Arithmetic system, arithmetic method, and program

The calculation system addresses machining issues by detecting overcutting and vibrations, enhancing machining precision and quality through data-driven signal analysis.

WO2025182134A1PCT designated stage Publication Date: 2025-09-04PANASONIC INTELLECTUAL PROPERTY MANAGEMENT CO LTD
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Patent Information

Application Number
PCT/JP2024/037326
Authority / Receiving Office
WO · WO
Patent Type
Applications
Current Assignee / Owner
Priority Date
2024-02-26
Filing Date
2024-10-21
Publication Date
2025-09-04

AI Technical Summary

Technical Problem

Existing machining technologies face issues with vibrations and tool wear during machining, leading to suboptimal machining quality and surface finish.

Method used

A calculation system and method that acquires machining data, calculates shape data, and performs signal analysis to detect overcutting, machining allowance margins, and identify vibration components, using signal analysis to improve machining quality.

Benefits of technology

Enhances machining precision by detecting overcutting and vibrations, allowing for improved surface finish and machining quality through adaptive control.

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Abstract

This arithmetic system comprises an acquisition unit, a calculation unit (processing shape calculation unit), and a function unit. The acquisition unit acquires processing data obtained during processing of a workpiece by a tool included in a processing machine. The calculation unit (processing shape calculation unit) calculates shape data pertaining to the processing shape of the workpiece on the basis of the processing data acquired by the acquisition unit. The function unit performs a signal analysis on the processing data and the shape data.
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Description

Calculation system, calculation method, and program

[0001] The present disclosure generally relates to a calculation system, a calculation method, and a program, and more particularly to a calculation system, a calculation method, and a program for calculating a machining shape of an object machined by a processing machine.

[0002] Patent Document 1 discloses a technique for calculating the processed shape of an object processed by a processing machine.

[0003] Patent No. 5942423

[0004] Considering the problem of vibrations that may occur during machining of an object due to inappropriate machining conditions in the machining machine or wear / deterioration of the tools of the machining machine, further improvement in the machining quality of the object (e.g., the quality of the machined surface shape) may be desired.

[0005] A computing system according to one aspect of the present disclosure includes an acquisition unit, a calculation unit, and a function unit. The acquisition unit acquires machining data obtained during machining of an object using a tool of a processing machine. The calculation unit calculates shape data relating to a machined shape of the object based on the machining data acquired by the acquisition unit. The function unit performs signal analysis on the machining data and the shape data.

[0006] A computing method according to one aspect of the present disclosure is a computing method executed by a computing system. The computing method includes an acquisition step, a calculation step, and a function step. The acquisition step acquires machining data obtained during machining of an object using a tool of a processing machine. The calculation step calculates shape data relating to the machined shape of the object based on the machining data acquired in the acquisition step. The function step performs signal analysis on the machining data and the shape data.

[0007] A program according to one aspect of the present disclosure is a program for causing one or more processors to execute the above-described calculation method.

[0008] The present disclosure has the advantage of being able to improve the processing quality of the object.

[0009] FIG. 1 is a block diagram of a machining system including a calculation system according to an embodiment. FIG. 2 is a block diagram of a PC to which the calculation system is applied. FIG. 3A is a conceptual diagram illustrating a feed direction during single-axis machining. FIG. 3B is a conceptual diagram illustrating a feed direction during two-axis machining. FIG. 4 is a block diagram of a milling model in the calculation system. FIG. 5 is a conceptual diagram of a tool and an object for explaining the milling model. FIG. 6 is a conceptual diagram for explaining machining data and shape data in the calculation system. FIG. 7A is a block diagram of an overcut detection function in the calculation system. FIG. 7B is a graph for explaining the detection function. FIG. 8A is a block diagram of a machining allowance margin detection function in the calculation system. FIG. 8B is a graph for explaining the detection function. FIG. 9 is a characteristic diagram of a motor torque command and a machined surface shape obtained by frequency analysis in the calculation system. FIG. 10A is a characteristic diagram of a motor torque command obtained by time-frequency analysis in the calculation system. FIG. 10B is a characteristic diagram of a machined surface shape obtained by time-frequency analysis in the calculation system of the same. FIG. 11 is a block diagram for explaining motor control (feedforward control, feedback control) in the calculation system of the same. FIG. 12 is a characteristic diagram of a motor rotation speed (machining data) including a vibration component acquired in pre-machining in the calculation system of the same. FIG. 13A is a waveform diagram of an amplitude of a frequency component (vibration component) in the machining data obtained from an extraction result by a frequency extraction unit in the calculation system of the same. FIG. 13B is a waveform diagram of an inverted waveform generated from the amplitude waveform shown in FIG. 13A by a command generation unit in the calculation system of the same. FIG. 13C is a waveform diagram obtained by applying linear regression (slope correction) to the amplitude waveform shown in FIG. 13A by a model generation unit in the calculation system of the same. FIG. 14 is a flowchart for explaining an operation example 1 in the calculation system of the same. FIG. 15 is a flowchart for explaining an operation example 2 in the calculation system of the same. FIG. 16 is a block diagram of a machining system including a first modification of the calculation system of the same.Fig. 17 is a block diagram of a processing system including a second modification of the computing system of the same embodiment. Fig. 18 is a block diagram of a processing system including a third modification of the computing system of the same embodiment.

[0010] (Summary) Below, a calculation system, a calculation method, and a program according to embodiments and modifications will be described with reference to the drawings. Note that the following embodiment and modifications are merely one of various embodiments of the present disclosure. Furthermore, the following embodiment and modifications can be modified in various ways depending on the design, etc., as long as the object of the present disclosure can be achieved. Furthermore, the configuration of each of the modifications can be appropriately combined with the following embodiment or other modifications.

[0011] Furthermore, the numerical values, shapes, materials, components, the arrangement and connection of the components, steps, the order of steps, and the like shown in the following embodiments and modified examples are merely examples and are not intended to limit the present disclosure. Note that "rotation" described below means rotation on one's own axis.

[0012] A calculation system 1 (see FIGS. 1 and 2) according to one embodiment is applied to a machining system. The machining system is a system equipped with a processing machine for processing an object (workpiece W1: see FIGS. 3A, 3B, and 5). The calculation system 1 has a function of calculating a processed shape of the object processed by the processing machine.

[0013] In the following embodiments, the processing machine is assumed to be a machine tool that cuts an object with a tool T1 such as an end mill (see Figures 3A, 3B, and 5), but the type of processing machine is not limited to a cutting machine tool.

[0014] 2, the calculation system 1 includes an acquisition unit 11, a calculation unit, and a function unit 12. The acquisition unit 11 acquires machining data obtained during machining of an object (workpiece W1) by a tool T1 of a processing machine. In the following embodiments, the "calculation unit" corresponds to the machining shape calculation unit 10 (see FIGS. 1 and 2).

[0015] In the following embodiments, the "machining data" includes the rotation speed of the tool T1 or the feed motor (servo motor 330) for moving the object. In the following embodiments, the "machining data" further includes the rotation speed of the spindle drive motor for rotating the tool T1.

[0016] The calculation unit (machining shape calculation unit 10) calculates shape data relating to the machining shape of the object based on the machining data acquired by the acquisition unit 11. In the following embodiment, the "machining shape" of the object is assumed to be the shape of the machining surface of the workpiece W1 (the surface along the virtual line S1 shown in FIGS. 3A and 3B), and may also be called the "machining surface shape." The function unit 12 performs signal analysis on the machining data and shape data.

[0017] According to the above-described configuration of the calculation system 1, the function unit 12 performs signal analysis on the machining data and shape data. Therefore, by utilizing the results of the signal analysis, it becomes easier to address problems caused by vibrations that may occur during machining of an object (workpiece W1). As a result, the calculation system 1 has the advantage of being able to improve the machining quality of the object. In the following embodiment, the calculation system 1 uses "signal analysis" to detect overcutting of the object, detect the machining allowance margin of the object, identify frequency components (vibration components) affecting the machined surface, and generate commands or function models to compensate for the identified vibration components.

[0018] Furthermore, a calculation method according to one aspect is a calculation method executed by the calculation system 1. The calculation method includes an acquisition step, a calculation step, and a function step. In the acquisition step, machining data obtained during machining of an object (workpiece W1) by a tool T1 possessed by a processing machine is acquired. In the calculation step, shape data relating to the machined shape of the object is calculated based on the machining data acquired in the acquisition step. In the function step, signal analysis is performed on the machining data and shape data. The above calculation method has the advantage of being able to improve the machining quality of the object.

[0019] This calculation method is used on a computer system (calculation system 1). That is, this calculation method can also be embodied as a computer program. A program according to one aspect is a program for causing one or more processors to execute the above calculation method. The program may be recorded on a computer-readable non-transitory recording medium.

[0020] (Details) (1) Overall Configuration The calculation system 1 and the processing system according to this embodiment will be described below.

[0021] FIG. 1 is a block diagram showing an example of a machining system according to this embodiment.

[0022] The machining system is a system for machining a workpiece W1, which is an object, and includes a calculation system 1 and a processing machine. The calculation system 1 is applied to such a machining system and has a function of calculating the machining shape of the object machined by the processing machine. In this embodiment, as an example, all of the functions of the calculation system 1 are provided in a PC 100 shown in FIGS. 1 and 2.

[0023] The PC 100 is assumed to be, for example, a notebook computer, but may also be a desktop computer. Software (referred to as "UI software 110" in FIGS. 1 and 2) that displays a user interface (UI) for operating the servo amplifier 200 is installed on the PC 100, and the UI software 110 includes all of the functions of the computing system 1.

[0024] For example, the processing machine is a machine tool that cuts a workpiece W1, which is an object fixed to a stage, with a tool T1 such as an end mill (see FIGS. 3A, 3B, and 5). As shown in FIG. 1, the processing machine includes a servo amplifier 200, a linear encoder 310, a motor encoder 320, and a servo motor 330. Note that FIG. 1 shows a processing machine capable of two-axis processing, and two sets of servo amplifier 200, linear encoder 310, motor encoder 320, and servo motor 330 are shown. The two sets of servo amplifier 200, linear encoder 310, motor encoder 320, and servo motor 330 basically have the same function except for the feed direction, so the same reference numerals are used for each set.

[0025] The servo amplifier 200 is a device for controlling the servo motor 330. The servo motor 330 is an example of a feed motor for moving the tool T1 or an object. The servo motor 330 is, for example, a rotary motor, but may also be a linear motor. The servo motor 330 moves the tool T1 and the object relatively by, for example, moving a stage to which the object is fixed.

[0026] As shown in FIG. 1, each set of servo amplifiers 200 includes a communication IF 210, a communication control unit 220, a motor controller 230, AD converters 240, 250 and 260, and a PWM controller 270.

[0027] The communication IF 210 is a communication interface such as a communication device for communicating with the PC 100. The communication control unit 220 controls communication with the PC 100 via the communication IF 210. For example, the communication control unit 220 transmits data (motor control information) necessary for calculating the machining shape of an object machined by the machining tool to the PC 100. The motor controller 230 controls the rotational speed of the servo motor 330. The motor controller 230 controls the PWM controller 270 to cause the PWM controller 270 to transmit a control signal for rotating the servo motor 330 to the servo motor 330. The motor controller 230 can also receive information indicating the rotational position and rotational speed of the servo motor 330 as feedback from the linear encoder 310, the motor encoder 320, and the servo motor 330 via the AD converters 240, 250, and 260. The motor controller 230 can further adjust the rotational position and rotational speed of the servo motor 330 using the feedback. That is, the motor controller 230 has a function of feedback control (FB control) 231 for the rotational position and rotational speed of the servo motor 330 as shown in FIG.

[0028] The PC 100 includes a UI software 110 and a communication IF 120 .

[0029] The communication IF 120 is a communication interface such as a communication device for communicating with the servo amplifier 200. The communication IF 120 receives machining data obtained during machining of an object by a tool T1 of the processing machine from the servo amplifier 200. The communication IF 120 also transmits operation information corresponding to the operation content obtained via a UI for operating the servo amplifier 200 to the servo amplifier 200.

[0030] As shown in FIGS. 1 and 2 , the UI software 110 includes a screen display unit 111, a data storage unit 112, a machining shape calculation unit 10, and a function unit 12. As shown in FIG. 2 , the UI software 110 further includes an acquisition unit 11 and a transmission unit 13 (not shown in FIG. 1 ). In other words, the calculation system 1 includes the acquisition unit 11, the machining shape calculation unit 10 (calculation unit), and the function unit 12. The calculation system 1 includes a computer system having one or more processors and memories. At least some of the functions of the calculation system 1 are realized by the processor of the computer system executing a program recorded in the memory of the computer system. The program may be recorded in the memory, provided via a telecommunications line such as the Internet, or provided by being recorded on a non-transitory recording medium such as a memory card.

[0031] The screen display unit 111 is a functional component that displays on a display a UI for operating the servo amplifier 200. The data storage unit 112 stores information (motor control information) and the like received from the servo amplifier 200. The data storage unit 112 also stores data such as that shown in FIG. 6, which will be described later.

[0032] The acquisition unit 11 is a functional component of the calculation system 1 that acquires machining data included in information (motor control information) received from the servo amplifier 200 via the communication IF 120. That is, the acquisition unit 11 acquires machining data obtained during machining of an object (workpiece W1) by a tool T1 of the processing machine.

[0033] The machining shape calculation unit 10 is a functional component of the calculation system 1 that calculates the machining shape of an object machined by a processing machine. That is, the machining shape calculation unit 10 (calculation unit) calculates shape data regarding the machining shape of the object based on the machining data acquired by the acquisition unit 11.

[0034] The function unit 12 is a functional component of the calculation system 1 that performs signal analysis on the processed data and shape data. As shown in Fig. 2, the function unit 12 has an analysis function unit 121, an index calculation unit 122, a threshold setting unit 123, a frequency extraction unit 124, and an FF (feedforward) generation unit 125. Details of each function of the function unit 12 will be described later.

[0035] The transmitting unit 13 transmits information including a feedforward command (or a function model) (described later) generated by the FF generating unit 125 to the servo amplifier 200 via the communication IF 120 .

[0036] The PC 100 is a computer including a processor (microprocessor), a memory, etc. The memory is a ROM (Read Only Memory), a RAM (Random Access Memory), etc., and can store programs executed by the processor. The functions of the machining shape calculation unit 10, the acquisition unit 11, the function unit 12, the transmission unit 13, etc. are realized by the processor, etc., which executes programs stored in the memory.

[0037] (2) Machining Shape Calculation Unit The function of the machining shape calculation unit 10 will be described in more detail below.

[0038] The machining shape calculation unit 10 calculates shape data relating to the machining shape of the object based on machining data obtained during machining of the object.

[0039] The machining data includes the rotational speed of the feed motor (servo motor 330) for moving the tool T1 or the object (workpiece W1). The machining data may further include the rotational speed of the spindle drive motor for rotating the tool T1. Furthermore, the machining data may further include torque data (motor torque command) of the servo motor 330. Specific examples of the machining data and details of the operation of the machining shape calculation unit 10 will be described later.

[0040] The screen display unit 111 may display the shape data calculated by the machining shape calculation unit 10. In this case, the screen display unit 111 is an example of a display unit that displays the shape data. For example, the screen display unit 111 reads and displays data such as that shown in FIG. 6 stored in the data storage unit 112.

[0041] Here, the feed direction D1 during single-axis machining and the feed direction D2 during two-axis machining when cutting an object with the tool T1 will be described.

[0042] Fig. 3A is a diagram showing an example of a feed direction D1 during single-axis machining. Fig. 3B is a diagram showing an example of a feed direction D2 during two-axis machining. The workpiece W1 shown in Figs. 3A and 3B is an object to be machined that is fixed to the stage. The material of the workpiece W1 is assumed to be metal, for example, but is not limited to metal and may be resin or wood.

[0043] For example, during single-axis machining, the stage is moved in the x direction by one servo motor 330. During two-axis machining, the stage is moved in the x direction by one of the two servo motors 330, and the stage is moved in the y direction by the other servo motor 330.

[0044] As shown in FIG. 3A, during single-axis machining, the workpiece W1 can be fed only in a fixed direction (e.g., the x-direction), allowing the workpiece W1 to be cut in a fixed direction. As shown in FIG. 3B, during two-axis machining, the workpiece W1 can be fed in any direction, allowing the workpiece W1 to be cut in any direction. While FIG. 1 shows components of a machine capable of two-axis machining, the machine may be capable of single-axis machining only. That is, the machine may have only one set of the servo amplifier 200, linear encoder 310, motor encoder 320, and servo motor 330. Furthermore, the machine may have three or more sets of the servo amplifier 200, linear encoder 310, motor encoder 320, and servo motor 330, allowing for three-axis or more machining. The virtual line S1 in FIGS. 3A and 3B is a line along the machining surface of the workpiece W1.

[0045] Next, the operation of the machining shape calculation unit 10 will be described in detail.

[0046] For example, the machining shape calculation unit 10 calculates shape data based on machining data and a milling model 400. That is, the machining shape calculation unit 10 has the milling model 400. Fig. 4 is a block diagram of the milling model 400. Fig. 5 is a conceptual diagram of a tool T1 and a workpiece W1 for explaining the milling model 400.

[0047] As shown in FIG. 4, the milling model 400 includes, for example, a cutting thickness calculator 410, a process gain 420, a compliance 430, and a difference calculator 440.

[0048] The cutting thickness calculation unit 410 calculates the cutting thickness H1 (see FIG. 5 ) of the workpiece W1 cut by the tool T1. Specifically, the cutting thickness calculation unit 410 calculates the cutting thickness H1 by adding the cutting thickness (called the static cutting thickness) set based on machining conditions such as the tool diameter, number of blades, or radial cutting depth to the cutting thickness (called the dynamic cutting thickness) corresponding to the machining surface S11 of the previous cycle and the relative displacement between the tool T1 and the workpiece W1. The dynamic cutting thickness is calculated by the difference calculation unit 440, which will be described later. As shown in FIG. 5 , because the machining surface S11 formed in the previous cycle is cut in the current cycle, the cutting thickness H1 of each cycle is affected by the dynamic cutting thickness of the previous cycle. Symbol S12 in FIG. 5 indicates the machining surface of the current cycle.

[0049] The process gain 420 calculates the cutting resistance according to the chip thickness H1 calculated by the chip thickness calculation unit 410. The cutting resistance occurs at the cutting edge action point P1 shown in FIG. 5, and the direction of force action rotates with the rotation of the tool T1. The symbol R1 in FIG. 5 indicates the rotation direction of the tool T1. The process gain 420 converts the cutting resistance in the tangential direction E1 and normal direction E2 of the rotation of the cutting edge at the cutting edge action point P1 into cutting resistance in the feed direction (e.g., the x direction in FIG. 3A) and the vertical direction (e.g., the y direction in FIG. 3A).

[0050] The compliance 430 calculates the relative displacement between the tool T1 and the workpiece W1 that occurs due to the cutting resistance in the feed direction and the vertical direction calculated by the process gain 420. It is assumed that the workpiece W1 is a rigid body.

[0051] The difference calculation unit 440 calculates, as the dynamic cutting thickness, the difference between the machining surface S11 in the previous cycle and the relative displacement calculated by the compliance 430. The dynamic cutting thickness is used to calculate the cutting thickness in the next cycle.

[0052] In this way, the cutting resistance causes a relative displacement between the tool T1 and the workpiece W1, and the relative displacement changes the cutting thickness.

[0053] The machining shape calculation unit 10 can calculate the trajectory of the tool T1, i.e., the change in coordinate of the cutting edge position of the tool T1, from the relative displacement calculated in the milling model 400. The machining shape calculation unit 10 can also calculate the coordinate of the machining surface of the workpiece W1 cut in accordance with the change in coordinate of the cutting edge position, i.e., the shape data of the machining shape.

[0054] The machining shape calculation unit 10 inputs the machining data and the calculated shape data to the function unit 12 and also stores them in the data storage unit 112 .

[0055] An example of the machining data and shape data output from the machining shape calculation unit 10 will now be described with reference to FIG.

[0056] The machining data and the shape data may each include information on the same time when the workpiece W1 was machined. It is preferable that the machining shape calculation unit 10 outputs the machining data and the shape data associated with the time.

[0057] 6 shows the machining data including the spindle speed (rotational speed of the spindle drive motor), the rotational speed and torque command of the x-axis feed axis motor (servo motor 330), and the rotational speed and torque command of the y-axis feed axis motor (servo motor 330). In other words, FIG. 6 shows an example of machining data included in the motor control information in the case of two-axis machining.

[0058] In addition, in FIG. 6, the x-axis machining surface coordinates and the y-axis machining surface coordinates calculated from the machining data are shown as shape data.

[0059] In Fig. 6, data with the same index is data at the same time. Although Fig. 6 shows indexes, the indexes may not be necessary, and time stamps may be shown instead of serial numbers.

[0060] The "rotational speed" referred to here is, for example, a rotational speed calculated (estimated) by the servo amplifier 200 based on the position (angle) of the servo motor 330 (or spindle drive motor) detected by the motor encoder 320. The "torque command" is a torque command for the servo motor 330 (or spindle drive motor) determined by position / speed feedback control in the motor controller 230 in the servo amplifier 200. A control signal is transmitted from the PWM controller 270 so that a drive current based on the torque command flows through the servo motor 330 (or spindle drive motor). Information on the rotational speed and torque command are included in the motor control information. In other words, the motor control information in this embodiment includes information on the motor control command and information on the motor control result. Motor control information other than the rotational speed and torque command may also be added to the data output from the machining shape calculation unit 10.

[0061] The data shown in Fig. 6 is stored in the data storage unit 112. The data shown in Fig. 6 may be displayed on the screen display unit 111. By linking (associating) the shape data with the machining data in this way, it is possible to understand the behavior of the motor when the machining surface is formed.

[0062] (3) Functional Unit The functions of the functional unit 12 will be described in more detail below.

[0063] The function unit 12 performs signal analysis on the processing data and shape data input from the processing shape calculation unit 10. Specifically, as shown in FIG. 2 , the function unit 12 has an analysis function unit 121, an index calculation unit 122, a threshold setting unit 123, a frequency extraction unit 124, and an FF generation unit 125.

[0064] The functional unit 12 has two main functions (referred to as a first function and a second function), and performs signal analysis for each function. Specifically, the functional unit 12 has a first function of detecting overcutting of the machined surface of the object and detecting the machining allowance margin, and a second function of identifying frequency components (vibration components) affecting the machined surface and compensating for the vibration components in motor control. The screen display unit 111 may display data of the analysis results of the signal analysis performed by the functional unit 12.

[0065] In this embodiment, the machining data and shape data that are the subject of signal analysis by the functional unit 12 are data from the same time range. Referring to FIG. 6 , the functional unit 12 performs signal analysis on, for example, the machining data and shape data within the range enclosed by the solid-line frame K1, i.e., the machining data and shape data with indexes "3" to "8." In other words, the functional unit 12 does not use, for example, data from indexes "4" to "10" within the dashed-line frame K2 for machining data and data from indexes "1" to "7" within the dashed-line frame K3 for shape data. As described above, the machining data and shape data with the same index are information from the same time when the workpiece W1 was machined. By performing signal analysis on data from the same time range in this way, the reliability of the signal analysis results can be improved.

[0066] [First Function (Excessive Cutting Detection)] The first function, "excessive cut detection," will be described below with reference to FIGS. 7A and 7B.

[0067] First, a brief description of the cutting process will be given. In cutting, the machining surface of the same object may be subjected to, for example, so-called "rough machining," "intermediate machining," and "finishing machining" processes in this order. In this embodiment, the acquisition of machining data, calculation of shape data, and various functions of the functional unit 12 may be performed in each of these "rough machining," "intermediate machining," and "finishing" processes. For example, if there is no machining allowance for the workpiece W1 after the "rough machining" process is completed, the cutting process is completed without performing the "intermediate machining" and subsequent processes. On the other hand, if there is a machining allowance margin, the machining conditions (cutting thickness, feed rate, etc.) may be adjusted in the subsequent processes to take the margin into account when performing cutting.

[0068] In cutting, a problem may occur in which the processing machine overcuts the workpiece W1 (particularly the machined surface) due to factors such as inappropriate processing conditions, blade wear / deterioration of the tool T1, or machine wear. The computing system 1 has a function to detect overcutting of the machined surface of the workpiece W1 and notify the outside.

[0069] This "excessive cutting detection" is performed by the index calculation unit 122, the threshold setting unit 123, and the comparator 126 (see FIG. 7A). In other words, the function unit 12 has the index calculation unit 122, the threshold setting unit 123, and the comparator 126.

[0070] The index calculation unit 122 acquires the shape data from the machining shape calculation unit 10. The index calculation unit 122 calculates an index related to the machining shape of the object from the shape data. The index calculation unit 122 inputs the calculated index to the comparator 126. Here, the index related to the machining shape of the object is a roughness index of the machining surface of the object.

[0071] Fig. 7B shows a graph (surface shape A1) relating to the machined surface calculated by the index calculation unit 122. The surface shape A1 in Fig. 7B is a shape based on the machined surface calculated by the index calculation unit 122, for example, in a rough machining process. The roughness index of the machined surface of the object can be calculated from the surface shape A1 as shown in Fig. 7B.

[0072] In FIG. 7B, the horizontal axis represents the distance of the machined surface, which corresponds to the distance along the x-direction in FIG. 3A, for example. Also, in FIG. 7B, the vertical axis represents the depth of the machined surface (labeled "surf" in FIG. 7B), which corresponds to the depth along the y-direction in FIG. 3A, for example. That is, in FIG. 7B, the jagged, wavy surface shape A1 represents the machined surface, the area below the surface shape A1 is the area of ​​the workpiece W1, and the area above the surface shape A1 is the cut area. The function unit 12 may display the graphed surface shape A1 of the machined surface as shown in FIG. 7B on the UI display via the screen display unit 111.

[0073] Examples of the "roughness index" include "arithmetic mean roughness," "maximum valley depth" indicating the depth of the deepest valley on the contour surface within the reference length, and "maximum height" indicating the sum of the height of the highest peak and the depth of the deepest valley on the contour surface within the reference length.

[0074] The threshold setting unit 123 sets a threshold that is a target value for the index. The threshold is a value that can be set based on the machining allowance of the workpiece W1. The threshold can be different for each process of "rough machining," "intermediate machining," and "finishing machining." For example, a default value is set as the threshold in advance. Threshold information is stored in the data storage unit 112. The threshold setting can be changed by the user via a UI that is used to operate the servo amplifier 200. When the threshold setting unit 123 receives a change in threshold setting, it updates the threshold information stored in the data storage unit 112. When "overcutting detection" is performed, the threshold setting unit 123 reads out the threshold stored in the data storage unit 112 and inputs it to the comparator 126.

[0075] The comparator 126 compares the calculated index with a threshold value and outputs a determination result indicating whether the calculated index exceeds the threshold value.

[0076] In addition, in Fig. 7B, to make it easier to intuitively understand "over-cutting," a dashed line B1 based on the (anticipated) maximum valley depth is shown along with the surface shape A1 in the rough machining process. In the example of Fig. 7B, the depth of the surface shape A1 exceeds (is below) the dashed line B1 at three positions surrounded by circles. In other words, in the example of Fig. 7B, it can be intuitively understood that over-cutting has occurred in three places on the surface.

[0077] If over-cutting has occurred based on the determination result from the comparator 126, the functional unit 12 creates a report including graphed data as shown in Fig. 7B and an error message indicating that over-cutting has been detected, and notifies the user by displaying the report on the display of the UI via the screen display unit 111. Even if over-cutting has not occurred based on the determination result from the comparator 126, the functional unit 12 may notify the user by displaying graphed data as shown in Fig. 7B and a report including a message indicating that the machined surface is good on the display of the UI.

[0078] When the user receives an error message indicating that overcutting has been detected, the user makes a decision to end cutting work on the workpiece W1 in question without performing any further steps.

[0079] [First Function (Detection of Allowance Margin)] The first function, "detection of allowance margin," will be described below with reference to FIGS. 8A and 8B. FIG.

[0080] In the "rough machining" and "medium machining" processes, the machining surface of the workpiece W1 may not be sufficiently machined due to factors such as inappropriate machining conditions, blade wear / deterioration of the tool T1, or machine wear, and a machining allowance margin may exist. The calculation system 1 has a function to detect the machining allowance margin of the machined surface of the workpiece W1 and notify the outside.

[0081] This "machining allowance margin detection" is performed by an index calculation unit 122, a threshold setting unit 123, and an output unit (subtractor 127: see FIG. 8A). In other words, the function unit 12 has an index calculation unit 122, a threshold setting unit 123, and an output unit (subtractor 127). It is assumed that the index calculation unit 122 and the threshold setting unit 123 referred to here are the same as the index calculation unit 122 and the threshold setting unit 123 in over-cutting detection. In other words, it is assumed that the index calculation unit 122 and the threshold setting unit 123 perform processing related to both "over-cutting detection" and "machining allowance margin detection." However, the index calculation unit 122 and the threshold setting unit 123 may be provided separately for "over-cutting detection" and "machining allowance margin detection."

[0082] The index calculation unit 122 acquires shape data from the machining shape calculation unit 10. The index calculation unit 122 calculates an index related to the machining shape of the object (workpiece W1) from the shape data. The index calculation unit 122 inputs the calculated index to the subtractor 127. Here, too, the index related to the machining shape of the object is a roughness index of the machined surface of the object.

[0083] Fig. 8B shows a graph (surface shape A2) relating to the machined surface calculated by the index calculation unit 122. The surface shape A2 in Fig. 8B is a shape based on the machined surface calculated by the index calculation unit 122, for example, in the intermediate machining step. The roughness index of the machined surface of the object can be calculated from the surface shape A2 as shown in Fig. 8B.

[0084] 8B, similarly to FIG. 7B, the horizontal axis represents the distance of the machined surface, and the vertical axis represents the depth of the machined surface (denoted as "surf" in FIG. 8B). That is, in FIG. 8B, the jagged, wavy surface shape A2 represents the machined surface, the area below the surface shape A2 is the area of ​​the workpiece W1, and the area above the surface shape A2 is the cut area. The index calculation unit 122 may display the graphed surface shape A2 of the machined surface as shown in FIG. 8B on the display of the UI via the screen display unit 111.

[0085] The threshold setting unit 123 sets a threshold that is a target value for the index. The threshold is a value that can be set based on the machining allowance of the workpiece W1. The threshold for detecting the machining allowance margin can be the same as the threshold for detecting over-cutting. The threshold can be different for each process of "rough machining," "intermediate machining," and "finishing machining." For example, a default value is set as the threshold in advance. Threshold information is stored in the data storage unit 112. The threshold setting can be changed by the user via a UI that is used to operate the servo amplifier 200. When the threshold setting unit 123 receives a change in threshold setting, it updates the threshold information stored in the data storage unit 112. When "machining allowance margin detection" is executed, the threshold setting unit 123 reads the threshold stored in the data storage unit 112 and inputs it to the subtractor 127.

[0086] The output unit (subtractor 127) calculates and outputs the difference between the calculated index and a threshold. For example, the subtractor 127 outputs the difference, which is the result of subtracting the threshold input from the threshold setting unit 123 from the index input from the index calculation unit 122 (subtraction result).

[0087] 8B, in order to make it easier to intuitively understand the "machining allowance margin," a dashed line B2 based on the (anticipated) maximum height is shown together with the surface shape A2 in the intermediate machining process. In the example of FIG. 8B, it can be intuitively understood from the difference C1 between the depth of the surface shape A2 and the dashed line B2 that the machining surface is not sufficiently removed and that a machining allowance margin exists.

[0088] Based on the subtraction result output from the subtractor 127, the functional unit 12 creates a report including graphed data such as that shown in FIG. 8B and a message indicating whether or not there is a machining allowance margin, and notifies the user by displaying the report on the UI display via the screen display unit 111.

[0089] When the user receives notification of the machining allowance margin, the user adjusts the machining conditions (cutting thickness, feed rate, etc.) for the corresponding workpiece W1 in the subsequent processes, taking the machining allowance margin into consideration.

[0090] It is not essential that the calculation system 1 has both the detection functions of overcut detection and machining allowance margin detection, and it may have only one of the detection functions.

[0091] [Second Function (Frequency Analysis)] The second function, "frequency analysis," will be described below with reference to FIG.

[0092] In cutting, "vibrations" may occur on the processing machine due to factors such as inappropriate processing conditions, blade wear / deterioration of the tool T1, or machine wear, resulting in unstable cutting and a deterioration in the quality of the machined surface. Specifically, the occurrence of "vibrations" may cause stripes or scratches to appear on the machined surface, resulting in processing defects. The calculation system 1 has the function of identifying the position and timing at which this "vibration" occurs and further compensating for the vibration component in subsequent processes.

[0093] The second function, "frequency analysis," is an analysis for identifying frequency components (vibration components) that affect the machined surface.

[0094] This "frequency analysis" is performed by the analysis function unit 121 (see FIG. 2). The analysis function unit 121 performs frequency analysis on the processed data and shape data in the same time range as signal analysis, and outputs the analysis results. One specific example of "processed data and shape data in the same time range" here is the processed data and shape data within the solid-line frame K1 in FIG. 6. That is, in FIG. 6, the analysis function unit 121 extracts data in a common index range and uses it as target data for frequency analysis. The user may be able to select, as appropriate via a UI, which index range of data to use as target data.

[0095] Here, the analysis function unit 121 performs frequency analysis using, for example, FFT (Fast Fourier Transform). Fig. 9 is a characteristic diagram obtained by frequency analysis of the motor torque command (machining data, in other words, motor control information) and the machined surface shape (shape data), with the horizontal axis representing frequency and the vertical axis representing intensity. The upper part of Fig. 9 shows characteristic Q1 of the motor torque command, and the lower part shows characteristic Q2 of the machined surface shape.

[0096] In the example of Figure 9, there are two regions (frequency bands) (dot-hatched regions Fr1 and Fr2) containing frequencies (frequency components) where intensity peaks are present in both the motor torque command characteristic Q1 and the machined surface shape characteristic Q2. The "peak" here refers to a frequency whose intensity is greater than the preceding and following frequencies and whose intensity is equal to or greater than a specified value. The specified value used to compare the motor torque command intensity and the specified value used to compare the machined surface shape intensity may be different.

[0097] In the example of Fig. 9, there are multiple regions (regions Fm1, Fm2, Fm3, ...) that contain frequency components whose peaks exist only in the characteristic Q1 of the motor torque command. Region Fm1 is a region that contains the cutting frequency (specifically, the frequency at which the blade of the tool T1 contacts the workpiece W1, which is 33 Hz in the example of Fig. 9). Regions Fm2, Fm3, ... are regions that contain frequencies that are n times the cutting frequency. Regions that contain frequencies that are four or more times the cutting frequency are not shown in Fig. 9.

[0098] As shown in Figure 6, the machining data and shape data are linked (corresponded) on the time axis. Therefore, by performing frequency analysis, it becomes easy to identify frequencies where intensity peaks exist in common (frequencies within regions Fr1 and Fr2 in Figure 9, hereinafter also referred to as "peak frequencies"). In other words, it is considered that the peak frequencies within regions Fr1 and Fr2 in the motor torque command form the peak frequencies within regions Fr1 and Fr2 that are caused by the roughness of the machined surface. As a result, it becomes easy to identify vibration components on the machine side (e.g., the servo motor 330 or the spindle drive motor) that affect the machined surface.

[0099] Here, the frequency extraction unit 124 (see FIG. 2) extracts frequencies at which intensity peaks are common (peak frequencies in regions Fr1 and Fr2 in FIG. 9). Based on the analysis results, the frequency extraction unit 124 extracts one or more frequencies at which intensity peaks appear in common between the processed data and the shape data. The frequency extraction unit 124 extracts one or more frequencies by filtering using a band-pass filter or the like, and outputs the extracted frequencies to the FF generation unit 125 (see FIG. 2). Details of the FF generation unit 125 will be described later.

[0100] In this way, the analysis function unit 121 performs frequency analysis (FFT) on the processing data and shape data in the same time range. Therefore, it is possible to analyze vibration components that occur on the processing machine side and affect the processed shape, and the processing quality of the object can be improved. Furthermore, the frequency extraction unit 124 extracts one or more frequencies where intensity peaks appear in common, so it is possible to identify vibration components with higher reliability, and further improve the processing quality of the object.

[0101] The function unit 12 may create a report including graphed data such as that shown in Fig. 9 based on the analysis results of the analysis function unit 121 and the extraction results of the frequency extraction unit 124, and notify the user by displaying the report on the UI display via the screen display unit 111. Alternatively, the user may check the graphed data such as that shown in Fig. 9 on the display and perform an operation input to designate one or more frequencies at which intensity peaks commonly appear via the UI. The frequency extraction unit 124 may extract one or more frequencies based on the designation.

[0102] [Second Function (Time-Frequency Analysis)] The second function, "time-frequency analysis," will be described below with reference to FIGS. 10A and 10B.

[0103] The second function, "time-frequency analysis," is also an analysis for identifying frequency components (vibration components) that affect the machined surface. The calculation system 1 may have a "time-frequency analysis" function instead of (or in addition to) the above-mentioned "frequency analysis" function. When the calculation system 1 has both the "frequency analysis" function and the "time-frequency analysis" function, the user may be able to select which function to execute via the UI.

[0104] This "time-frequency analysis" is performed by the analysis function unit 121 (see FIG. 2). The analysis function unit 121 performs time-frequency analysis on the processed data and shape data in the same time range as signal analysis, and outputs the analysis results. One specific example of the "processed data and shape data in the same time range" referred to here is the processed data and shape data in the range surrounded by the solid-line frame K1 in FIG. 6, as in the above-mentioned "frequency analysis." In other words, in FIG. 6, the analysis function unit 121 extracts data in a common index range and uses it as target data for time-frequency analysis. The user may be able to select, as appropriate, which index range of data to use as target data via a UI.

[0105] Here, the analysis function unit 121 performs analysis using, for example, CWT (Continuous Wavelet Transform) as the time-frequency analysis. Fig. 10A is a characteristic diagram (spectrogram: grayscaled) obtained by time-frequency analysis of a motor torque command (machining data, in other words, motor control information). Fig. 10B is a characteristic diagram (spectrogram: grayscaled) obtained by time-frequency analysis of a machined surface shape (shape data). Both Fig. 10A and Fig. 10B have the same time scale, with the horizontal axis representing time and the vertical axis representing frequency.

[0106] 10A and 10B, there are two regions in each of the motor torque command and the machined surface shape that contain frequencies (frequency components) with peaks of intensity at the same time (timing). That is, the region Fr3 enclosed by a rectangular frame in Fig. 10A and the region Fr5 enclosed by a rectangular frame in Fig. 10B contain peak frequencies at the same timing. Furthermore, the region Fr4 enclosed by a rectangular frame in Fig. 10A and the region Fr6 enclosed by a rectangular frame in Fig. 10B contain peak frequencies at the same timing.

[0107] As shown in Figure 6, the machining data and shape data are linked (corresponded) on the time axis. Therefore, by performing time-frequency analysis (CWT), it becomes easy to identify frequencies where intensity peaks exist in common (peak frequencies in regions Fr3 to Fr6 in Figures 10A and 10B). In other words, it is considered that the peak frequencies in regions Fr3 and Fr4 in the motor torque command form the peak frequencies in regions Fr5 and Fr6 caused by the roughness of the machined surface. As a result, it becomes easy to identify the vibration components of the machine tool (e.g., the servo motor 330 or the spindle drive motor) that affect the machined surface.

[0108] In particular, in the case of time-frequency analysis (CWT), it is easier to identify the occurrence timing (in other words, the occurrence position) of frequencies that share common intensity peaks compared to the case of frequency analysis (FFT) shown in Figure 9.

[0109] Here, the frequencies at which intensity peaks are common (peak frequencies within regions Fr3 to Fr6 in FIGS. 10A and 10B) are extracted by the frequency extraction unit 124 (see FIG. 2). That is, based on the analysis results, the frequency extraction unit 124 extracts one or more frequencies at which intensity peaks appear in common at the same time in the processed data and the shape data. The frequency extraction unit 124 extracts one or more frequencies by filtering using a band-pass filter or the like, and outputs the extracted frequencies to the FF generation unit 125 (see FIG. 2).

[0110] In this way, the analysis function unit 121 performs time-frequency analysis (CWT) on the machining data and shape data in the same time range. Therefore, it is possible to analyze the vibration components that occur on the machining machine side and affect the machining shape, and the machining quality of the target object (workpiece W1) can be improved. In addition, since it is possible to identify the occurrence timing, which is difficult to do with the analysis results using FFT, the frequency extraction unit 124 extracts one or more frequencies that have common intensity peaks appearing "at the same time." Therefore, it is possible to identify vibration components with higher reliability, and the machining quality of the target object can be further improved.

[0111] The function unit 12 may create a report including spectrograms such as those shown in FIGS. 10A and 10B based on the analysis results of the analysis function unit 121 and the extraction results of the frequency extraction unit 124, and notify the user by displaying the report on the UI display via the screen display unit 111. Alternatively, the user may check the spectrograms such as those shown in FIGS. 10A and 10B on the display and perform an operation input via the UI to specify one or more frequencies at which intensity peaks appear in common "at the same time." The frequency extraction unit 124 may extract one or more frequencies based on the specification.

[0112] [Second Function (Vibration Component Compensation Function)] The second function, "vibration component compensation function," will be described below with reference to FIGS. 11, 12, and 13A to 13C.

[0113] First, the motor control performed by the motor controller 230 of the servo amplifier 200 will be described with reference to Fig. 11. As shown in Fig. 11, the motor controller 230 has the functions of feedback (FB) control 231 and feedforward (FF) control 232.

[0114] The motor controller 230 includes, for example, a position control system. The position control system receives a position command regarding the position (angle) of the servo motor 330 from an external device such as a higher-level controller. The position control system also receives the position (angle) of the servo motor 330 detected by the motor encoder 320 as the control result of the servo motor 330. The position control system determines a speed command (for example, the rotational speed of the servo motor 330) so that the position command and the control result of the servo motor 330 coincide with each other. The "speed command" (see FIG. 11) output from the position control system is input to the feedback control 231 and the flip-flop control 232.

[0115] The motor controller 230 also includes, for example, a speed control system. The speed control system determines and outputs a motor torque command so that the speed command from the position control system matches the rotation speed of the servo motor 330 estimated based on the detected position (angle) of the servo motor 330. That is, the motor torque command is output from the feedback control 231.

[0116] Furthermore, the speed control system uses a feedforward (FF) control model to determine a feedforward torque command (FF torque command) corresponding to the rotational speed of the servo motor 330 based on the speed command from the position control system, and outputs a signal including the FF torque command. That is, the FF torque command is output from the FF control 232.

[0117] The FF torque command of the FF control 232 is added to the motor torque command of the FB control 231, and a command signal including the result of this addition is input to the PWM controller 270 (see FIG. 1, not shown in FIG. 11). Then, the PWM controller 270 transmits a control signal to the servo motor 330 to rotate the servo motor 330 based on the command signal. The FF torque command from the FF control 232 improves the responsiveness of the servo motor 330.

[0118] Although the motor control has been described using the feed motor (servo motor 330) as an example, the spindle drive motor can also be controlled in the same manner.

[0119] The second function, “vibration component compensation function,” is a function that is assigned (set) to the “FF control model” used in the FF control 232 .

[0120] The FF generation unit 125 (see FIG. 2) of the function unit 12 acquires the extraction result (information on one or more frequencies) from the frequency extraction unit 124 and generates an FF command or a function model to be applied in the FF control 232 .

[0121] Specifically, the frequency extraction unit 124 (described above) extracts vibration components affecting the machined surface from the motor torque command (machining data) and shape data acquired in the previous process (e.g., rough machining), and outputs the extracted vibration components to the FF generation unit 125. Based on the extraction results by the frequency extraction unit 124, the FF generation unit 125 extracts vibration components (frequency components) affecting the machined surface in the motor rotation speed (machining data) by filtering or the like. Then, the FF generation unit 125 generates an FF command or a function model to be applied in the FF control 232 in motor control in the next process (e.g., intermediate process).

[0122] In other words, the calculation system 1 extracts common vibration components (frequency components) that affect the machined surface from each data (shape data, motor torque command data, and motor rotation speed data) by matching in the frequency extraction unit 124 and the FF generation unit 125. The user may check the graphs shown in Figures 9, 10A, and 10B on the UI display, determine the vibration components (frequency components) to be extracted, and specify them via the UI. The frequency extracted from each data may be single or multiple.

[0123] 12 shows the change over time in the motor rotation speed of the machining data acquired in the previous process. The multiple plots Pt1 in Fig. 12 show the rotation speeds of the vibration components (frequency components) that affect the machined surface in the motor rotation speed data, based on the extraction results by the frequency extraction unit 124.

[0124] The generation of the FF command will now be described.

[0125] For example, the FF generating unit 125 can function as a command generating unit that generates an FF command. The command generating unit (FF generating unit 125) extracts frequency components in the machining data (here, the motor rotation speed) from the extraction result by the frequency extracting unit 124, and generates an inverted waveform Wa2 (see FIG. 13B) related to the frequency components. FIG. 13A is a waveform diagram showing a waveform Wa1 of amplitude related to the frequency components (vibration components) affecting the machining surface at the motor rotation speed. The command generating unit generates data of an inverted waveform Wa2 (inverse characteristic waveform data) by inverting the waveform Wa1 shown in FIG. 13A.

[0126] The command generator outputs the inverted waveform Wa2 as an FF command to be applied in motor control of a feed motor (servo motor 330) for moving the tool T1 or an object. For example, the command generator outputs the data of the inverted waveform Wa2 to the servo amplifier 200 as an FF command so that the data is set in an FF control model for motor control of the servo motor 330 in the next process (e.g., an intermediate process). The motor controller 230 of the servo amplifier 200 generates an FF torque command based on the speed command in the FF control 232 using the FF control model in which the data of the inverted waveform Wa2 is set. Note that the "data of the inverted waveform Wa2" sent to the servo amplifier 200 may be, for example, information modeled as table data of the amplitude of the inverted waveform Wa2 for each position (time).

[0127] By using such an FF command, the vibration components generated in the previous process (e.g., rough machining) are compensated for in the next process (e.g., intermediate process). As a result, vibrations generated on the processing machine side are suppressed, and the occurrence of processing defects such as stripes or scratches on the processed surface can be suppressed.

[0128] The generation of a function model will be described below. Note that the computing system 1 may have a function of "generating a function model" instead of or in addition to the above-mentioned function of "generating an FF command." When the computing system 1 has both the function of "generating an FF command" and the function of "generating a function model," the user may be able to select which function to execute via a UI.

[0129] For example, the FF generating unit 125 can function as a model generating unit that generates a function model. The model generating unit (FF generating unit 125) extracts frequency components in the machining data (here, the motor rotation speed) and amplitudes related to the frequency components from the extraction results by the frequency extracting unit 124. For example, an example of the extraction results by the model generating unit can indicate a waveform Wa1 of amplitudes related to frequency components (vibration components) affecting the machining surface at the motor rotation speed, as shown in Fig. 13A used in the description of "Generation of FF command."

[0130] The model generation unit outputs a function model based on the frequency components and amplitude to be applied to an FF control model in motor control. The motor control is motor control of a feed motor (servo motor 330) for moving a tool T1 or an object. For example, the model generation unit generates a function model (mathematical formula model) that compensates for the amplitude of the waveform Wa1 shown in FIG. 13A and outputs it to the servo amplifier 200 to be set in the FF control model in motor control of the servo motor 330 in the next process (e.g., intermediate process). The motor controller 230 of the servo amplifier 200 generates an FF torque command based on a speed command in FF control 232 using the FF control model in which the function model is set.

[0131] The model generation unit may generate a function model by further applying linear regression to the amplitude and output the function model to be applied to the feedforward control model. Figure 13C is a waveform diagram of a waveform Wa3 obtained by further applying linear regression (slope correction) to the amplitude of the waveform Wa1 shown in Figure 13A. For example, the model generation unit may generate a function model that compensates for the amplitude of the waveform Wa3 shown in Figure 13C.

[0132] By using such a function model, the vibration components generated in the previous process (e.g., rough machining) are compensated for in the next process (e.g., intermediate process). As a result, vibrations generated on the processing machine side are suppressed, and the occurrence of processing defects such as stripes or scratches on the processed surface can be suppressed.

[0133] 12 and 13A to 13C, and may notify the user by displaying the report on the UI display via the screen display unit 111. The user may also be able to check the FF command (data of the inverted waveform Wa2) or information on the function model generated by the FF generating unit 125 on the display, and specify via the UI whether or not to actually apply the FF command or information on the function model in the next process (e.g., intermediate process).

[0134] (4) Operation of the Calculation System A series of operation flows in a machining system to which the calculation system 1 is applied will be described below with reference to Figures 14 and 15. The flowcharts shown in Figures 14 and 15 are merely examples of operation flows, and the order of processes may be changed as appropriate, and processes may be added or omitted as appropriate. Note that the flowcharts shown in Figures 14 and 15 mainly show the operation flow related to the second function in the calculation system 1 as an example.

[0135] FIG. 14 is a flowchart of an operation example 1 in which the FF generating unit 125 functions as a "command generating unit that generates an FF command."

[0136] The processing machine performs, for example, a rough cutting process on the object as cutting processing during actual operation (step ST1). This processing is not limited to processing during actual operation, but may also be processing during a test operation performed before operation.

[0137] The calculation system 1 acquires machining data obtained during machining of an object by a tool T1 of the processing machine (step ST2: acquisition step).

[0138] The calculation system 1 calculates shape data relating to the processed shape of the object based on the processing data acquired in step ST2 (step ST3: calculation step).

[0139] The calculation system 1 executes signal analysis on the processing data and shape data (step ST4: functional step).

[0140] The calculation system 1 extracts vibration components from the results of the signal analysis (step ST5).

[0141] The arithmetic system 1 generates inverse characteristic waveform data as shown in FIG. 13B based on the extracted vibration components (step ST6).

[0142] The arithmetic system 1 transmits the inverse characteristic waveform data in the form of table data to the servo amplifier 200 and sets it in the FF control model (step ST7).

[0143] The operation flow then returns to step ST1, and the next process (intermediate machining) for the same object is performed in the same manner. In the motor control for the next intermediate machining, the FF control model of the inverse characteristic waveform data generated in step ST6 of the roughing process is applied.

[0144] If no vibration component is extracted in intermediate step ST5, intermediate steps ST6 and ST7 may be skipped. On the other hand, if a vibration component is extracted in intermediate step ST5, intermediate steps ST6 and ST7 are executed. Then, in the motor control of the next process (finishing), the FF control model of the inverse characteristic waveform data generated in intermediate step ST6 is applied.

[0145] 15 is a flowchart of an operation example 2 in which the FF generating unit 125 functions as a "model generating unit that generates a function model." Steps ST1A, ST2A, ST3A, ST4A, and ST5A in Fig. 15 are substantially the same as steps ST1, ST2, ST3, ST4, and ST5 in Fig. 14 described above, and therefore will not be described here.

[0146] The arithmetic system 1 generates a function model that compensates for the amplitude of the waveform Wa3 as shown in FIG. 13C based on the extracted vibration component (step ST6A).

[0147] The arithmetic system 1 transmits the function model to the servo amplifier 200 and sets it in the FF control model (step ST7A).

[0148] The operation flow then returns to step ST1A, and the next process (intermediate machining) for the same object is performed in the same manner. In the motor control for the next intermediate machining, the FF control model of the function model generated in step ST6A of the roughing process is applied.

[0149] If no vibration component is extracted in step ST5A of intermediate machining, steps ST6A and ST7A of intermediate machining may be skipped. On the other hand, if a vibration component is extracted in step ST5A of intermediate machining, steps ST6A and ST7A of intermediate machining are executed. Then, in the motor control of the next process (finishing machining), the FF control model of the function model generated in step ST6A of intermediate machining is applied.

[0150] (5) Advantages As described above, according to the computing system 1 of this embodiment, the functional unit 12 performs signal analysis on the machining data and shape data. Therefore, by utilizing the results of the signal analysis, it becomes easier to address problems caused by vibrations that may occur during machining of an object. In particular, in cutting, factors such as improper machining conditions, blade wear / deterioration of the tool T1, or machine wear can cause vibrations on the machining machine side, resulting in unstable cutting and a deterioration in the quality of the machined surface. For example, vibrations can cause stripes or scratches on the machined surface, resulting in machining defects.

[0151] In this regard, the "signal analysis" by the functional unit 12 can detect over-cutting of the object, detect the machining allowance margin of the object, identify frequency components (vibration components) affecting the machined surface, and generate FF commands and function models to compensate for the identified vibration components. As a result, the calculation system 1 has the advantage of being able to improve the machining quality of the object.

[0152] To explain the advantages in more detail, signal analysis of the machining data and shape data tends to eliminate the need for correction of the attachment error of the object to the machining machine. Furthermore, the cycle time for measuring the roughness of the machined surface and for error correction tends to be reduced. Furthermore, measurement of shape data is unnecessary, and overcutting and machining allowance margins can be detected from the shape data. Furthermore, frequency components (vibration components) of the servo motor 330 or spindle drive motor that affect the machined surface can be easily extracted. Furthermore, signal analysis of the machining data and shape data obtained in the previous process tends to facilitate correction of the machining conditions (cutting thickness, feed rate, etc.) for the next process. Furthermore, signal analysis of the machining data and shape data obtained in the previous process tends to facilitate compensation for vibration components in motor control in the next process.

[0153] (6) Modifications Modifications of the above embodiment are listed below. The configuration of each of the following modifications can be appropriately combined with the above embodiment or other modifications.

[0154] The same functions as those of the computing system 1 according to the above embodiment may be realized as a computing method, a computer program, or a non-transitory recording medium on which a computer program is recorded.

[0155] The computing system 1 in the present disclosure includes a computer system. The computer system is primarily composed of a processor and memory as hardware. The processor executes a program stored in the memory of the computer system to realize the functions of the computing system 1 in the present disclosure. The program may be pre-recorded in the memory of the computer system, provided via a telecommunications line, or provided in a non-transitory recording medium such as a memory card, optical disk, or hard disk drive that is readable by the computer system. The processor of the computer system is composed of one or more electronic circuits including a semiconductor integrated circuit (IC) or a large-scale integrated circuit (LSI). The integrated circuits, such as ICs or LSIs, are referred to by different names depending on the degree of integration, and include integrated circuits called system LSIs, very large-scale integrations (VLSIs), or ultra-large-scale integrations (ULSIs). Furthermore, field-programmable gate arrays (FPGAs), which are programmed after the LSI is manufactured, or logic devices that allow the reconfiguration of internal connections or internal circuit partitions of the LSI, can also be used as processors. The electronic circuits may be integrated into one chip or distributed across multiple chips. The chips may be integrated into one device or distributed across multiple devices. The computer system referred to here includes a microcontroller having one or more processors and one or more memories. Therefore, the microcontroller is also composed of one or more electronic circuits including a semiconductor integrated circuit or a large-scale integrated circuit.

[0156] Furthermore, it is not essential that the multiple functions of the computing system 1 are concentrated in one housing. For example, the components of the computing system 1 may be distributed across multiple housings.

[0157] Conversely, multiple functions of the computing system 1 may be integrated into one housing. Furthermore, at least some of the functions of the computing system 1, for example, some of the functions of the computing system 1 may be realized by the cloud (cloud computing) or the like.

[0158] (6.1) Modification 1 A calculation system 1 according to Modification 1 and a processing system including the calculation system 1 will be described below with reference to Fig. 16. Note that, in the calculation system 1 and processing system according to Modification 1, components similar to those of the calculation system 1 and processing system according to the above embodiment will be assigned the same reference numerals, and detailed descriptions thereof may be omitted.

[0159] In the above embodiment, as shown in FIG. 1, an example has been described in which all of the functions of the computing system 1 are implemented in the PC 100 on which software for displaying a UI for operating the servo amplifier 200 is installed, but this is not limited to this.

[0160] 16, all of the functions of the computing system 1 according to the first modification are implemented in a host controller 500. Software for controlling the servo amplifier 200 is installed in the host controller 500. The host controller 500 is, for example, a motion controller (such as a programmable logic controller (PLC) or an industrial personal computer (IPC)).

[0161] The host controller 500 includes host software 510 and a communication IF 520. The communication IF 520 is a communication interface such as a communication device for communicating with the servo amplifier 200. The communication IF 520 receives machining data obtained during machining of an object by a tool T1 of the processing machine from the servo amplifier 200. The communication IF 520 also transmits commands to the servo amplifier 200.

[0162] The host software 510 includes a screen display unit 511, a data storage unit 512, a machining shape calculation unit 10, and a function unit 12 (analysis function unit 121, index calculation unit 122, threshold setting unit 123, frequency extraction unit 124, and FF generation unit 125). The machining shape calculation unit 10 and the function unit 12 shown in Fig. 16 have basically the same functions as those shown in Fig. 1. Although not shown in Fig. 16, the host software 510 further has basically the same functions as the acquisition unit 11 and transmission unit 13 shown in Fig. 2.

[0163] The screen display unit 511 displays, for example, machining data, shape data, and the results (graphs, etc.) of signal analysis by the function unit 12 on a display. The data storage unit 512 stores information received from the servo amplifier 200. The data storage unit 512 also stores data such as that shown in Fig. 6. The host software 510 also performs calculations of commands sent to the servo amplifier 200 and processes feedback signals from the servo amplifier 200.

[0164] The calculation system 1 according to the first modification also has the advantage of being able to improve the processing quality of the object.

[0165] (6.2) Modification 2 A calculation system 1 according to Modification 2 and a processing system including the calculation system 1 will be described below with reference to Fig. 17. Note that, in the calculation system 1 and processing system according to Modification 2, components similar to those of the calculation system 1 and processing system according to the above embodiment will be assigned the same reference numerals, and detailed descriptions thereof may be omitted.

[0166] In the above embodiment, as shown in FIG. 1, an example has been described in which all of the functions of the computing system 1 are implemented in the PC 100 on which software for displaying a UI for operating the servo amplifier 200 is installed, but this is not limited to this.

[0167] As shown in Fig. 17, all of the functions of the calculation system 1 according to the modified example 2 are implemented in each of a plurality of (two sets of in Fig. 17) servo amplifiers 200. The machining shape calculation unit 10 and the function unit 12 of each servo amplifier 200 shown in Fig. 17 have basically the same functions as those shown in Fig. 1.

[0168] 17, each servo amplifier 200 also has basically the same functions as the acquisition unit 11 and transmission unit 13 shown in FIG. 2. However, the acquisition unit of each servo amplifier 200 acquires processing data from its own communication control unit 220. The transmission unit of each servo amplifier 200 transmits information including an FF command or a function model generated by the FF generation unit 125 to its own communication control unit 220.

[0169] For example, if a processing machine has a plurality of servo amplifiers 200, each servo amplifier 200 will have a plurality of functions of the arithmetic system 1 (such as the machining shape calculation unit 10 and the function unit 12), and one of the arithmetic systems 1 provided in each servo amplifier 200 may act as a master and perform calculations. Alternatively, certain functions of the arithmetic systems 1 provided in each servo amplifier 200 (for example, the machining shape calculation unit 10) may perform the same calculation. Alternatively, certain functions of the arithmetic systems 1 provided in each servo amplifier 200 (for example, the machining shape calculation unit 10) may perform distributed processing, and the respective results may be integrated.

[0170] The servo amplifier 200 may also have the screen display function and / or data storage function of the PC 100. For example, a display may be connected to the servo amplifier 200 to display data, or a USB (Universal Serial Bus) memory may be connected to the servo amplifier 200 to store data in the USB memory. Alternatively, the machining data, shape data, and the results of signal analysis by the function unit 12 (e.g., graphs) may be transmitted from the communication IF 210 of the servo amplifier 200 to the PC 100, and the screen display unit 111 of the PC 100 may display the data on the display, as in the above embodiment. Furthermore, as in the above embodiment, data such as that shown in FIG. 6 may be stored in the data storage unit 512 of the PC 100.

[0171] The calculation system 1 according to the second modification also has the advantage of being able to improve the processing quality of the object.

[0172] (6.3) Modification 3 A calculation system 1 according to Modification 3 and a processing system including the calculation system 1 will be described below with reference to Fig. 18. Note that, in the calculation system 1 and processing system according to Modification 3, components similar to those of the calculation system 1 and processing system according to the above embodiment may be assigned the same reference numerals, and detailed descriptions thereof may be omitted.

[0173] In the above embodiment, as shown in FIG. 1, an example has been described in which all of the functions of the computing system 1 are implemented in the PC 100 on which software for displaying a UI for operating the servo amplifier 200 is installed, but this is not limited to this.

[0174] A part (functional unit 12) of the plurality of functions of the arithmetic system 1 according to the modified example 3 is implemented in the PC 100 (or the upper controller 500 as in the modified example 1) as in the above embodiment, as shown in Fig. 18. On the other hand, another part (machining shape calculation unit 10) of the plurality of functions of the arithmetic system 1 according to the modified example 3 is implemented in each of the plurality of servo amplifiers 200 as in the modified example 2, as shown in Fig. 18.

[0175] The machining shape calculation unit 10 of each servo amplifier 200 and the function unit 12 of the PC 100 shown in FIG. 18 have basically the same functions as those shown in FIG.

[0176] 18, each servo amplifier 200 also has basically the same functions as the acquisition unit 11 shown in FIG. 2. Similarly to the above embodiment, the PC 100 also includes a transmission unit 13. The acquisition unit of each servo amplifier 200 acquires machining data from its own communication control unit 220. Each servo amplifier 200 transmits the machining data and the shape data calculated by the machining shape calculation unit 10 to the PC 100 via the communication IF 210. Upon receiving the machining data and the shape data from each servo amplifier 200, the PC 100 performs signal analysis in the function unit 12. Similarly to the above embodiment, the transmission unit 13 of the PC 100 transmits information including an FF command or a function model generated by the FF generation unit 125 to the servo amplifier 200.

[0177] The calculation system 1 according to the third modification also has the advantage of being able to improve the processing quality of the object.

[0178] (6.4) Other Modifications In the above embodiment, an example was described in which the machining data included both the rotation speed of the feed motor (servo motor 330) and the rotation speed of the spindle drive motor, but this is not limiting. For example, the machining data may include the rotation speed of the feed motor.

[0179] In the above embodiment, an example has been described in which the machining shape calculation unit 10 calculates shape data based on machining data and the milling model 400, but it is sufficient to calculate shape data using machining data obtained during machining of the object, and it is not necessary to use the milling model 400.

[0180] In the above embodiment, an example was described in which a stage to which an object is fixed is moved by a feed motor (servo motor 330), but the tool T1 and the object may also be moved relative to each other by moving the tool T1.

[0181] In the above embodiment, an example has been described in which the processing machine is equipped with the linear encoder 310 , but the processing machine does not necessarily have to be equipped with the linear encoder 310 .

[0182] (Summary) The above-described embodiments and the like disclose the following aspects.

[0183] A calculation system (1) according to a first aspect includes an acquisition unit (11), a calculation unit (machining shape calculation unit 10), and a function unit (12). The acquisition unit (11) acquires machining data obtained during machining of an object (workpiece W1) by a tool (T1) of a processing machine. The calculation unit (machining shape calculation unit 10) calculates shape data relating to the machining shape of the object (workpiece W1) based on the machining data acquired by the acquisition unit (11). The function unit (12) performs signal analysis on the machining data and the shape data.

[0184] According to the above aspect, the functional unit (12) performs signal analysis on the processing data and shape data. Therefore, by using the results of the signal analysis, it becomes easier to take measures against problems caused by vibrations that may occur during processing of the target object (workpiece W1). As a result, the calculation system (1) has the advantage of being able to improve the processing quality of the target object (workpiece W1).

[0185] Regarding the calculation system (1) according to the second aspect, in the first aspect, the machining data includes the rotational speed of the tool (T1) or the feed motor (servo motor 330) for moving the object (workpiece W1).

[0186] According to the above aspect, the reliability of the analysis results of the signal analysis can be improved.

[0187] In the second aspect of the computing system (1) according to the third aspect, the machining data further includes a rotational speed of a spindle drive motor for rotating the tool (T1).

[0188] According to the above aspect, the reliability of the analysis results of the signal analysis can be further improved.

[0189] Regarding the calculation system (1) according to the fourth aspect, in any one of the first to third aspects, the function unit (12) has an index calculation unit (122), a threshold setting unit (123), and a comparator (126). The index calculation unit (122) calculates an index related to the machined shape of the target object (workpiece W1) from shape data. The threshold setting unit (123) sets a threshold that serves as a target value for the index. The comparator (126) compares the calculated index with the threshold and outputs a determination result indicating whether the calculated index exceeds the threshold.

[0190] According to the above aspect, for example, by notifying the user of the output judgment result, the user can know whether the indicator related to the machining shape exceeds the threshold value. For example, the user can know that too much cutting has occurred, and can more appropriately adjust the machining conditions, etc. As a result, the machining quality of the target object (workpiece W1) can be further improved.

[0191] Regarding the calculation system (1) according to the fifth aspect, in any one of the first to fourth aspects, the function unit (12) has an index calculation unit (122), a threshold setting unit (123), and an output unit (subtractor 127). The index calculation unit (122) calculates an index related to the machined shape of the target object (workpiece W1) from shape data. The threshold setting unit (123) sets a threshold that serves as a target value related to the index. The output unit (subtractor 127) calculates and outputs the difference between the calculated index and the threshold.

[0192] According to the above aspect, for example, by notifying the user of the output difference, the user can know the extent of the difference. For example, the user can know the machining allowance margin, etc., and can more appropriately adjust the machining conditions, etc. Furthermore, for example, in the next machining (process), the user can perform machining taking the margin into consideration. As a result, the machining quality of the target object (workpiece W1) can be further improved.

[0193] Regarding the calculation system (1) according to the sixth aspect, in the fourth or fifth aspect, the index relating to the machined shape of the object (workpiece W1) is a roughness index of the machined surface of the object (workpiece W1).

[0194] According to the above aspect, the roughness of the machined surface of the object can be improved.

[0195] With respect to the calculation system (1) according to the seventh aspect, in any one of the first to sixth aspects, the processing data and shape data that are the subject of signal analysis performed by the functional unit (12) are data in the same time range.

[0196] According to the above aspect, the reliability of the analysis results of the signal analysis can be improved.

[0197] Regarding the calculation system (1) according to the eighth aspect, in the seventh aspect, the function unit (12) has an analysis function unit (121) that performs frequency analysis of processed data and shape data in the same time range as signal analysis and outputs the analysis results.

[0198] According to the above aspect, it is possible to analyze vibration components that are generated on the processing machine side and that affect the processed shape, and it is possible to further improve the processing quality of the target object (workpiece W1).

[0199] In the eighth aspect of the present invention, the functional unit (12) further includes a frequency extraction unit (124) that extracts one or more frequencies at which intensity peaks appear in common between the processed data and the shape data, based on the analysis results.

[0200] According to the above aspect, it is possible to identify vibration components with higher reliability, and the processing quality of the target object (workpiece W1) can be further improved.

[0201] Regarding the calculation system (1) according to the tenth aspect, in the seventh aspect, the function unit (12) has an analysis function unit (121) that performs time-frequency analysis on processed data and shape data in the same time range as signal analysis and outputs the analysis results.

[0202] According to the above aspect, it is possible to analyze vibration components that are generated on the processing machine side and that affect the processed shape, and it is possible to further improve the processing quality of the target object (workpiece W1).

[0203] In the tenth aspect of the computing system (1) according to the eleventh aspect, the functional unit (12) further includes a frequency extraction unit (124). The frequency extraction unit (124) extracts one or more frequencies at which intensity peaks appear in common at the same time in the processed data and the shape data, based on the analysis results.

[0204] According to the above aspect, it is possible to identify vibration components with higher reliability, and the processing quality of the target object (workpiece W1) can be further improved.

[0205] Regarding the calculation system (1) according to the twelfth aspect, in the ninth or eleventh aspect, the function unit (12) further includes a command generation unit (FF generation unit 125). The command generation unit (FF generation unit 125) extracts frequency components in the machining data from the extraction result by the frequency extraction unit (124) and generates an inverted waveform (Wa2) related to the frequency components. The command generation unit (FF generation unit 125) outputs the inverted waveform (Wa2) as a feedforward command to be applied in motor control. The motor control is motor control of a feed motor (servo motor 330) for moving a tool (T1) or an object (workpiece W1).

[0206] According to the above-described embodiment, it becomes easier to apply a feedforward command to, for example, motor control in the next machining process, which compensates for (cancels) vibration components generated in the machining machine and affecting the machined shape. As a result, the machining quality of the target object (workpiece W1) can be further improved.

[0207] Regarding the calculation system (1) according to the thirteenth aspect, in the ninth or eleventh aspect, the function unit (12) further includes a model generation unit (FF generation unit 125). The model generation unit (FF generation unit 125) extracts frequency components in the machining data and amplitudes related to the frequency components from the extraction results by the frequency extraction unit (124). The model generation unit (FF generation unit 125) outputs a function model based on the frequency components and amplitudes to be applied to a feedforward control model in motor control. The motor control is motor control of a feed motor (servo motor 330) for moving a tool (T1) or an object (workpiece W1).

[0208] According to the above-described embodiment, it becomes easier to apply a function model that compensates for (cancels out) vibration components that are generated on the processing machine side and affect the processed shape, for example, to motor control in the next processing (step), thereby further improving the processing quality of the target object (workpiece W1).

[0209] Regarding the calculation system (1) according to the fourteenth aspect, in the thirteenth aspect, the model generation unit (FF generation unit 125) generates a function model to which linear regression is further applied for amplitude, and outputs the function model to be applied to the feedforward control model.

[0210] According to the above aspect, the accuracy of compensation for vibration components can be further improved.

[0211] A calculation method according to a fifteenth aspect is a calculation method executed by a calculation system (1). The calculation method includes an acquisition step, a calculation step, and a function step. In the acquisition step, machining data obtained during machining of an object (workpiece W1) by a tool (T1) possessed by a processing machine is acquired. In the calculation step, shape data relating to the machined shape of the object (workpiece W1) is calculated based on the machining data acquired in the acquisition step. In the function step, signal analysis is performed on the machining data and the shape data.

[0212] According to the above aspect, it is possible to provide a calculation method that can improve the processing quality of the target object (workpiece W1).

[0213] A program according to a sixteenth aspect is a program for causing one or more processors to execute the calculation method according to the fifteenth aspect.

[0214] According to the above aspect, it is possible to provide a function that can improve the processing quality of the target object (workpiece W1).

[0215] The configurations according to the second to fourteenth aspects are not essential for the computing system (1) and may be omitted as appropriate.

[0216] REFERENCE SIGNS LIST 1 Calculation system 10 Machining shape calculation unit (calculation unit) 11 Acquisition unit 12 Function unit 122 Index calculation unit 123 Threshold value setting unit 124 Frequency extraction unit 125 FF generation unit (command generation unit, model generation unit) 126 Comparator 127 Subtractor (output unit) 330 Servo motor (feed motor) T1 Tool W1 Workpiece (object) Wa2 Inverted waveform

Claims

1. A computing system comprising: an acquisition unit that acquires machining data obtained during machining of an object using a tool possessed by a processing machine; a calculation unit that calculates shape data relating to the machined shape of the object based on the machining data acquired by the acquisition unit; and a functional unit that performs signal analysis on the machining data and the shape data.

2. The computing system according to claim 1, wherein the machining data includes a rotation speed of a feed motor for moving the tool or the object.

3. The computing system according to claim 2, wherein the machining data further includes a rotation speed of a spindle drive motor for rotating the tool.

4. The computing system according to any one of claims 1 to 3, wherein the functional unit comprises: an index calculation unit that calculates an index relating to the processed shape of the object from the shape data; a threshold setting unit that sets a threshold that is a target value for the index; and a comparator that compares the calculated index with the threshold and outputs a determination result as to whether the calculated index exceeds the threshold.

5. A computing system according to any one of claims 1 to 4, wherein the functional unit comprises: an index calculation unit that calculates an index relating to the processed shape of the object from the shape data; a threshold setting unit that sets a threshold that is a target value for the index; and an output unit that calculates and outputs the difference between the calculated index and the threshold.

6. The calculation system according to claim 4 or 5, wherein the index relating to the machined shape of the object is a roughness index of the machined surface of the object.

7. The computing system according to any one of claims 1 to 6, wherein the processing data and the shape data that are the targets of the signal analysis performed by the functional unit are data within the same time range.

8. The computing system according to claim 7, wherein the functional unit has an analysis functional unit that performs frequency analysis of the processed data and the shape data in the same time range as the signal analysis and outputs the analysis results.

9. The computing system according to claim 8, wherein the functional unit further comprises a frequency extraction unit that extracts, based on the analysis results, one or more frequencies at which intensity peaks appear in common in the processing data and the shape data.

10. The computing system according to claim 7, wherein the functional unit has an analysis functional unit that performs time-frequency analysis of the processed data and the shape data in the same time range as the signal analysis and outputs the analysis results.

11. The computing system according to claim 10, wherein the functional unit further comprises a frequency extraction unit that extracts, based on the analysis results, one or more frequencies at which intensity peaks appear in common at the same time in the processed data and the shape data.

12. The computing system according to claim 9 or 11, wherein the functional unit further includes a command generation unit, which extracts frequency components in the machining data from the extraction results of the frequency extraction unit, generates an inverted waveform relating to the frequency components, and outputs the inverted waveform as a feedforward command to be applied in motor control of a feed motor for moving the tool or the object.

13. The computing system according to claim 9 or 11, wherein the functional unit further comprises a model generation unit, which extracts frequency components in the machining data and amplitudes related to the frequency components from the extraction results of the frequency extraction unit, and outputs a function model based on the frequency components and the amplitudes to be applied to a feedforward control model in motor control for a feed motor for moving the tool or the object.

14. The computing system according to claim 13, wherein the model generation unit generates the function model by further applying linear regression to the amplitude, and outputs the function model to be applied to the feedforward control model.

15. A calculation method executed by a calculation system, comprising: an acquisition step of acquiring machining data obtained during machining of an object using a tool possessed by a processing machine; a calculation step of calculating shape data relating to the machined shape of the object based on the machining data acquired in the acquisition step; and a functional step of performing signal analysis on the machining data and the shape data.

16. A program for causing one or more processors to execute the computational method of claim 15.

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