilitate the sorting by the operator. However, the method described is unsuitable for monitoring the production process itself.EP 1 642 366 B1 discloses a laser welding process control system and method for real-time monitoring of a weld seam quality when creating a weld seam. In the case of deviations in the welding quality, operating interventions in the welding process are made possible and fault flags are produced.US 2015 / 0001196 A1 discloses a device for monitoring a laser weld bead, wherein weld bead defects are determined by means of an image signal reflected from the weld bead surface. The determined weld defects may then be determined more accurately and / or may require intervention in the welding operation.The aforementioned prior art cannot meet the requirements for a rapid fault detection in conjunction with a rapid and targeted correction of the cause of the fault.Object of the InventionIt is the object of the invention to enable a rapid and targeted detection and correction of defects during the production process with a laser processing machine.DESCRIPTION OF THE INVENTIONThis object is achieved according to the invention by a computer-assisted monitoring method having the features of claim 1.According to the invention, a computer-assisted monitoring method is proposed. The monitoring method is thus carried out using at least one computer.The monitoring method is particularly suitable for monitoring a production process which is carried out with a laser processing machine.The monitoring method has at least the following method steps:In a method step a), continuous provision of production records of a production region of the laser processing machine is provided.Production records are to be understood above and below as meaning visual, production-related and / or sensory records of the production region of the laser processing machine. For example, but not by way of limitation, visual make records are to be understood as photographs and / or video records. Furthermore, for example, but not by way of limitation, sensory production records are to be understood as measured values from various sensors, in particular sensors of the laser processing machine and / or data logs of the laser processing machine during the production method. Furthermore, for example, production-related production plans, production parameters, etc. can be understood as production records.Continuous provision is understood to mean provision at regular intervals. The provision is preferably effected at time intervals of less than 1 second, particularly preferably at time intervals of less than 0.1 second, during the entire production process.The production records are typically provided by the laser processing machine and / or by additional measurement and recording means, in particular by a monitoring system described above and below.Preferably, a plurality of manufacturing records are provided. This allows particularly extensive monitoring of the production region and of the production process to be carried out and possible fault events to be detected at an early stage.In a subsequent method step b) of the monitoring method, a comparison of the production records with predetermined monitoring events is provided. An actual fault event can be determined by the comparison. Preferably, the fault event is ascertained before the occurrence of possible subsequent damage by the fault event itself. Preferably, the manufacturing records are compared with a plurality of predetermined monitoring events.A fault event can be understood to mean a deviation from a predetermined manufacturing sequence, which can lead to an impairment of the process quality and / or to damage to the laser processing machine, the environment and / or the workpieces to be manufactured. A typical fault event is tilting of a manufactured workpiece, as a result of which a risk of collision between the workpiece and movable machine parts of the laser processing machine can arise. Another typical error event is an increased process lighting due to an insufficient adaptation of the manufacturing parameters to the workpiece to be machined.Predetermined monitoring events are understood to mean production records of preceding production processes which have led to the occurrence of a fault event. By comparing the predetermined monitoring events with the provided manufacturing records, it is thus possible to infer the occurrence of an error event for the monitored manufacturing process if there is a sufficient agreement.A deviation from the production sequence can thus be effected by comparing the production records with production records characteristic of fault events. If the manufacturing records have, for example, a high agreement with manufacturing records in which a fault event has occurred, then an impending occurrence of the fault event can be concluded.In a further method step c) of the monitoring method, a determination of an event location for the determined actual fault event in the production area of the laser processing machine is provided. In other words, the position of the fault event is determined in the production area of the laser processing machine, which promotes a targeted correction of the fault event.The event location can be determined by evaluating the coordinates associated with the production record having the deviation. For example, it can be provided that the position coordinates of a processing head of the laser processing machine are used for the position determination of the fault event in the case of elevated process lamps.A method step d) of the monitoring method provides for determining at least one visual event record of the event location from the production records. In other words, a record of the production region is determined, in which the fault event is visually recognizable.In a method step e) of the monitoring method, a monitoring report is visually output, wherein the monitoring report comprises at least the monitoring event, the event location and an event record at the time of occurrence of the monitoring event. In other words, according to the invention, in addition to an error message, additional visual information relating to the error event is output. This allows an operator to remedy the fault event and the cause of the fault in a targeted and quick manner.In summary, according to the invention, a monitoring method is proposed which, in addition to outputting an error message, provides additional automatically generated visual information about the error itself and about the cause of the error. This allows direct steering of the operator's perception to the cause of the fault event, which would otherwise be difficult or not accessible at all. Such a meaningful fault description enables a targeted correction of the fault and of the cause of the fault. The downtime of the laser processing machine and the maintenance effort are minimized. From a plurality of production records, the information required for remedying the fault event is automatically selected and displayed in a manner appropriate to the fault situation.In a preferred embodiment of the monitoring method, it is provided in method step c) that the event location is determined by evaluating area coordinates of the manufacturing area of the laser processing machine stored for the manufacturing records. In other words, each production record is assigned unique area coordinates within the production area of the laser processing machine. For example, it can be provided that an imaging device for recording a predetermined partial area of the production area is set and aligned.In addition, an embodiment of the monitoring method is preferred in which at least one actual fault event is determined by outputting a fault message of the laser processing machine. In other words, an error message generated by the laser processing machine can be further processed by the monitoring method, as a result of which additional information on the cause of the error can be provided. As a result, laser processing machines can be effectively incorporated into the monitoring method, as a result of which the monitoring quality can be further increased.The fault message of the laser processing machine can be determined, for example, by ascertaining a process deviation by the machine sensors of the laser processing machine. Furthermore, for example, an increased process lighting can be detected as a result of an unfavorable setting of the process parameters. Typically, the error message of the laser processing machine contains the area coordinates of the processing head of the laser processing machine, whereby the event location as well as a visual event record of the process light can be provided.In a preferred embodiment of the monitoring method, the at least one visual event record is determined as a function of the record alignment with the event location. In particular, in the determination of the visual event record, masking of the event location by moving machine parts of the laser processing machine can be taken into account. The visual event record can alternatively or additionally be determined as a function of the distance of a recording device from the event location, wherein production records which have been recorded by a recording device with a short distance from the event location are in particular favored.Further preferred is an embodiment of the monitoring method in which, in method step a), visual production records of the entire production region are provided. By visually recording the entire manufacturing area, a particularly extensive and complete monitoring of the manufacturing process can be ensured.In a preferred embodiment of the monitoring method, at least 3, preferably at least 6, particularly preferably at least 12, different visual production records of the production region are provided. Different manufacturing records are typically understood to mean records by different recording apparatuses. The inventors have recognized that the previously described numbers of different visual manufacturing records represent a good relationship in terms of monitoring accuracy and process costs.In a preferred development of the monitoring method, the provided visual production records are recorded onto the production region from at least 3 different recording directions. Typically, manufacturing records are recorded by different orientations of the recording devices on the manufacturing area. Preferably, the recording devices are distributed at regular intervals around the manufacturing area. This allows a particularly extensive recording of the production area taking account of movable machine parts.The underlying object is furthermore achieved by a monitoring system.The monitoring system is set up and designed for use in a monitoring method described above and below.The monitoring system has an evaluation unit. The evaluation unit is preferably designed as a computer or as a part of a computer.The evaluation unit is configured to receive provided production records described above and below. In other words, the evaluation unit can be designed to receive different file formats via different transmission means.The evaluation unit is also designed to compare at least one predetermined monitoring event with the provided production records and to determine an error event. A comparison is typically carried out by means of, in particular self-learning, algorithms, as a result of which a particularly rapid comparison with a multiplicity of monitoring events can be carried out.The evaluation unit is furthermore designed to determine an event record of the event location for a determined fault event.The monitoring system also has an output unit for outputting a monitoring report. The output unit is typically designed for visually outputting the monitoring report. The output unit can be designed as a mobile display, in particular as a smartphone.In a preferred embodiment, the monitoring system comprises at least one visual recording device for providing at least one visual production record of the production region of the laser processing machine. As a result, a region of the production region to be monitored can be determined independently of the laser processing machine, as a result of which the monitoring accuracy can be further increased. Typically, the at least one visual recording device is designed as a camera.More preferred is an embodiment wherein the monitoring system includes two or more visual recording devices for providing two or more visual make records. The recording apparatuses have different recording orientations on the manufacturing area. This makes it possible to ensure particularly complete monitoring of the production region independently of the positions of the movable machine parts of the laser processing machine.In a preferred embodiment, the monitoring system further comprises a monitoring sensor system, wherein the monitoring sensor system is designed to provide production records. The monitoring sensor system preferably comprises the machine sensors of the laser processing machine. As a result, the monitoring system can be extended cost-effectively with production records, in particular machine logs, of the laser processing machine and the monitoring quality can be further increased.In one embodiment of the monitoring system, the output unit is designed as a display of the machine controller of the laser processing machine. This allows output to be effected immediately at the laser processing machine in a cost-effective manner.An embodiment of the monitoring system is further preferred, in which the evaluation unit is designed to evaluate production records of two or more production regions of two or more laser processing machines. As a result, the evaluation device can be used centrally for monitoring a plurality of laser processing machines, as a result of which the monitoring costs can be reduced.Further advantages of the invention will become apparent from the description and the drawing. Likewise, the features mentioned above and those set out further below can be used according to the invention individually or together in any desired combinations. The embodiments shown and described are not to be understood as a final enumeration, but rather have exemplary character for describing the invention.DETAILED DESCRIPTION OF THE INVENTION AND DRAWINGFIG. 1 shows schematically a monitoring method according to the invention for a production process carried out using a laser processing machine. FIG. 2 shows a schematic illustration of a production arrangement having a laser processing machine and a monitoring system. FIG. 3 shows a schematic illustration of a partial section of the production arrangement from FIG. 2 when a monitoring event has occurred.FIG. 1 shows a computer-supported monitoring method 10 according to the invention. In particular, the manufacturing process is carried out by means of a laser processing machine 12 (see FIGS. 2, 3 ).The monitoring method 10 is explained in more detail below with reference to the remaining FIGS. 2, 3.The computer-assisted monitoring method 10 has at least the following method steps:In a method step 14 of the monitoring method 10, continuous provision of production records 16 (see FIGS. 2, 3 ) of a production region 18 (see FIG. 2 ) of the laser processing machine 12 is provided.Manufacturing records 16 may be visual manufacturing records 20 (see FIGS. 2, 3 ), such as photographs and / or video records, as well as sensory manufacturing records 22 (see FIG. 2 ), such as sensor records and / or data logs of a machine controller 24 (see FIG. 2 ) of the laser processing machine 12.In other words, various records of the manufacturing process of the laser processing machine 12 and / or of workpieces 26 to be manufactured or manufactured (see FIG. 3 ) can be used or processed further by the monitoring method 10.Preferably, a plurality of, in particular a plurality of, production records 16 are provided. Particularly preferably, the, in particular visual, production records 20 relate to the entire production region 18 of the laser processing machine 12.A subsequent method step 28 of the monitoring method 10 provides for comparing the production records 16 with predetermined monitoring events 30 (see FIG. 2 ) for ascertaining an actually occurring or occurring fault event 32 (see FIG. 3 ).A fault event 32 is to be understood above and below as an event during the production by the laser processing machine 12 that can lead to losses in quality during the production and / or to damage or downtime of the laser processing machine 12 or of the entire production process. The occurrence, the profile and / or the initial trajectory of such an event to be monitored can be predetermined by way of example by means of known characteristic manufacturing records, for example, such that an evaluation of identical or similar manufacturing records 16 can reliably indicate the initial trajectory and / or the occurrence of an error event 32.For example, it can be provided that continuously provided sensory production records 22 of the laser processing machine 12 are checked for compliance with known fault events. This can be done in a simple manner by evaluating the data logs of the laser processing machine 12 and characteristic error messages of the laser processing machine 12 contained therein. Such an error message can relate, for example, to an error cut by the laser processing machine 12 or an error positioning of the laser processing machine 12 with respect to the workpiece 26, which error message is detected by machine sensors 34 (see FIG. 2 ) in the processing head 36 (see FIGS. 2, 3 ) of the laser processing machine 12.Furthermore, for example, provision can be made for continuously provided visual production records 20 of the production region 18 of the laser processing machine 12 to be compared with known predetermined visual monitoring events 30. Tilting of a manufactured workpiece 26 or a thermal deformation of the workpiece 26 or of a provided workpiece blank 37 (see FIGS. 2, 3 ) can thus be detected by visual comparison of the visual manufacturing records 20 with the visual monitoring events 30.A further method step 38 of the monitoring method 10 provides for a determination of an event location 40 (see FIG. 3 ) for the determined actual fault event 32 in the production region 18 of the laser processing machine 12.In other words, an entry location of the fault event 32 that has occurred is determined in the production region 18. This allows an operator and / or a person entrusted with the correction of the fault event 32 to be additionally provided with information on the cause and discoverability of the fault event 32. This significantly shortens the duration for remedying the fault event 32, as a result of which the downtime of the laser processing machine 12 can be kept short.The determination of the event location 40 is preferably carried out by evaluating area coordinates 42 (see FIG. 3 ) of the production area 18 of the laser processing machine 12 stored with respect to the production records 16.For example, the incident location 40 can be determined by evaluating the position coordinates of the machining head 36 associated with an error message of the machine sensors 34 of the laser machining machine 12.Furthermore, for example, the event location 40 can be effected by evaluating the area coordinates 42 stored for a visual production record 20. In a particular embodiment, the manufacturing area 18 recorded by a visual manufacturing record 20 is known. As a result, the visual production record 20 can be assigned particularly quickly and reliably. The area coordinates 42 can be stored manually or automatically determined by image evaluation algorithms.In a further method step 44 of the monitoring method 10, a determination of at least one visual event record 46 (see FIG. 3 ) of the event location 40 from the production records 20 is provided.A visual event record 46 is to be understood above and below as a visual record of the fault event 32 that has occurred. In other words, in method step 44, a visual production record 20 is determined that shows the fault event 32.According to the invention, provision is made in a method step 48 of the monitoring method 10 for a visual output of a monitoring report 50 (see FIG. 2 ) to take place. The monitoring report 50 includes at least the designation of the fault event 32, the event location 40, and at least one event record 46 at the time of occurrence of the fault event 32. This allows for particularly effective and rapid recovery of the fault event 32 since recovery interrupts can be performed in a targeted manner.The at least one output event record 46 preferably extends to a time window of 2 or more, particularly preferably 10 or more, seconds around the point in time of occurrence of the fault event 32. In addition, the occurrence of future fault events 32 can be avoided by remedying the cause.FIG. 2 shows a production arrangement 52 with a monitoring system 54 and a laser processing machine 12.The monitoring system 54 is designed and particularly suitable for use in the monitoring method 10 described above (see FIG. 1 ).The monitoring system 54 comprises an evaluation unit 56 according to the invention. The evaluation unit 56 is configured to receive the provided production records 16. The production records 16 can be received wirelessly or by cable.Preferably, the production records 16 of the production area 18 are transmitted from the laser processing machine 12 to the evaluation unit 56 via a secure Internet connection. As a result, the evaluation unit 56 can be used for the central monitoring of different production processes on different laser processing machines 12.The evaluation unit 56 is also designed to compare at least one predetermined monitoring event 30 with the provided production records 16. The comparison can be carried out by means of predetermined algorithms, preferably using self-learning algorithms. As a result, the comparison can be carried out particularly quickly and reliably by the evaluation unit 56.The evaluation unit 56 is furthermore designed to determine at least one event record 46 (see FIG. 3 ) of the event location 40 (see FIG. 3 ) for an actually occurring or determined fault event 32 (see FIG. 3 ). The determination of the event record 46 is preferably carried out by means of the aforementioned, in particular self-learning, algorithms.The monitoring system 54 also has an output unit 58 for outputting the monitoring report 50. Typically, the output unit 58 is designed as a display 60 of the machine controller 24 of the laser processing machine 12. This allows for the immediate provision of information that can be used to remedy the fault event 32.The monitoring system 54 comprises a plurality, here five, of recording devices 62 a- e, here cameras, for providing visual production records 20, here videos, of the production area 18.Preferably, the recording devices 62a-e have different recording orientations 64a-e on the manufacturing area 18, as shown. This allows the production region 18 to be recorded from different perspectives, so that hidden regions which can arise, for example, as a result of the movement of the processing head 36 can be avoided.In other words, the visual make records 20 provided may preferably be recorded from different recording directions due to the different recording orientations 64 a- eof the recording devices 62 a- e.In a special embodiment, it can be provided that the visual event record 46 determined in method step d) of the monitoring method 10 is determined as a function of the record alignment with the event location 40 (see FIG. 3 ). This makes it possible, for example, to exclude visual production records 20 in which the incident location 40 is hidden in perspective, for example by the machining head 36.As illustrated, the recording devices 62 a- emay be configured to record sub-regions 66 a- eof the manufacturing region 18. The sub-regions 66 a- emay complement one another and / or overlap, such that the entire production region 18 can be recorded as completely as possible. This makes it possible to ensure particularly complete and high-resolution monitoring of the production region 18.The monitoring system 54 may include a central memory 68. The central memory 68 may be configured to store predetermined monitoring events 30 and / or to store manufacturing records 16. The central memory 68 is preferably used as a basis for further development of the algorithms used for evaluation, in particular self-learning algorithms.FIG. 3 shows a partial section of the production arrangement 52 in a side view of the production region 18 of the laser processing machine 12.The workpiece blank 37 arranged on a workpiece support 70 of the laser processing machine 12 is processed or cut here by means of the action of a laser beam 72 of the laser processing machine 12.A manufactured workpiece 26 is tilted during manufacturing by the laser processing machine 12 and protrudes beyond the workpiece blank 37 by a protrusion 73. The protrusion 73 is larger than a processing distance 74 of the processing head 36 of the laser processing machine 12 which is moved parallel to the workpiece blank 37 along the arrow directions 76. This creates the risk of a collision between the processing head 36 and the workpiece 26, which can lead to damage to the workpiece 26 and / or the laser processing machine 12 and to a standstill time of the laser processing machine 12. The tilted workpiece 26 is thus the cause of an error event 32.By carrying out the monitoring method 10 (see FIG. 1 ), the fault event 32 can be detected by evaluating, for example here a visual production record 20 of the event location 40, before damage occurs to the laser processing machine 12 and / or to the workpiece 26. In this case, the operator will inform the fault event 32 on the output unit 58 (see FIG. 2 ) together with the event location 40. According to the invention, an event record 46, here a video record of the tilted workpiece 26, is also displayed, so that a targeted correction of the fault event 32 can be initiated.List of reference characters10 Monitoring method; 12 Laser processing machine; 14 Method step; 16 Production record; 18 Production region; 20 Visual Production record; 22 Sensory Production record; 24 Machine controller; 26 Workpiece; 28 Method step; 30 Monitoring event; 32 Fault event; 34 Machine sensors; 36 Processing head; 37 Workpiece blank; 38 Method step; 40 Event location; 42 Region coordinates; 44 Method step; 46 Event record; 48 Method step; 50 Monitoring report; 52 Production arrangement; 54 Monitoring system; 56 Evaluation unit; 58 Output unit; 60 Display; 62a-e Recording device; 64a-e Record alignment; 66a-e Partial region; 68 Memory; 70 Workpiece overlay; 72 Laser beam; 73 Protrusion 74 Processing distance; 76 Arrow direction.References included in the specificationThis list of documents cited by the applicant has been produced in an automated manner and is only included for the better information of the reader. The list is not part of the German patent application or utility model application. The DPMA does not take any adhesion for any faults or omissions.Patent Literature citedWO 2020 / 078683 A1
[0006] EP 1 642 366 B1
[0007] US 2015 / 0001196 A1
[0008]
Claims
Computer-aided monitoring method (10) for a manufacturing process carried out with a laser processing machine (12), comprising the method steps: a) continuously providing (14) manufacturing records (16) of a manufacturing region (18) of the laser processing machine (12); b) comparing (28) the manufacturing records (16) with predetermined monitoring events (30) in order to determine at least one actual fault event (32); c) determining (38) an event location (40) for the determined actual fault event (32) in the manufacturing region (18) of the laser processing machine (12); d) determining (44) at least one visual event record (46) of the event location (40) from the manufacturing records (16); e) visually outputting (48) a monitoring report (50), wherein the monitoring report (50) comprises at least the fault event (32), the event location (40) and an event record (46) at the time of occurrence of the fault event (32).Monitoring method (10) according to Claim 1, wherein, in method step c), the event location (40) is determined by evaluating region coordinates (42) of the production region (18) of the laser processing machine (12) stored with respect to the production records (16).Monitoring method (10) according to claim 1 or 2, wherein the at least one actual fault event (32) is determined by outputting a fault message of the laser processing machine (12).Monitoring method (10) according to one of the preceding claims, wherein the at least one visual event record (46) is determined as a function of a record alignment (64a-e) with the event location (40).Monitoring method (10) according to one of the preceding claims, wherein in method step a) visual production records (20) of the entire production region (18) are provided.Monitoring method (10) according to one of the preceding claims, wherein at least 3, preferably at least 6, particularly preferably at least 12, visual production records (20) of the production region (18) are provided.Monitoring method (10) according to claim 5 or 6, wherein the provided visual production records (20) are recorded on the production area (18) from at least 3 different recording directions.Monitoring system (54) for use in a monitoring method (10) according to one of the preceding claims, having - an evaluation unit (56) for receiving provided manufacturing records (16); for comparing at least one predetermined monitoring event (30) with the provided manufacturing records (16); and for determining an event location (40) and an event record (46) of the event location (40) for a determined fault event (32); - an output unit (58) for outputting a monitoring report (50).Monitoring system (54) according to claim 8, further comprising at least one visual recording device (62a-e), in particular a camera, for providing at least one visual production record (20).The monitoring system (54) of claim 9, comprising two or more visual recorders (62a-e) for providing two or more visual make records (20), the recorders (62a-e) having different record orientations (64a-e) on the make area (18).Monitoring system (54) according to one of Claims 8 to 10, further comprising a monitoring sensor system, in particular comprising the machine sensors (34) of the laser processing machine (12), wherein the monitoring sensor system is designed to provide the production records (16).Monitoring system (54) according to one of Claims 8 to 11, wherein the output unit (58) is designed as a display (60) of a machine controller (24) of the laser processing machine (12).Monitoring system (54) according to one of Claims 8 to 12, wherein the evaluation unit (56) is designed to evaluate production records (16) of two or more production regions (18) of two or more laser processing machines (12).
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