Patent Publication Number: US-2023161320-A1

Title: Processing system, display system, processing apparatus, processing method for processing apparatus, and processing program

Description:
The present disclosure relates to a processing system, a display system, a processing apparatus, a processing method for the processing apparatus, and a processing program. This application is based upon and claims the benefit of priority from International Application No. PCT/JP2020/016248, filed Apr. 13, 2020, the disclosure of which is incorporated herein in its entirety. 
    
    
     TECHNICAL FIELD 
     Background Art 
     PTL 1 (U.S. Patent Application Publication No. 2015/0261207) discloses the following method. A method for setting or monitoring operating parameters of a workpiece processing machine, where the workpiece processing machine has a tool holder and means for moving a workpiece and the tool holder relative to one another at least along a first axis, wherein, during the processing operation of the tool holder fitted with a workpiece and during application of the tool to a workpiece, values for at least one of the following (a) to (c) measured variables occurring on the tool during interaction between the tool and the workpiece and transmitted to the tool holder are recorded, and are recorded for the machining sequence, wherein the ascertained values for the at least one measured variable are used, in order to set, in a coordinated manner, the operating parameters with respect to an extended service life of the tool used, at the same time in conjunction with a processing time falling below a maximum machining time, or to monitor the processing operation with respect to a reproducibility of the processing operation, or in order to monitor a tool wear or a machine error of the workpiece processing machine. 
     (a) an axial force acting in a direction parallel to the first axis
 
(b) a torque present relative to the first axis or to an axis oriented parallel to the first axis
 
(c) bending torques or bending torque components according to direction and amount
 
     Prior Art Document 
     Patent Literature 
     
         
         PTL 1: U.S. Patent Application Publication No. 2015/0261207 
         PTL 2: European Patent Application Publication No. 3486737 
         PTL 3: Japanese Unexamined Patent Application Publication No. 2006-071485 
         PTL 4: Japanese Unexamined Patent Application Publication No. 11(1999)-118625 
       
    
     Non-Patent Literature 
     
         
         Non Patent Literature 1: Kaneko and three others, “Instantaneous rigid force model based on oblique cutting to predict milling force”, Transactions of the Japan Society of Mechanical Engineers, 2017, Vol. 83, No. 856, p. 17-00247 
       
    
     SUMMARY OF INVENTION 
     A processing system of the present disclosure includes a cutting tool for milling, a plurality of sensors, and a processing unit. The plurality of sensors each is configured to measure a physical quantity that indicates a state related to loads on the cutting tool during cutting. The processing unit is configured to generate, based on measurement results from the respective sensors at a plurality of measurement time points, measurement data that is related to the loads in two directions on a plane perpendicular to a rotation axis of the cutting tool and that includes two-dimensional data at each of the measurement time points, and to perform a determination process concerning cutting in which the cutting tool is used, based on a two-dimensional shape indicated by the generated measurement data. 
     A processing apparatus of the present disclosure includes a measurement result obtaining unit configured to obtain measurement results from a plurality of sensors, the measurement results being physical quantities each indicating a state related to loads on a cutting tool for milling during cutting, a generation unit configured to generate, based on the measurement results from the respective sensors at a plurality of measurement time points obtained by the measurement result obtaining unit, measurement data that is related to the loads in two directions on a plane perpendicular to a rotation axis of the cutting tool and that includes two-dimensional data at each of the measurement time points, and a determination unit configured to perform a determination process concerning cutting in which the cutting tool is used, based on a two-dimensional shape indicated by the measurement data generated by the generation unit. 
     A processing method for a processing apparatus of the present disclosure includes obtaining measurement results from a plurality of sensors, the measurement results being physical quantities each indicating a state related to loads on a cutting tool for milling during cutting, generating, based on the obtained measurement results from the respective sensors at a plurality of measurement time points, measurement data that is related to the loads in two directions on a plane perpendicular to a rotation axis of the cutting tool and that includes two-dimensional data at each of the measurement time points, and performing a determination process concerning cutting in which the cutting tool is used, based on a two-dimensional shape indicated by the generated measurement data. 
     A processing program of the present disclosure for use in a processing apparatus causes a computer to function as a measurement result obtaining unit configured to obtain measurement results from a plurality of sensors, the measurement results being physical quantities each indicating a state related to loads on a cutting tool for milling during cutting, a generation unit configured to generate, based on the measurement results from the respective sensors at a plurality of measurement time points obtained by the measurement result obtaining unit, measurement data that is related to the loads in two directions on a plane perpendicular to a rotation axis of the cutting tool and that includes two-dimensional data at each of the measurement time points, and a determination unit configured to perform a determination process concerning cutting in which the cutting tool is used, based on a two-dimensional shape indicated by the measurement data generated by the generation unit. 
     A display system of the present disclosure includes a cutting tool for milling, a plurality of sensors, and a processing apparatus. The plurality of sensors each is configured to measure a physical quantity that indicates a state related to loads on the cutting tool during cutting. The processing apparatus is configured to generate, based on measurement results from the respective sensors at a plurality of measurement time points, measurement data that is related to the loads in two directions on a plane perpendicular to a rotation axis of the cutting tool and that includes two-dimensional data at each of the measurement time points, and to perform a process of displaying a two-dimensional shape indicated by the generated measurement data. 
     A processing apparatus of the present disclosure includes a measurement result obtaining unit configured to obtain measurement results from a plurality of sensors, the measurement results being physical quantities each indicating a state related to loads on a cutting tool for milling during cutting, a generation unit configured to generate, based on the measurement results from the respective sensors at a plurality of measurement time points obtained by the measurement result obtaining unit, measurement data that is related to the loads in two directions on a plane perpendicular to a rotation axis of the cutting tool and that includes two-dimensional data at each of the measurement time points, and a display processing unit configured to perform a process of displaying a two-dimensional shape that is indicated by the measurement data generated by the generation unit. 
     A processing method of the present disclosure for a processing apparatus includes obtaining measurement results from a plurality of sensors, the measurement results being physical quantities each indicating a state related to loads on a cutting tool for milling during cutting, generating, based on the obtained measurement results from the respective sensors at a plurality of measurement time points, measurement data that is related to the loads in two directions on a plane perpendicular to a rotation axis of the cutting tool and that includes two-dimensional data at each of the measurement time points, and performing a process of displaying a two-dimensional shape that is indicated by the generated measurement data. 
     A processing program of the present disclosure for use in a processing apparatus causes a computer to function as a measurement result obtaining unit configured to obtain measurement results from a plurality of sensors, the measurement results being physical quantities each indicating a state related to loads on a cutting tool for milling during cutting, a generation unit configured to generate, based on the measurement results from the respective sensors at a plurality of measurement time points obtained by the measurement result obtaining unit, measurement data that is related to the loads in two directions on a plane perpendicular to a rotation axis of the cutting tool and that includes two-dimensional data at each of the measurement time points, and a display processing unit configured to perform a process of displaying a two-dimensional shape that is indicated by the measurement data generated by the generation unit. 
     An aspect of the present disclosure can be realized not only as a processing system including such a characteristic processing unit but also as a semiconductor integrated circuit that realizes a part or all of the processing system. Further, one aspect of the present disclosure can be realized not only as a processing apparatus including such a characteristic processing unit but also as a semiconductor integrated circuit that realizes a part or all of the processing apparatus. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         FIG.  1    is a diagram showing a configuration of a processing system according to an embodiment of the present disclosure. 
         FIG.  2    is a cross-sectional view showing a configuration of a cutting tool according to the embodiment of the present disclosure. 
         FIG.  3    is an arrow view showing the configuration of the cutting tool according to the embodiment of the present disclosure. 
         FIG.  4    is a diagram showing a configuration of a processing apparatus in a cutting system according to the embodiment of the present disclosure. 
         FIG.  5    is a perspective view schematically showing the cutting tool according to the embodiment of the present disclosure. 
         FIG.  6    is a diagram showing an example of measurement data generated by a generation unit in the processing apparatus according to the embodiment of the present disclosure. 
         FIG.  7    is a diagram showing an example of measurement data generated by the generation unit in the processing apparatus according to the embodiment of the present disclosure. 
         FIG.  8    is a diagram showing an example of measurement data generated by the generation unit in the processing apparatus according to the embodiment of the present disclosure. 
         FIG.  9    is a diagram showing another example of measurement data generated by the generation unit in the processing apparatus according to the embodiment of the present disclosure. 
         FIG.  10    is a diagram showing another example of measurement data generated by the generation unit in the processing apparatus according to the embodiment of the present disclosure. 
         FIG.  11    is a diagram showing another example of measurement data generated by the generation unit in the processing apparatus according to the embodiment of the present disclosure. 
         FIG.  12    is a diagram showing an example of calculation data obtained by a calculation data obtaining unit in the processing apparatus according to the embodiment of the present disclosure. 
         FIG.  13    is a diagram showing an example of calculation data obtained by the calculation data obtaining unit in the processing apparatus according to the embodiment of the present disclosure. 
         FIG.  14    is a diagram showing an example of calculation data obtained by the calculation data obtaining unit in the processing apparatus according to the embodiment of the present disclosure. 
         FIG.  15    is a diagram showing another example of calculation data obtained by the calculation data obtaining unit in the processing apparatus according to the embodiment of the present disclosure. 
         FIG.  16    is a diagram showing another example of the calculation data obtained by the calculation data obtaining unit in the processing apparatus according to the embodiment of the present disclosure. 
         FIG.  17    is a diagram showing another example of calculation data obtained by the calculation data obtaining unit in the processing apparatus according to the embodiment of the present disclosure. 
         FIG.  18    is a diagram showing an example of a database in a storage unit of the processing apparatus according to the embodiment of the present disclosure. 
         FIG.  19    is a diagram showing an example of a method of calculating a degree of difference by the processing unit in the processing apparatus according to the embodiment of the present disclosure. 
         FIG.  20    is a diagram showing an example of a condition determination process by the processing unit in the processing apparatus according to the embodiment of the present disclosure. 
         FIG.  21    is a diagram showing an example of measurement data generated by the generation unit in the processing apparatus according to the embodiment of the present disclosure. 
         FIG.  22    is a diagram showing an example of measurement data generated by the generation unit in the processing apparatus according to the embodiment of the present disclosure. 
         FIG.  23    is a diagram showing an example of a calculation result of a degree of difference by the processing unit in the processing apparatus according to the embodiment of the present disclosure. 
         FIG.  24    is a diagram showing an example of a calculation result of a degree of difference by the processing unit in the processing apparatus according to the embodiment of the present disclosure. 
         FIG.  25    is a diagram showing an example of a result of an abnormality determination process by the processing unit in the processing apparatus according to the embodiment of the present disclosure. 
         FIG.  26    is a diagram showing an example of a display screen displayed on a display unit in the processing apparatus according to the embodiment of the present disclosure. 
         FIG.  27    is a flowchart defining an example of an operation procedure when the processing apparatus in the cutting system according to the embodiment of the present disclosure obtains various kinds of information and sensor measurement values. 
         FIG.  28    is a flowchart defining an example of an operation procedure when the processing apparatus in the cutting system according to the embodiment of the present disclosure performs the abnormality determination process. 
         FIG.  29    is a flowchart defining an example of an operation procedure when the processing apparatus in the cutting system according to the embodiment of the present disclosure performs a condition estimation process. 
         FIG.  30    is a diagram showing an example of a sequence of a determination process and a display process in the cutting system according to the embodiment of the present disclosure. 
         FIG.  31    is a diagram showing an example of a method for calculating a degree of rotational symmetry of a two-dimensional shape by the processing unit in the processing apparatus according to a modification of the embodiment of the present disclosure. 
         FIG.  32    is a diagram showing a relationship between a degree of difference calculated by the processing unit in the processing apparatus according to the modification of the embodiment of the present disclosure and a rotation angle. 
         FIG.  33    is a diagram showing an example of a display screen displayed on the display unit in the processing apparatus according to the modification of the embodiment of the present disclosure. 
         FIG.  34    is a flowchart defining an example of an operation procedure when the processing apparatus in the cutting system according to the modification of the embodiment of the present disclosure performs an abnormality determination process. 
     
    
    
     DESCRIPTION OF EMBODIMENTS 
     Conventionally, there has been proposed a technique in which a sensor is attached to a cutting tool and an abnormality of a cutting blade in the cutting tool is detected based on a measurement result by the sensor during cutting. 
     Problems to be Solved by Present Disclosure 
     There is a demand for a technique capable of realizing excellent functions relating to the state of cutting using a cutting tool beyond the technique of PTL 1. 
     The present disclosure has been made in order to solve the above-described problem, and an object thereof is to provide a processing system, a display system, a processing apparatus, a processing method for the processing apparatus, and a processing program capable of realizing excellent functions relating to a state of cutting using a cutting tool. 
     Advantageous Effects of Present Disclosure 
     According to the present disclosure, it is possible to realize excellent functions relating to the state of cutting using a cutting tool. 
     Description of Embodiments of Present Disclosure 
     First, the contents of the embodiments of the present disclosure will be listed and explained. 
     (1) A processing system according to an embodiment of the present disclosure includes a cutting tool for milling, a plurality of sensors, and a processing unit. The plurality of sensors each is configured to measure a physical quantity that indicates a state related to loads on the cutting tool during cutting. The processing unit is configured to generate, based on measurement results from the respective sensors at a plurality of measurement time points, measurement data that is related to the loads in two directions on a plane perpendicular to a rotation axis of the cutting tool and that includes two-dimensional data at each of the measurement time points, and to perform a determination process concerning cutting in which the cutting tool is used, based on a two-dimensional shape indicated by the generated measurement data. 
     In this manner, with the configuration in which the determination process is performed based on the two-dimensional shape indicated by the measurement data including the plurality of pieces of two-dimensional data generated based on the measurement results from the plurality of sensors, for example, it is possible to perform the determination related to cutting with a simple process based on the analysis result of the two-dimensional shape. Therefore, it is possible to realize an excellent function regarding the state of cutting using the cutting tool. 
     (2) The processing unit is configured to obtain calculation data that is calculated based on a shape of the cutting tool and that includes a plurality of pieces of two-dimensional data, at a plurality of time points, related to the loads in the two directions on the plane perpendicular to the rotation axis, and to perform the determination process, further based on a two-dimensional shape indicated by the obtained calculation data. 
     With such a configuration, for example, it is possible to perform a determination regarding cutting based on a degree of similarity between the two-dimensional shape of the two-dimensional data to be generated when normal and ideal cutting is performed and the two-dimensional shape of the actually generated two-dimensional data. 
     (3) The processing unit is configured to obtain the calculation data that is calculated further based on a cutting condition when the cutting tool is used, and to perform the determination process concerning an abnormality in cutting in which the cutting tool is used, based on a result of comparing a two-dimensional shape indicated by first measurement data that includes a plurality of pieces of two-dimensional data corresponding to the plurality of measurement time points in a first period with a two-dimensional shape indicated by first calculation data that is calculated based on the cutting condition in the first period. 
     With such a configuration, it is possible to detect an abnormality in cutting based on the degree of deviation of the two-dimensional shape of the actually generated two-dimensional data from the ideal two-dimensional shape. 
     (4) The processing unit is configured to perform the determination process, based on the two-dimensional shape indicated by the calculation data that differs depending on the cutting condition. 
     With such a configuration, it is possible to detect an abnormality in cutting performed under various cutting conditions. 
     (5) The processing unit is configured to perform the determination process, further based on a result of comparing a two-dimensional shape indicated by second measurement data that includes a plurality of pieces of two-dimensional data corresponding to the plurality of measurement time points in a second period different from the first period with the two-dimensional shape indicated by the first measurement data. 
     With such a configuration, in a case where an abnormality has occurred in advance at a certain point in the past, it is possible to detect further occurrence of an abnormality, expansion of an abnormality, and the like. 
     (6) The processing unit is configured to perform the determination process, further based on a result of comparing a two-dimensional shape indicated by second measurement data that includes a plurality of pieces of two-dimensional data corresponding to the plurality of measurement time points in a second period different from the first period with a two-dimensional shape indicated by second calculation data that is calculated based on the cutting condition in the second period. 
     With such a configuration, it is possible to specify the cause of the abnormality in more detail based on the degree of deviation of the two-dimensional shape of the two-dimensional data actually generated at a certain point in time in the past from the ideal two-dimensional shape. 
     (7) The processing unit is configured to perform the determination process, further based on a result of comparing the cutting condition in the first period with the cutting condition in a second period different from the first period. 
     With such a configuration, it is possible to specify the cause of the abnormality in more detail based on presence or absence of a change in the cutting condition. 
     (8) The processing unit is configured to perform the determination process, based on a degree of similarity between the two-dimensional shape indicated by the measurement data and the two-dimensional shape indicated by the calculation data. 
     With such a configuration, since the determination process can be performed based on the degree of deviation of the two-dimensional shape of the actually generated two-dimensional data from the ideal two-dimensional shape, it is possible to more accurately detect an abnormality in cutting, for example. 
     (9) The processing unit is configured to perform the determination process concerning a cutting condition of cutting in which the cutting tool is used. 
     With such a configuration, it is possible to estimate the cutting condition based on the calculation data indicating the two-dimensional shape having a high degree of similarity with the two-dimensional shape of the actually generated two-dimensional data among the plurality of calculation data. 
     (10) The processing unit is configured to generate the measurement data that includes a plurality of pieces of two-dimensional data corresponding to the plurality of measurement time points in a period of time taken for the cutting tool to rotate a plurality of times. 
     With such a configuration, it is possible to perform a more accurate determination process using measurement data in which variation for each rotation of the cutting tool is reduced. 
     (11) The processing unit is configured to generate the measurement data in which a rotation angle between two pieces of two-dimensional data adjacent to each other around the rotation axis is 5° or less and to obtain the calculation data in which a rotation angle between two pieces of two-dimensional data adjacent to each other around the rotation axis is 5° or less. 
     With such a configuration, it is possible to more precisely compare the two-dimensional shape indicated by the measurement data with the two-dimensional shape indicated by the calculation data, and thus it is possible to perform a more accurate determination process. 
     (12) The processing unit is configured to perform the determination process concerning cutting in which the cutting tool is used, based on a degree of rotational symmetry of the two-dimensional shape indicated by the measurement data. 
     With such a configuration, it is possible to make a determination regarding cutting with a simple process using more limited information. 
     (13) A processing apparatus according to the embodiment of the present disclosure includes a measurement result obtaining unit configured to obtain measurement results from a plurality of sensors, the measurement results being physical quantities each indicating a state related to loads on a cutting tool for milling during cutting, a generation unit configured to generate, based on the measurement results from the respective sensors at a plurality of measurement time points obtained by the measurement result obtaining unit, measurement data that is related to the loads in two directions on a plane perpendicular to a rotation axis of the cutting tool and that includes two-dimensional data at each of the measurement time points, and a determination unit configured to perform a determination process concerning cutting in which the cutting tool is used, based on a two-dimensional shape indicated by the measurement data generated by the generation unit. 
     In this manner, with the configuration in which the determination process is performed based on the two-dimensional shape indicated by the measurement data including the plurality of pieces of two-dimensional data generated based on the measurement results from the plurality of sensors, for example, it is possible to perform the determination related to cutting with a simple process based on the analysis result of the two-dimensional shape. Therefore, it is possible to realize an excellent function regarding the state of cutting using the cutting tool. 
     (14) A processing method according to the embodiment of present disclosure for a processing apparatus includes obtaining measurement results from a plurality of sensors, the measurement results being physical quantities each indicating a state related to loads on a cutting tool for milling during cutting, generating, based on the obtained measurement results from the respective sensors at a plurality of measurement time points, measurement data that is related to the loads in two directions on a plane perpendicular to a rotation axis of the cutting tool and that includes two-dimensional data at each of the measurement time points, and performing a determination process concerning cutting in which the cutting tool is used, based on a two-dimensional shape indicated by the generated measurement data. 
     In this manner, by the method of performing the determination process on the basis of the two-dimensional shape indicated by the measurement data including the plurality of pieces of two-dimensional data generated based on the measurement results from the plurality of sensors, for example, it is possible to perform the determination regarding the cutting with a simple process based on the analysis result of the two-dimensional shape. Therefore, it is possible to realize an excellent function regarding the state of cutting using the cutting tool. 
     (15) A processing program according to the embodiment of the present disclosure for use in a processing apparatus causes a computer to function as a measurement result obtaining unit configured to obtain measurement results from a plurality of sensors, the measurement results being physical quantities each indicating a state related to loads on a cutting tool for milling during cutting, a generation unit configured to generate, based on the measurement results from the respective sensors at a plurality of measurement time points obtained by the measurement result obtaining unit, measurement data that is related to the loads in two directions on a plane perpendicular to a rotation axis of the cutting tool and that includes two-dimensional data at each of the measurement time points and a determination unit configured to perform a determination process concerning cutting in which the cutting tool is used, based on a two-dimensional shape indicated by the measurement data generated by the generation unit. 
     In this manner, with the configuration in which the determination process is performed based on the two-dimensional shape indicated by the measurement data including the plurality of pieces of two-dimensional data generated based on the measurement results from the plurality of sensors, for example, it is possible to perform the determination related to cutting with a simple process based on the analysis result of the two-dimensional shape. Therefore, it is possible to realize an excellent function regarding the state of cutting using the cutting tool. 
     (16) A display system according to the embodiment of the present disclosure includes a cutting tool for milling, a plurality of sensors, and a processing apparatus. The plurality of sensors each is configured to measure a physical quantity that indicates a state related to loads on the cutting tool during cutting. The processing apparatus is configured to generate, based on measurement results from the respective sensors at a plurality of measurement time points, measurement data that is related to the loads in two directions on a plane perpendicular to a rotation axis of the cutting tool and that includes two-dimensional data at each of the measurement time points, and to perform a process of displaying a two-dimensional shape indicated by the generated measurement data. 
     In this manner, with the configuration in which the processing of displaying the two-dimensional shape indicated by the measurement data including the plurality of pieces of two-dimensional data generated based on the measurement results from the plurality of sensors is performed, for example, it is possible to cause the user to visually recognize the load in the cutting tool using the two-dimensional shape. Therefore, it is possible to realize an excellent function regarding the state of cutting using the cutting tool. 
     (17) The processing apparatus is configured to obtain calculation data that is calculated based on a shape of the cutting tool and that includes a plurality of pieces of two-dimensional data, at a plurality of time points, related to the loads in the two directions on the plane perpendicular to the rotation axis, and to perform a process of further displaying a two-dimensional shape indicated by the obtained calculation data. 
     With such a configuration, for example, the user can compare the two-dimensional shape of the two-dimensional data to be generated when normal and ideal cutting is performed with the two-dimensional shape of the actually generated two-dimensional data. 
     (18) The processing apparatus is configured to perform a process of further displaying information indicating a degree of similarity between the two-dimensional shape indicated by the measurement data and the two-dimensional shape indicated by the calculation data. 
     With such a configuration, it is possible to cause the user to recognize the degree of deviation of the two-dimensional shape of the actually generated two-dimensional data from the ideal two-dimensional shape. 
     (19) The processing apparatus is configured to estimate a cutting condition when the cutting tool is used and to perform a process of further displaying a result of estimation. 
     With such a configuration, it is possible for the user to check that the cutting condition intended by the user matches the estimated cutting condition. 
     (20) A processing apparatus according to the embodiment of present disclosure includes a measurement result obtaining unit configured to obtain measurement results from a plurality of sensors, the measurement results being physical quantities each indicating a state related to loads on a cutting tool for milling during cutting, a generation unit configured to generate, based on the measurement results from the respective sensors at a plurality of measurement time points obtained by the measurement result obtaining unit, measurement data that is related to the loads in two directions on a plane perpendicular to a rotation axis of the cutting tool and that includes two-dimensional data at each of the measurement time points, and a display processing unit configured to perform a process of displaying a two-dimensional shape that is indicated by the measurement data generated by the generation unit. 
     In this manner, with the configuration in which the processing of displaying the two-dimensional shape indicated by the measurement data including the plurality of pieces of two-dimensional data generated based on the measurement results from the plurality of sensors is performed, for example, it is possible to cause the user to visually recognize the load in the cutting tool using the two-dimensional shape. Therefore, it is possible to realize an excellent function regarding the state of cutting using the cutting tool. 
     (21) A processing method according to the embodiment of present disclosure for a processing apparatus includes obtaining measurement results from a plurality of sensors, the measurement results being physical quantities each indicating a state related to loads on a cutting tool for milling during cutting, generating, based on the obtained measurement results from the respective sensors at a plurality of measurement time points, measurement data that is related to the loads in two directions on a plane perpendicular to a rotation axis of the cutting tool and that includes two-dimensional data at each of the measurement time points, and performing a process of displaying a two-dimensional shape that is indicated by the generated measurement data. 
     In this manner, by the method of performing the process of displaying the two-dimensional shape indicated by the measurement data including the plurality of pieces of two-dimensional data generated based on the measurement results from the plurality of sensors, for example, it is possible to cause the user to visually recognize the load in the cutting tool using the two-dimensional shape. Therefore, it is possible to realize an excellent function regarding the state of cutting using the cutting tool. 
     (22) A processing program according to the embodiment of present disclosure for use in a processing apparatus causes a computer to function as a measurement result obtaining unit configured to obtain measurement results from a plurality of sensors, the measurement results being physical quantities each indicating a state related to loads on a cutting tool for milling during cutting, a generation unit configured to generate, based on the measurement results from the respective sensors at a plurality of measurement time points obtained by the measurement result obtaining unit, measurement data that is related to the loads in two directions on a plane perpendicular to a rotation axis of the cutting tool and that includes two-dimensional data at each of the measurement time points, and a display processing unit configured to perform a process of displaying a two-dimensional shape that is indicated by the measurement data generated by the generation unit. 
     In this manner, with the configuration in which the processing of displaying the two-dimensional shape indicated by the measurement data including the plurality of pieces of two-dimensional data generated based on the measurement results from the plurality of sensors is performed, for example, it is possible to cause the user to visually recognize the load in the cutting tool using the two-dimensional shape. Therefore, it is possible to realize an excellent function regarding the state of cutting using the cutting tool. 
     Hereinafter, embodiments of the present disclosure will be described with reference to the drawings. In the drawings, the same or corresponding portions are denoted by the same reference signs, and description thereof will not be repeated. Further, at least a part of the embodiments described below may be arbitrarily combined. 
     [Processing System] 
       FIG.  1    is a diagram showing a configuration of a processing system according to the embodiment of the present disclosure. Referring to  FIG.  1   , a processing system  301  includes a cutting tool  101  for milling, a plurality of strain sensors  20 , and a processing apparatus  201 . Processing system  301  is an example of a display system. Processing apparatus  201  is an example of a processing unit in processing system  301 . 
     [Cutting Tool] 
     Cutting tool  101  is, for example, an end mill used in a machine tool such as a milling machine, and is used for milling an object to be cut made of metal or the like. Cutting tool  101  is, for example, an indexable end mill. Cutting tool  101  is used while being held by a tool holder  210  such as an arbor. 
     Cutting tool  101  includes a shaft part  10 , a housing  24 , a battery  22 , a wireless communication device  23 , and a blade fitting part  12 . Shaft part  10  includes a shank part  11 . In  FIG.  1   , housing  24  is indicated by a two dot chain line which is an imaginary line. 
     Blade fitting part  12  is provided closer to the distal end than shaft part  10  in cutting tool  101 . Blade fitting part  12  includes, for example, four blade fixing parts  13 . An insert  14  is attached to each blade fixing part  13 . Blade fitting part  12  may be configured to include one, two, or four or more blade fixing parts  13 . 
     Tool holder  210  is attached to a main shaft  220  of the machine tool. Main shaft  220  has a columnar shape and applies a rotational force to tool holder  210 . Tool holder  210  is a columnar member disposed on an extension line of main shaft  220 . Specifically, an upper end portion of tool holder  210  is held by main shaft  220 . In addition, a lower end portion of tool holder  210  holds shank part  11  of cutting tool  101 . 
     For example, a strain sensor  20  may be attached to the peripheral surface of shaft part  10  via an adhesive or a pressure-sensitive adhesive. Strain sensor  20  may be attached to a peripheral surface of tool holder  210 . 
     Housing  24  stores strain sensor  20 . Specifically, housing  24  includes a bottom plate portion and a side wall portion (not shown). Housing  24  covers strain sensor  20  from below and from the side. 
     Battery  22  and wireless communication device  23  are housed in housing  24 . For example, battery  22  and wireless communication device  23  are fixed to a bottom plate portion or a side wall portion of housing  24 . Wireless communication device  23  includes a communication circuit such as a communication integrated circuit (IC), for example. Battery  22  is connected to strain sensor  20  and wireless communication device  23  via a power line (not shown). Battery  22  supplies power to strain sensor  20  and wireless communication device  23  via a power line. The power line is provided with a switch for switching on and off of power supply. 
     For example, processing system  301  includes three strain sensors  20 . Processing system  301  may be configured to include a smaller number of strain sensors  20  than the number of inserts  14  in cutting tool  101 , or may be configured to include a larger number of strain sensors  20  than the number of inserts  14  in cutting tool  101 . In addition, processing system  301  may be configured to include a number of strain sensors  20  that is not correlated with the number of inserts  14  in cutting tool  101 . 
       FIG.  2    is a cross-sectional view showing a configuration of the cutting tool according to the embodiment of the present disclosure.  FIG.  2    is a cross-sectional view taken along line II-II in  FIG.  1   . Referring to  FIG.  2   , strain sensors  20 A,  20 B, and  20 C are provided in shaft part  10  as strain sensors  20 . A Strain sensor  20 B is provided at a position shifted by 90° from the position at which a strain sensor  20 C is provided in the circumferential direction of shaft part  10 . A strain sensor  20 A is provided at a position shifted by 90° from the position at which strain sensor  20 B is provided in the circumferential direction of shaft part  10 . Strain sensors  20 A and  20 C are provided at point-symmetric positions with respect to a rotation axis  17  of shaft part  10 . For example, strain sensors  20 A,  20 B, and  20 C may be provided at the same position in a direction along rotation axis  17  of shaft part  10 , or may be provided at positions different from each other. 
     Strain sensors  20 A,  20 B, and  20 C may be provided on the peripheral surface of shaft part  10  or tool holder  210  as described above, for example, regardless of the position of blade fitting part  12 . That is, strain sensors  20 A,  20 B, and  20 C do not need to be provided at positions along rotation axis  17  from blade fixing part  13  on the peripheral surface of shaft part  10  or tool holder  210 . 
     Hereinafter, for the sake of description, in a plane orthogonal to rotation axis  17 , a direction from rotation axis  17  to a position where strain sensor  20 A is provided is referred to as an X direction, and a direction from rotation axis  17  to the position where strain sensor  20 B is provided is referred to as a Y direction. 
       FIG.  3    is an arrow view showing the configuration of the cutting tool according to the embodiment of the present disclosure.  FIG.  3    is an arrow view seen from the direction III in  FIG.  1   . Referring to  FIG.  3   , blade fitting part  12  includes blade fixing parts  13 A,  13 B,  13 C, and  13 D as blade fixing part  13 . Blade fixing parts  13 A,  13 B,  13 C, and  13 D are provided in this order at positions shifted by 90° in the clockwise direction in the circumferential direction of blade fitting part  12 . Inserts  14 A,  14 B,  14 C, and  14 D are attached to blade fixing parts  13 A,  13 B,  13 C, and  13 D as inserts  14 , respectively. Each insert  14 A,  14 B,  14 C, and  14 D has a cutting edge. 
     Insert  14  is, for example, an indexable insert. Insert  14  is attached to blade fixing part  13  by screwing, for example. Note that insert  14  may be fixed to blade fixing part  13  by means other than screwing. In addition, cutting tool  101  may be a so-called solid end mill including a cutting blade integrated with shaft part  10  instead of blade fitting part  12 . 
     Strain sensor  20  measures a physical quantity indicating a state related to a load of cutting tool  101  during cutting. More specifically, strain sensor  20  measures the shear strain ε of shaft part  10  as a physical quantity indicating a state related to a load of cutting tool  101  during cutting. 
     For example, strain sensor  20  measures the shear strain ε in a period from a time ts, which is a start time of cutting, to a time te, which is an end time of cutting, and transmits an analog signal having a level corresponding to the shear strain ε to wireless communication device  23  via a signal line (not illustrated). 
     Wireless communication device  23  performs analog-to-digital (AD) conversion on the analog signal received from strain sensor  20  at a predetermined sampling period, and generates a sensor measurement value that is a digital value after the conversion. More specifically, wireless communication device  23  generates a sensor measurement value sx by performing AD conversion on an analog signal of the shear strain ε received from strain sensor  20 A, generates a sensor measurement value sy by performing AD conversion on an analog signal of the shear strain ε received from strain sensor  20 B, and generates a sensor measurement value sr by performing AD conversion on an analog signal of the shear strain received from strain sensor  20 C. 
     Wireless communication device  23  adds a time stamp indicating a sampling timing to the generated sensor measurement values sx, sy, and sr, and stores the sensor measurement values sx, sy, and sr to which the time stamps are added in a storage unit (not illustrated). Wireless communication device  23  obtains one or a plurality of sets of the sensor measurement values sx, sy, and sr from the storage unit in a predetermined cycle, for example, generates a wireless signal including the obtained sensor measurement values sx, sy, and sr and identification information of corresponding strain sensor  20 , and transmits the generated wireless signal to processing apparatus  201 . 
     [Processing Apparatus] 
       FIG.  4    is a diagram showing a configuration of a processing apparatus in a cutting system according to the embodiment of the present disclosure. Referring to  FIG.  4   , processing apparatus  201  includes a wireless communication unit  110 , a generation unit  120 , a calculation data obtaining unit  130 , a processing unit  140 , a shape information obtaining unit  151 , a condition information obtaining unit  152 , a display unit  160 , and a storage unit  170 . Wireless communication unit  110  is an example of a measurement result obtaining unit. Processing unit  140  is an example of a determination unit and an example of a display processing unit. 
     Wireless communication unit  110  is provided with a communication circuit such as a communication IC, for example. Generation unit  120 , calculation data obtaining unit  130 , processing unit  140 , shape information obtaining unit  151 , and condition information obtaining unit  152  are provided with a processor such as a central processing unit (CPU) and a digital signal processor (DSP), for example. Storage unit  170  is, for example, a nonvolatile memory. Display unit  160  is, for example, a display. Note that display unit  160  may be provided outside processing apparatus  201 . 
     &lt;Shape Information Obtaining Unit&gt; 
     Shape information obtaining unit  151  obtains shape information indicating the shape of cutting tool  101  used for cutting. More specifically, shape information obtaining unit  151  obtains shape information indicating a tool diameter, a number of blades which is the number of inserts  14 , a helix angle, an insert pitch which is an angular interval of inserts  14  around rotation axis  17 , and a gash. Here, the tool diameter is a diameter of a circumscribed circle of the cutting edge of insert  14 , and is also referred to as an outside diameter or an edge diameter. For example, shape information obtaining unit  151  obtains the shape information from CAM (Computer Aided Manufacturing), which is software for creating a machining program of a machine tool, and stores the obtained shape information in storage unit  170 . 
     &lt;Condition Information Obtaining Unit&gt; 
     Condition information obtaining unit  152  obtains condition information indicating a cutting condition in cutting using cutting tool  101 . More specifically, condition information obtaining unit  152  obtains the condition information indicating the axial cutting amount and the radial cutting amount. For example, condition information obtaining unit  152  obtains the condition information from the CAM before the start of cutting, and stores the obtained condition information in storage unit  170 . 
     &lt;Wireless Communication Unit&gt; 
     Wireless communication unit  110  obtains a measurement result from strain sensor  20 , the measurement result being a physical quantity indicating a state related to a load of cutting tool  101  during cutting. 
     More specifically, wireless communication unit  110  performs wireless communication with wireless communication device  23  in cutting tool  101 . Wireless communication device  23  and wireless communication unit  110  perform wireless communication using a communication protocol such as ZigBee® compliant with IEEE802.15.4, Bluetooth® compliant with IEEE802.15.1, and UWB (Ultra Wide Band) compliant with IEEE802. 15. 3a. A communication protocol other than the above may be used between wireless communication device  23  and wireless communication unit  110 . 
     Wireless communication unit  110  obtains the sensor measurement values sx, sy, and sr and the identification information from the wireless signal received from wireless communication device  23  in cutting tool  101 . Then, wireless communication unit  110  stores the sensor measurement values sx, sy, and sr in storage unit  170  in association with the identification information. 
     &lt;Generation Unit&gt; 
     Generation unit  120  generates measurement data MD including two-dimensional data for each measurement time point regarding loads in two directions in a plane perpendicular to rotation axis  17  based on measurement results from each strain sensor  20  at a plurality of measurement time points obtained by wireless communication unit  110 . 
     More specifically, generation unit  120  generates the two-dimensional data based on the sensor measurement values sx, sy, and sr stored in storage unit  170  by wireless communication unit  110 . 
       FIG.  5    is a perspective view schematically showing the cutting tool according to the embodiment of the present disclosure. Referring to  FIG.  5   , when cutting is performed by cutting tool  101 , a load, that is, a cutting force F [N], is applied from the cutting object to the cutting edge in a cutting force exertion plane  18  which is a plane perpendicular to rotation axis  17  and which passes through the cutting edge of insert  14 . 
     For example, generation unit  120  generates two-dimensional data indicating a load Fx in the X direction and a load Fy in the Y direction received by cutting tool  101  in cutting force exertion plane  18  based on the sensor measurement values sx, sy, and sr. 
     More specifically, storage unit  170  stores conversion formulas for converting the sensor measurement values sx, sy, and sr into the loads Fx, Fy, and Fz. For example, these conversion formulas are prepared in advance using the techniques described in PTL 3 and PTL 4, etc. More specifically, these conversion formulas are conversion matrices created in advance based on the sensor measurement values sx, sy, and sr obtained when a known load is applied to cutting tool  101 . 
     Generation unit  120  generates two-dimensional data indicating the loads Fx and Fy based on the sensor measurement values sx, sy, and sr and the conversion matrix in storage unit  170 . Generation unit  120  may be configured to generate the shear strain ε at the position where strain sensor  20 A is provided and the two-dimensional data indicating the shear strain ε at the position where the strain sensor  20 B is provided, based on the sensor measurement values sx, sy, and sr. 
     Generation unit  120  generates a plurality of pieces of two-dimensional data in a target period T based on a plurality of sensor measurement values sx, sy, and sr in the target period T starting from time (P×m) at a generation timing according to a generation cycle P. Here, m is a positive integer. The generation cycle P may be the same as the target period T, and each target period T may be continuous. In addition, the generation cycle P may be shorter than the target period T, and each target period T may partially overlap each other. Further, the generation cycle P may be longer than the target period T, and each target period T may be intermittently provided. 
     For example, generation unit  120  generates the measurement data MD including two-dimensional data corresponding to a plurality of measurement time points in a period required for cutting tool  101  to make a plurality of rotations. More specifically, the target period T is a period required for cutting tool  101  to make a plurality of rotations. 
     Generation unit  120  generates the measurement data MD composed of a plurality of pieces of two-dimensional data for each target period T at a generation timing according to the generation cycle P, and stores the generated measurement data MD in storage unit  170  in association with the target period T. 
       FIGS.  6  to  8    are diagram showing examples of measurement data generated by the generation unit in the processing apparatus according to the embodiment of the present disclosure.  FIGS.  6  to  8    show the measurement data MD generated by generation unit  120  when cutting is performed by setting a radial direction cutting amount ae to A 1 , A 2 , and A 3 , respectively, using cutting tool  101  having “4” blades, on a two-dimensional coordinate C 1  in which the vertical axis represents the load Fy [N], the horizontal axis represents the load Fx [N], and the origin corresponds to rotation axis  17 . Here, A 1 &lt;A 2 &lt;A 3 . 
     Referring to  FIGS.  6  to  8   , a two-dimensional shape SMD indicated by the measurement data MD generated by generation unit  120  becomes closer to a circle as a radial direction cutting amount ae at the time of cutting is larger. This is because, when cutting tool  101  having the same tool diameter is used, the number of inserts  14  simultaneously acting on the object to be cut, that is, the number of simultaneously acting blade increases as the radial direction cutting amount ae during cutting increases. 
     Specifically, for example, when cutting is performed with the radial cutting amount ae set to A 1 , the number of simultaneously acting blades is always one. In this case, as shown in  FIG.  6   , the measurement data MD generated by generation unit  120  indicates a substantially cross-shaped two-dimensional shape SMD corresponding to the number of blades. On the other hand, for example, when cutting is performed with the radial cutting amount ae set to A 3 , the number of simultaneously acting blades is always two or three. In this case, as shown in  FIG.  8   , the measurement data MD generated by generation unit  120  indicates the two-dimensional shape SMD having a substantially circular shape. As described above, the measurement data MD generated by generation unit  120  indicates the two-dimensional shape SMD corresponding to the cutting condition such as the radial cutting amount ae. 
     For example, generation unit  120  generates the measurement data MD in which the rotation angle of two pieces of two-dimensional data adjacent to each other around rotation axis  17  is 5° or less. More specifically, the rotation angle about the origin of two of pieces two-dimensional data adjacent to each other in the two-dimensional coordinate C 1  is 5° or less. The rotation angle is preferably 2° or less, and more preferably 1° or less. 
       FIGS.  9  to  11    are diagrams showing other examples of measurement data generated by the generation unit in the processing apparatus according to the embodiment of the present disclosure.  FIGS.  9  to  11    show the measurement data MD generated by generation unit  120  on the two-dimensional coordinate C 1  when cutting is performed by setting the radial direction cutting amount ae to B 1 , B 2 , and B 3 , respectively, using cutting tool  101  having “6” blades. Here, B 1 &lt;B 2 &lt;B 3 . 
     Referring to  FIGS.  9  to  11   , similarly to  FIGS.  6  to  8   , the two-dimensional shape SMD indicated by the measurement data MD generated by generation unit  120  becomes closer to a circle as the radial direction cutting amount ae at the time of cutting is larger. 
     Referring to  FIGS.  9  and  10   , the measurement data MD generated by generation unit  120  indicates the two-dimensional shape SMD having a substantially star-shaped hexagonal shape corresponding to the number of blades. In this way, the measurement data MD generated by generation unit  120  indicates the two-dimensional shape SMD corresponding to the shape of cutting tool  101  such as the number of blades. 
     &lt;Calculation Data Obtaining Unit&gt; 
     Calculation data obtaining unit  130  obtains a calculation data CD including a plurality of pieces of two-dimensional data related to loads in two directions in a plane perpendicular to rotation axis  17  at a plurality of time points during cutting, which are calculated based on the shape of cutting tool  101 . 
     More specifically, calculation data obtaining unit  130  obtains the calculation data CD including a plurality of pieces of two-dimensional data indicating a cutting area vector Vd in cutting force exertion plane  18  calculated in advance by simulation using the shape of cutting tool  101  and the cutting condition. 
       FIGS.  12  to  14    are diagrams showing examples of calculation data obtained by the calculation data obtaining unit in the processing apparatus according to the embodiment of the present disclosure.  FIGS.  12  to  14    show the calculation data CD indicating the cut area vector Vd when cutting is performed under the same cutting conditions using same cutting tool  101  as when the measurement data MD shown in  FIGS.  6  to  8    is generated, on a two-dimensional coordinate C 2  in which the vertical axis represents a cut area Sy [mm{circumflex over ( )}2] in the Y-direction, the horizontal axis represents a cut area Sx [mm{circumflex over ( )}2] in the X-direction, and the origin corresponds to rotation axis  17 . Here, “a{circumflex over ( )}b” means that a raised to the power of b. 
     Referring to  FIGS.  12  to  14   , a two-dimensional shape SCD indicated by the calculation data CD obtained by calculation data obtaining unit  130  becomes closer to a circle as the radial direction cutting amount ae at the time of cutting is larger, similarly to the two-dimensional shape SMD indicated by the measurement data MD in  FIGS.  6  to  8   . Referring to  FIG.  12   , the calculation data CD obtained by calculation data obtaining unit  130  shows the two-dimensional shape SCD having a substantially cross shape corresponding to the number of blades, similarly to the measurement data MD shown in  FIG.  6   . 
     For example, calculation data obtaining unit  130  obtains the calculation data CD in which a rotation angle between two pieces of two-dimensional data adjacent to each other around rotation axis  17  is 2° or less. More specifically, a rotation angle about the origin of two pieces of two-dimensional data adjacent to each other in the two-dimensional coordinate C 2  is 2° or less. For example, calculation data obtaining unit  130  may obtain the calculation data CD which is a set of continuous two-dimensional data. 
       FIGS.  15  to  17    are diagrams showing other examples of calculation data obtained by the calculation data obtaining unit in the processing apparatus according to the embodiment of the present disclosure.  FIGS.  15  to  17    show, on the two-dimensional coordinate C 2 , the calculation data CD indicating the cutting-area vectors Vd when cutting is performed under the same cutting conditions using same cutting tool  101  as that used when the measurement data MD shown in  FIGS.  9  to  11    are generated. 
     Referring to  FIGS.  15  to  17   , the two-dimensional shape SCD indicated by the calculation data CD obtained by calculation data obtaining unit  130  becomes closer to a circle as the radial direction cutting amount ae at the time of cutting is larger, similarly to the two-dimensional shape SMD indicated by the measurement data MD in  FIGS.  9  to  11   . Referring to  FIGS.  15  and  16   , the calculation data CD obtained by calculation data obtaining unit  130  indicates the two-dimensional shape SCD having a substantially star-shaped hexagonal shape corresponding to the number of blades, similarly to the measurement data MD shown in  FIGS.  9  and  10   . 
     For example, storage unit  170  stores a plurality of pieces of the calculation data CD. Calculation data obtaining unit  130  obtains the calculation data CD from storage unit  170 . 
       FIG.  18    is a diagram showing an example of a database in the storage unit of the processing apparatus according to the embodiment of the present disclosure. Referring to  FIG.  18   , storage unit  170  stores a database DB indicating a correspondence relationship between the shape and cutting condition of cutting tool  101  and the calculation data CD. 
     More specifically, the administrator of processing system  301  calculates a cutting area vector Vch in cutting force exertion plane  18  for each insert  14  at the time of cutting using cutting tool  101  using the above-described shape information and the condition information and an instantaneous cutting force model described in Non-PTL 1 or the like. Then, the administrator calculates the total sum of the calculated cutting area vectors Vch for each insert  14  as the cutting area vector Vd. The administrator calculates the cutting area vector Vd for each shape and cutting condition of cutting tool  101 , generates the database DB indicating the correspondence relationship between the calculation data CD indicating the calculated cutting area vector Vd and the shape and cutting condition of cutting tool  101 , and stores the generated database DB in storage unit  170 . 
     For example, processing unit  140  outputs a calculation data request indicating that the calculation data CD in the target period T is to be obtained to calculation data obtaining unit  130 . 
     Calculation data obtaining unit  130  receives the calculation data request from processing unit  140 , and obtains shape information indicating the shape of cutting tool  101  used for cutting in the target period T from storage unit  170 . Then, calculation data obtaining unit  130  obtains a plurality of pieces of the calculation data CD corresponding to the shape indicated by the shape information from the database DB in storage unit  170 . 
     As an example, calculation data obtaining unit  130  obtains shape information indicating that the shape of cutting tool  101  used for cutting in the target period T is a shape a from storage unit  170 . Then, calculation data obtaining unit  130  obtains calculation data CDaw, CDax, CDay, CDaz, . . . corresponding to the shape information from the database DB in storage unit  170 . 
     For example, calculation data obtaining unit  130  obtains the calculation data CD calculated further based on the cutting condition using cutting tool  101 . More specifically, calculation data obtaining unit  130  receives a calculation data request from processing unit  140 , and obtains shape information indicating the shape of cutting tool  101  used for cutting in the target period T and the condition information indicating the cutting condition in the target period T from storage unit  170 . Then, calculation data obtaining unit  130  obtains one piece of calculation data CD corresponding to the shape information and the condition information from the database DB in storage unit  170 . 
     As an example, calculation data obtaining unit  130  obtains shape information indicating that the shape of cutting tool  101  used for cutting in the target period T is a shape b and condition information indicating that the cutting condition in the target period T is a condition x from storage unit  170 . Then, calculation data obtaining unit  130  obtains calculation data CDbx corresponding to the shape information and the condition information from the database DB in storage unit  170 . 
     Calculation data obtaining unit  130  outputs the obtained one or more pieces of the calculation data CD to processing unit  140  as a response to the calculation data request received from processing unit  140 . 
     &lt;Processing Unit&gt; 
     Processing unit  140  performs a determination process related to cutting using cutting tool  101  based on the two-dimensional shape SMD indicated by the measurement data MD generated by generation unit  120 . For example, processing unit  140  may perform a determination process regarding cutting using cutting tool  101  further based on the two-dimensional shape SCD indicated by the calculation data CD obtained by calculation data obtaining unit  130 . 
     More specifically, when generation unit  120  stores the measurement data MD in the target period T in storage unit  170 , processing unit  140  outputs a calculation data request indicating that the calculation data CD in the target period T is to be obtained to calculation data obtaining unit  130 . As described above, calculation data obtaining unit  130  outputs one or more pieces of the calculation data CD to processing unit  140  as a response to the calculation data request. Processing unit  140  receives one or more pieces of the calculation data CD in the target period T from calculation data obtaining unit  130 , obtains measurement data MD in the target period T in storage unit  170 , and performs a determination process based on the two-dimensional shape SCD indicated by one or more pieces of calculation data CD received from calculation data obtaining unit  130  and the two-dimensional shape SMD indicated by the obtained measurement data MD. 
     For example, processing unit  140  calculates a degree of difference D 1  between the two-dimensional shape SCD and the two-dimensional shape SMD using an image processing technology, and performs a determination process based on the calculated degree of difference D 1 . Here, as the degree of difference D 1  is higher, a degree of similarity between the two-dimensional shape SCD and the two-dimensional shape SMD is lower, and as the degree of difference D 1  is lower, the degree of similarity between the two-dimensional shape SCD and the two-dimensional shape SMD is higher. 
       FIG.  19    is a diagram showing an example of a method of calculating the degree of difference by the processing unit in the processing apparatus according to the embodiment of the present disclosure. Referring to  FIG.  19   , processing unit  140  generates a binary image GMD in which a plot of the two-dimensional data in the measurement data MD in the target period T and a region surrounded by the two-dimensional shape SMD indicated by the measurement data MD are white and a region outside the two-dimensional shape SMD is black. In addition, processing unit  140  generates a binary image GCD in which a region surrounded by the two-dimensional shape SCD indicated by the calculation data CD in the target period T received from calculation data obtaining unit  130  is white and a region outside the two-dimensional shape SCD is black. 
     Processing unit  140  calculates areas of portions where colors do not match in the binary image GMD and the binary image GCD as the degree of difference D 1 . Specifically, processing unit  140  calculates, as the degree of difference D 1 , XORsum, which is a sum of exclusive ORs XOR of corresponding pixels in the binary image GMD and the binary image GCD. 
     For example, processing unit  140  performs an image adjustment process of adjusting the magnification of the size of the white region in the binary image GCD and the phases around the center so that the sum XORsum calculated based on the binary image GMD and the binary image GCD becomes smaller, and determines the smallest value of the calculated sum XORsum as the degree of difference D 1 . 
     Here, the calculation data CD does not indicate the absolute value of the cutting force, but indicates the cutting area vector Vd as described above. Thus, the size of the calculation data CD on the two-dimensional coordinate C 2  is different from the size of the measurement data MD on the two-dimensional coordinate C 1 . Further, the phases of the calculation data CD around the origin of the two-dimensional coordinates C 2  may be different from the phases of the measurement data MD around the origin of the two-dimensional coordinates C 1 . 
     On the other hand, according to the configuration in which processing unit  140  performs the image adjustment processing and determines the smallest value of the calculated total values XORsum as the degree of difference D 1 , the degree of difference D 1  can be calculated at least as an indicator indicating the difference between the geometric shape of the calculation data CD and the geometric shape of the measurement data MD. 
     (Condition Determination Process) 
     Processing unit  140  may perform a condition determination process that is a determination process regarding a cutting condition of cutting using cutting tool  101 . 
     More specifically, processing unit  140  receives, from calculation data obtaining unit  130 , a plurality of pieces of the calculation data CD in the target period T obtained by calculation data obtaining unit  130  based on the shape information. Processing unit  140  calculates the degree of difference D 1  between the two-dimensional shape SCD indicated by the plurality of pieces of the calculation data CD and the two-dimensional shape SMD indicated by the measurement data MD in the target period T respectively, and estimates the cutting condition using cutting tool  101  based on each calculated degree of difference D 1 . 
       FIG.  20    is a diagram showing an example of the condition determination process by the processing unit in the processing apparatus according to the embodiment of the present disclosure.  FIG.  20    shows the measurement data MD and calculation data CDaw, CDax, CDay, and CDaz. 
     Referring to  FIG.  20   , for example, processing unit  140  receives the calculation data CDaw, CDax, CDay, and CDaz from calculation data obtaining unit  130  as the plurality of pieces of the calculation data CD in the target period T. Processing unit  140  calculates the degree of difference D 1  between the two-dimensional shape SMD indicated by the measurement data MD in the target period T and each two-dimensional shape SCD indicated by the calculation data CDaw, CDax, CDay, and CDaz received from calculation data obtaining unit  130  using the above-described calculation method. 
     For example, processing unit  140  specifies a similar calculation data CDsim that is the calculation data CD corresponding to the two-dimensional shape SCD in which the degree of difference D 1  from the two-dimensional shape SMD has the smallest value and is equal to or less than a predetermined threshold value Tha. For example, processing unit  140  specifies a calculation data CDay as the similar calculation data CDsim. 
     Referring again to  FIG.  18   , processing unit  140  obtains the cutting condition corresponding to the identified similar calculation data CDsim from the database DB in storage unit  170 . Specifically, processing unit  140  obtains a cutting condition y corresponding to the calculation data CDay which is the similar calculation data CDsim. Then, processing unit  140  estimates the actual cutting condition in the cutting based on the obtained cutting condition y. 
     For example, processing unit  140  estimates that an axial direction cutting amount in an actual cutting condition is an axial direction cutting amount apy indicated by the cutting condition y. Further, for example, processing unit  140  estimates that an radial direction cutting amount in an actual cutting condition is an radial direction cutting amount aey indicated by the cutting condition y. Processing unit  140  stores the estimation information indicating an estimation result in storage unit  170  in association with the target period T. 
     On the other hand, for example, when all the calculated degrees of difference D 1  are larger than the threshold value Tha, processing unit  140  determines that the similar calculation data CDsim does not exist. In this case, processing unit  140  determines that an abnormality has occurred in cutting, and stores determination information indicating the determination result in storage unit  170  in association with the target period T. 
     (Anomaly Determination Process) 
     Processing unit  140  performs an abnormality determination process, which is a determination process regarding an abnormality of cutting using cutting tool  101 , based on a result of comparing a two-dimensional shape SMD 1  indicated by measurement data MD 1  including a plurality of pieces of two-dimensional data corresponding to a plurality of measurement time points in a target period T 1  with a two-dimensional shape SCD 1  indicated by a calculation data CD 1  calculated based on a cutting condition in the target period T 1 . The target period T 1  is an example of a first period. The measurement data MD 1  is an example of first measurement data. The calculation data CD 1  is an example of first calculation data. 
     For example, processing unit  140  may perform the abnormality determination process based on the two-dimensional shape SCD indicated by the different calculation data CD for each cutting condition. 
     More specifically, processing unit  140  receives, from calculation data obtaining unit  130 , one calculation data CD 1  in the target period T 1  obtained by calculation data obtaining unit  130  based on the shape information and the condition information. Processing unit  140  calculates the degree of difference D 1  between the two-dimensional shape SCD 1  indicated by the calculation data CD 1  and the two-dimensional shape SMD 1  indicated by the measurement data MD 1  in the target period T 1 , and detects an abnormality related to the setting of cutting tool  101 , an abnormality related to the object to be cut, and various abnormalities such as loss and wear of insert  14  based on the calculated degree of difference D 1 . For example, processing unit  140  compares the calculated degree of difference D 1  with a predetermined threshold value Th 1 , and detects various abnormalities based on the comparison result. 
       FIGS.  21  and  22    are diagrams showing examples of measurement data generated by the generation unit in the processing apparatus according to the embodiment of the present disclosure.  FIG.  21    shows the measurement data MD 1  in a target period T 1 A, which is the target period T 1  in a state where no loss of insert  14  occurs, on the two-dimensional coordinate C 1 .  FIG.  22    shows the measurement data MD 1  in a target period T 1 B, which is the target period T 1  after the target period T 1 A in a state where loss of insert  14  has occurred, on the two-dimensional coordinate C 1 . Referring to  FIGS.  21  and  22   , before and after loss of insert  14  occurs, a slight change occurs in the two-dimensional shape SMD 1  indicated by the measurement data MD 1  generated by generation unit  120 . 
       FIGS.  23  and  24    are diagrams showing examples of calculation results of degrees of difference by the processing unit in the processing apparatus according to the embodiment of the present disclosure.  FIG.  23    shows a calculation result of a degree of difference D 1 A which is the degree of difference D 1  between the two-dimensional shape SMD 1  indicated by the measurement data MD 1  and the two-dimensional shape SCD 1  indicated by the calculation data CD 1  in the target period T 1 A shown in  FIG.  21   .  FIG.  24    shows a calculation result of a degree of difference D 1 B which is the degree of difference D 1  between the two-dimensional shape SMD 1  indicated by the measurement data MD 1  and the two-dimensional shape SCD 1  indicated by the calculation data CD 1  in the target period T 1 B shown in  FIG.  22   . 
     Referring to  FIG.  23   , processing unit  140  calculates the degree of difference D 1 A and compares the calculated degree of difference D 1 A with the threshold value Th 1 . For example, the degree of difference D 1 A is 765.4 and the threshold value Th 1  is 900. Since the degree of difference D 1 A is equal to or less than the threshold value Th 1 , processing unit  140  determines that no abnormality has occurred in cutting. 
     Referring to  FIG.  24   , processing unit  140  calculates the difference D 1 B and compares the calculated difference D 1 B with the threshold value Th 1 . For example, the difference D 1 B is 991.9. Since the degree of difference D 1 B is larger than the threshold value Th 1 , processing unit  140  determines that an abnormality has occurred. 
     Processing unit  140  generates comparison information CR 1  indicating a result of comparing the degree of difference D 1  and the threshold value Th 1 , and stores the generated comparison information CR 1  in storage unit  170  in association with the target period T 1 . 
     (Other Example 1 of Abnormality Determination Process) 
     Processing unit  140  performs an abnormality determination process further based on a result of comparing a two-dimensional shape SMD 2  indicated by the measurement data MD 2  including a plurality of pieces of two-dimensional data corresponding to a plurality of measurement time points in a target period T 2  and the two-dimensional shape SMD 1  indicated by the measurement data MD 1 . The target period T 2  is an example of a second period. The target period T 2  is a period different from the target period T 1 , and is, for example, a period before the target period T 1 . The measurement data MD 2  is an example of second measurement data. 
     More specifically, when the measurement data MD 1  in the target period T 1  is stored in storage unit  170  by generation unit  120 , processing unit  140  calculates a degree of difference D 2  between the two-dimensional shape SMD 1  indicated by the measurement data MD 1  and the two-dimensional shape SMD 2  indicated by the measurement data MD 2  in the target period T 2  in storage unit  170  using an image processing technology. 
     More specifically, processing unit  140  generates a binary image GMD 1  based on the two-dimensional shape SMD 1  and generates a binary image GMD 2  based on the two-dimensional shape SMD 2  in the same manner as the method of calculating the degree of difference D 1 . Then, processing unit  140  calculates areas of portions in which colors do not match in the binary image GMD 1  and the binary image GMD 2  as the degree of difference D 2 . Here, as the degree of difference D 2  is higher, the similarity between the two-dimensional shape SMD 1  and the two-dimensional shape SMD 2  is lower, and as the degree of difference D 2  is lower, the similarity between the two-dimensional shape SMD 1  and the two-dimensional shape SMD 2  is higher. 
     For example, processing unit  140  detects a change in the cutting condition, an abnormality related to the object to be cut, and various abnormalities such as loss and wear of insert  14  based on the degree of difference D 2  between the two-dimensional shape SMD 1  and the two-dimensional shape SMD 2 . 
     More specifically, processing unit  140  compares the calculated degree of difference D 2  with a predetermined threshold value Th 2 . In a case where the degree of difference D 2  is equal to or less than the threshold value Th 2 , processing unit  140  determines that no abnormality has occurred in the cutting. On the other hand, in a case where the degree of difference D 2  is larger than the threshold value Th 2 , processing unit  140  determines that an abnormality has occurred. 
     In this way, with the configuration in which the abnormality determination process based on the degree of difference D 2  is performed, it is possible to detect an abnormality based on a temporal change in the measurement data MD. Further, with the configuration in which the abnormality determination process based on the degree of difference D 2  is performed in addition to the abnormality determination process based on the degree of difference D 1 , for example, in a case where cutting is continuously performed even after an abnormality is detected in the abnormality determination process based on the degree of difference D 1  in the target period T 2 , it is possible to detect further occurrence of an abnormality, expansion of the abnormality, and the like. 
     Processing unit  140  generates comparison information CR 2  indicating a comparison result between the degree of difference D 2  and the threshold value Th 2 , and stores the generated comparison information CR 2  in storage unit  170  in association with the target period T 1 . 
     (Another Example 2 of Abnormality Determination Process) 
     For example, processing unit  140  performs the abnormality determination process further based on a result of comparing the two-dimensional shape SMD 2  indicated by the measurement data MD 2  including a plurality of pieces of two-dimensional data corresponding to a plurality of measurement time points in the target period T 2  and a two-dimensional shape SCD 2  indicated by a calculation data CD 2  calculated based on the cutting condition in the target period T 2 . The calculation data CD 2  is an example of second calculation data. 
     More specifically, when pieces of the comparison information CR 1  and CR 2  in the target period T 1  are generated, processing unit  140  obtains the comparison information CR 1  in the target period T 2  from storage unit  170 , and performs the abnormality determination process based on pieces of the comparison information CR 1  and CR 2  in the target period T 1  and the comparison information CR 1  in the target period T 2 . 
     In addition, for example, the abnormality determination process is performed further based on a result of comparing the cutting condition in the target period T 1  and the cutting condition in the target period T 2 . 
     More specifically, processing unit  140  obtains the cutting condition in the target period T 1  and the cutting condition in the target period T 2  from storage unit  170 , and compares the obtained cutting conditions. Specifically, processing unit  140  determines whether or not the cutting condition in the target period T 1  matches the cutting condition in the target period T 2 . Processing unit  140  generates comparison information CR 3  indicating a result of comparing the cutting condition in the target period T 1  and the cutting condition in the target period T 2 , and stores the generated comparison information CR 3  in storage unit  170  in association with the target period T 1 . 
     When pieces of the comparison information CR 1 , CR 2 , and CR 3  in the target period T 1  are generated, processing unit  140  obtains the comparison information CR 1  in the target period T 2  from storage unit  170 , and performs the abnormality determination process based on pieces of the comparison information CR 1 , CR 2 , and CR 3  in the target period T 1 , and the comparison information CR 1  in the target period T 2 . 
       FIG.  25    is a diagram showing an example of a result of the abnormality determination process by the processing unit in the processing apparatus according to the embodiment of the present disclosure.  FIG.  25    shows the correspondence between the pattern of each comparison result indicated by pieces of the comparison information CR 1 , CR 2 , and CR 3 , presence or absence of abnormality, and the cause of abnormality. In  FIG.  25   , “Found” indicates that the item is estimated to be the cause of the abnormality. 
     Referring to  FIG.  25   , processing unit  140  determines that an abnormality has occurred when the degree of difference D 1  in the target period T 1  is larger than the threshold value Th 1 , the degree of difference D 2  in the target period T 1  is larger than the threshold value Th 2 , the degree of difference D 1  in the target period T 2  is equal to or less than the threshold value Th 1 , and the cutting condition in the target period T 1  is equal to the cutting condition in the target period T 2 , as shown in pattern C, for example. In addition, in this case, processing unit  140  estimates that a defect of the workpiece, loss of the cutting edge, and wear of the cutting edge are causes of the abnormality. This is because the fact that the similarity between the two-dimensional shape SMD and the two-dimensional shape SCD is high in the past target period T 2  while the similarity between the two-dimensional shape SMD and the two-dimensional shape SCD is low in the current target period T 1  means that there is a possibility that loss or the like of the cutting edge has occurred in the period between the target period T 2  and the target period T 1  or a defective portion of the workpiece has been cut in the target period T 1 . 
     In addition, for example, as shown in a pattern F, when the degree of difference D 1  in the target period T 1  is equal to or less than the threshold value Th 1 , the degree of difference D 2  in the target period T 1  is larger than the threshold value Th 2 , the degree of difference D 1  in the target period T 2  is equal to or less than the threshold value Th 1 , and the cutting condition in the target period T 1  does not match with the cutting condition in the target period T 2 , processing unit  140  determines that no abnormality has occurred. This is because the cutting conditions do not match with each other in the target periods T 1  and T 2 , and thus it is not a problem that the degree of difference D 2  is larger than the threshold value Th 2 . On the other hand, a high degree of similarity between the two-dimensional shape SMD and the two-dimensional shape SCD in the target periods T 1  and T 2  means that normal cutting is performed. 
     (Display Process) 
     Processing unit  140  performs a process of displaying the two-dimensional shape SMD indicated by the measurement data MD generated by generation unit  120 . For example, processing unit  140  performs a process of further displaying the two-dimensional shape SCD indicated by the calculation data CD obtained by calculation data obtaining unit  130 . 
       FIG.  26    is a diagram showing an example of a display screen displayed on the display unit in the processing apparatus according to the embodiment of the present disclosure. Referring to  FIG.  26   , processing unit  140  performs a process of displaying a display screen DS including the calculation data CD received from calculation data obtaining unit  130  and the measurement data MD obtained from storage unit  170  on display unit  160 . 
     More specifically, processing unit  140  performs a process of displaying the display screen DS including the calculation data CD 2  in the target period T 2  which is the target period T immediately after the start of the cutting, the measurement data MD 2  in the target period T 2 , the calculation data CD 1  in the target period T 1  which is the latest target period T, and the measurement data MD 1  in the target period T 1  on display unit  160 . 
     For example, processing unit  140  continues to display the calculation data CD 2  and the measurement data MD 2  until cutting ends, and updates the calculation data CD 1  and the measurement data MD 1  on the display screen DS with the measurement data MD and the calculation data CD of a new target period T every time generation unit  120  stores the measurement data MD of the new target period T in storage unit  170 . 
     For example, processing unit  140  performs a process of further displaying information indicating the similarity between the two-dimensional shape SMD indicated by the measurement data MD and the two-dimensional shape SCD indicated by the calculation data CD. More specifically, processing unit  140  performs a process of displaying, on display unit  160 , the display screen DS including a graph G 1  indicating a temporal change in the degree of difference D 1  as information indicating the degree of similarity between the two-dimensional shape SMD and the two-dimensional shape SCD. Further, for example, processing unit  140  performs a process of displaying the display screen DS including the respective comparison results indicated by pieces of the comparison information CR 1 , CR 2 , and CR 3  on display unit  160 . 
     In addition, for example, processing unit  140  performs a process of further displaying an estimation result of the cutting condition using cutting tool  101 . More specifically, processing unit  140  periodically obtains condition information from storage unit  170 , for example, and performs a process of displaying, on display unit  160 , the display screen DS including a graph G 2  indicating a temporal change in the axial direction cutting amount ap indicated by the obtained condition information and a graph G 3  indicating a temporal change in the radial direction cutting amount ae indicated by the obtained condition information. Then, processing unit  140  displays the axial direction cutting amount apy indicated by the cutting condition y, which is the estimated cutting condition, on the graph G 2  as the estimation result indicated by the estimation information in storage unit  170 . Further, processing unit  140  displays the radial direction cutting amount aey indicated by the cutting condition y on the graph G 3  as the estimation result indicated by the estimation information in storage unit  170 . 
     Thus, the user can compare the cutting condition estimated based on the measurement data MD and the calculation data CD with the preset cutting condition. Therefore, when the set cutting condition exceeds the range of the estimated cutting condition, the user can determine that some abnormality such as cutting performed under a cutting condition different from the set cutting condition has occurred. 
     More specifically, processing unit  140  further displays a threshold value ThapH, which is a value obtained by adding a predetermined value to the axial direction cutting amount apy, and a threshold value ThapL, which is a value obtained by subtracting the predetermined value from the axial direction cutting amount apy, on the graph G 2 . In addition, processing unit  140  further displays a threshold value ThaeH, which is a value obtained by adding a predetermined value to the radial direction cutting amount aey, and a threshold value ThaeL, which is a value obtained by subtracting the predetermined value from the radial direction cutting amount aey, on the graph G 3 . Thus, when the axial direction cutting amount ap is larger than the threshold value ThapH or the axial direction cutting amount ap is less than the threshold value ThapL, the user can determine that some abnormality has occurred. Further, when the radial direction cutting amount ae is larger than the threshold value ThaeH or the radial direction cutting amount ae is less than the threshold value ThaeL, the user can determine that some abnormality has occurred. 
     [Flow of Operation] 
     Each device in the cutting system according to the embodiment of the present disclosure is provided with a computer including a memory, and an arithmetic processing unit such as a CPU in the computer reads a program including a part or all of each step of the following flowcharts and sequences from the memory and executes the program. The programs of these devices are distributed in a state of being stored in recording media such as an HDD (Hard Disk Drive), a CD-ROM (Compact Disc Read Only Memory), a DVD-ROM (Digital Versatile Disk Read Only Memory), and a semiconductor memory. The programs of the plurality of devices can be installed from the outside. For example, the programs of the plurality of devices can be installed from the recording medium. Further, for example, the programs of the plurality of devices can be downloaded and installed from a predetermined server or the like via a network typified by an electric communication line, a wireless communication line, a wired communication line, and the Internet. In addition, for example, the programs of the plurality of devices can be downloaded from a predetermined server or the like by data broadcasting or the like and installed. 
       FIG.  27    is a flowchart defining an example of an operation procedure when the processing apparatus in the cutting system according to the embodiment of the present disclosure obtains various kinds of information and sensor measurement values. Referring to  FIG.  27   , at first, processing apparatus  201  obtains shape information and condition information from the CAM before starting cutting (step S 102 ). 
     Next, after the start of cutting, processing apparatus  201  waits for a wireless signal from wireless communication device  23  in cutting tool  101  (NO in step S 104 ), and upon receiving the wireless signal (YES in step S 104 ), obtains the sensor measurement values sx, sy, and sr and the identification information from the received wireless signal (step S 106 ). Next, processing apparatus  201  stores the obtained sensor measurement values sx, sy, and sr and the identification information in storage unit  170  (step S 108 ), and waits for a new wireless signal from wireless communication device  23  in cutting tool  101  (NO in step S 104 ). 
       FIG.  28    is a flowchart defining an example of an operational procedure when the processing apparatus in the cutting system performs an abnormality determination process according to the embodiment of the present disclosure. Referring to  FIG.  28   , at first, processing apparatus  201  waits for a generation timing according to the generation cycle P (NO in step S 202 ), and when the generation timing arrives (YES in step S 202 ), generates measurement data MD 1  composed of a plurality of pieces of two-dimensional data in the target period T 1  based on a plurality of sensor measurement values sx, sy, and sr in the target period T 1  (step S 204 ). 
     Next, processing apparatus  201  obtains calculation data CD 1  in the target period T 1  (step S 206 ). 
     Next, processing apparatus  201  calculates the degree of difference D 1  between the two-dimensional shape SMD 1  indicated by the measurement data MD 1  in the target period T 1  and the two-dimensional shape SCD 1  indicated by the calculation data CD 1  in the target period T 1 . In addition, processing apparatus  201  calculates the degree of difference D 2  between the two-dimensional shape SMD 1  indicated by the measurement data MD 1  in the target period T 1  and the two-dimensional shape SMD 2  indicated by the measurement data MD 2  in the past target period T 2  (step S 208 ). 
     Next, processing apparatus  201  compares the calculated degree of difference D 1  with the threshold value Th 1 . Further, processing apparatus  201  compares the calculated degree of difference D 2  with the threshold value Th 2  (step S 210 ). 
     Next, processing apparatus  201  performs an abnormality determination process based on the result of comparing the degree of difference D 1  in the target period T 1  and the threshold value Th 1 , the result of comparing the degree of difference D 2  in the target period T 1  and the threshold value Th 2 , the result of comparing the degree of difference D 1  in the past target period T 2  and the threshold value Th 1 , and the result of comparing the cutting condition in the target period T 1  and the cutting condition in the target period T 2  (step S 212 ). 
     Next, processing apparatus  201  performs a process of displaying, on display unit  160 , the display screen DS including the two-dimensional shape SCD 2  indicated by the calculation data CD 2  in the target period T 2  and the two-dimensional shape SMD 2  indicated by the measurement data MD 2 , the two-dimensional shape SCD 1  indicated by the calculation data CD 1  in the target period T 1  and the two-dimensional shape SMD 1  indicated by the measurement data MD 1 , and the graph G 1  indicating a temporal change in the degree of difference D 1  (step S 214 ). 
     Next, processing apparatus  201  waits for a new generation timing (NO in step S 202 ). 
       FIG.  29    is a flowchart defining an example of an operation procedure when the processing apparatus in the cutting system according to the embodiment of the present disclosure performs a condition estimation process. Referring to  FIG.  29   , at first, processing apparatus  201  waits for a generation timing according to the generation cycle P (NO in step S 302 ), and when the generation timing arrives (YES in step S 302 ), generates measurement data MD 1  composed of a plurality of pieces of two-dimensional data in the target period T 1  based on a plurality of sensor measurement values sx, sy, and sr in the target period T 1  (step S 304 ). 
     Next, processing apparatus  201  obtains the calculation data CDaw, CDax, CDay, and CDaz as the calculation data CD 1  in the target period T 1  (step S 306 ). 
     Next, processing apparatus  201  calculates the degree of difference D 1  between the two-dimensional shape SMD 1  indicated by the measurement data MD 1  in the target period T 1  and the two-dimensional shape SCD indicated by the calculation data CDaw, CDax, CDay, and CDaz respectively (step S 308 ). 
     Next, processing apparatus  201  specifies, for example, the calculation data CDay as the similar calculation data CDsim among a plurality of the calculated degrees of difference D 1  (step S 310 ). 
     Next, processing apparatus  201  estimates the actual cutting condition in cutting based on the cutting condition y corresponding to the calculation data CDay which is the similar calculation data CDsim (Step S 312 ). 
     Next, processing apparatus  201  performs a process of displaying the display screen DS including the graph G 2  indicating the axial cutting amount apy indicated by the cutting condition y which is the estimated cutting condition and the graph G 3  indicating the radial cutting amount aey indicated by the cutting condition y on display unit  160  (step S 314 ). 
     Next, processing apparatus  201  waits for a new generation timing (NO in step S 302 ). 
       FIG.  30    is a diagram showing an example of a sequence of a determination process and a display process in the cutting system according to the embodiment of the present disclosure. Referring to  FIG.  30   , at first, cutting tool  101  starts cutting (step S 402 ). Next, strain sensor  20  provided in cutting tool  101  starts measurement of the shear strain of shaft part  10  (step S 404 ). Next, cutting tool  101  includes the sensor measurement values sx, sy, and sr based on the analog signal from strain sensor  20  in a wireless signal and transmits the wireless signal to processing apparatus  201  (Step S 406 ). 
     Next, processing apparatus  201  obtains the sensor measurement values sx, sy, sr from the wireless signal received from cutting tool  101 , and generates the measurement data MD in the target period T based on the obtained sensor measurement values sx, sy, sr and the conversion matrix in storage unit  170  (step S 408 ). Next, processing apparatus  201  obtains calculation data CD in the target period T (step S 410 ). Next, processing apparatus  201  performs a determination process based on the two-dimensional shape SMD indicated by the measurement data MD and the two-dimensional shape SCD indicated by the calculation data CD (step S 412 ). Next, processing apparatus  201  performs display process (Step S 414 ). 
     Next, cutting tool  101  transmits new sensor measurement values sx, sy, and sr based on the analog signal from strain sensor  20 , included in a wireless signal, to processing apparatus  201  (step S 416 ). 
     By the way, there is a demand for a technique capable of realizing excellent functions relating to the state of cutting using a cutting tool. 
     For example, PTL 1 describes that an abnormality of a cutting blade is detected based on a result of comparing a two-dimensional shape indicated by two-dimensional data generated in advance based on measurement results from sensors and a two-dimensional shape indicated by two-dimensional data generated based on measurement results from sensors during cutting. However, using the technique described in PTL 1, it is necessary to generate in advance the two-dimensional data corresponding to all cutting tools  101  to be used, and the technique described in PTL 1 is not practical. 
     In addition, using the technique described in PTL 2, a two-dimensional projection view obtained from measurement results from sensors becomes asymmetric due to an influence of a positional deviation in a rotation axis direction of each cutting edge and a radial direction of a shaft, and abnormality or the like of the cutting edge may not be accurately detected. 
     On the other hand, in processing system  301  according to the embodiment of the present disclosure, as described above, with the configuration in which the determination process is performed based on the two-dimensional shape indicated by the measurement data including a plurality of pieces of two-dimensional data generated based on the measurement results from the plurality of sensors and the two-dimensional shape indicated by the calculation data including a plurality of pieces of two-dimensional data calculated based on the shape of the cutting tool, for example, it is possible to perform a determination regarding cutting based on the degree of similarity between the two-dimensional shape of the two-dimensional data to be generated when normal and ideal cutting is performed and the two-dimensional shape of the actually generated two-dimensional data. Therefore, it is possible to realize an excellent function regarding the state of cutting using the cutting tool. 
     Modification 
     In processing apparatus  201  according to the embodiment of the present disclosure, processing unit  140  is configured to calculate the sum XORsum of exclusive ORs XOR for each corresponding pixel in the binary image GMD based on the measurement data MD and the binary image GCD based on the calculation data CD as the degree of difference D 1  between the two-dimensional shape SCD and the two-dimensional shape SMD, but is not limited thereto. Processing unit  140  may be configured to calculate the degree of difference or the degree of similarity between the two-dimensional shape SCD and the two-dimensional shape SMD, instead of the total value XORsum or in addition to the total value XORsum, using an image processing technique such as Average Hash, Perceptual Hash, histogram comparison, feature point matching, template matching, or class classification. 
     In processing system  301  according to the embodiment of the present disclosure, strain sensor  20  is configured to measure the shear strain ε of shaft part  10 , but is not limited thereto. Strain sensor  20  may be configured to measure the strain ε of shaft part  10  in a direction parallel to rotation axis  17 . In this case, for example, generation unit  120  generates the measurement data MD including the two-dimensional data indicating a moment Mx generated by a load in the X direction and a moment My generated by a load in the Y direction in cutting force exertion plane  18  based on the sensor measurement value indicating the vertical strain measured by strain sensor  20 . 
     In addition to strain sensor  20  that measures the shear strain ε, processing system  301  may be configured to include one or more strain sensors  20  that measure the vertical strain. Processing system  301  may be configured to include other sensors such as an acceleration sensor, a speed sensor, and a displacement sensor instead of strain sensor  20  or in addition to strain sensor  20  as the plurality of sensors. In this case, generation unit  120  generates measurement data MD including two-dimensional data indicating acceleration in the X-direction and acceleration in the Y-direction of cutting tool  101  in cutting force exertion plane  18 , measurement data MD including two-dimensional data indicating velocity in the X-direction and velocity in the Y-direction of cutting tool  101  in cutting force exertion plane  18 , or measurement data MD including two-dimensional data indicating displacement in the X-direction and displacement in the Y-direction of cutting tool  101  in cutting force exertion plane  18  based on the measurement result by the sensor. 
     Further, in processing apparatus  201  according to the embodiment of the present disclosure, calculation data obtaining unit  130  is configured to obtain the calculation data CD indicating the cutting area vector Vd calculated in advance, but is not limited thereto. Calculation data obtaining unit  130  may be configured to obtain calculation data CD indicating a load Fx and a load Fy calculated in advance based on information such as a feed rate per tooth of insert  14 , a workpiece, and a rake angle of cutting tool  101 . However, the calculation data CD indicating the cutting area vector Vd can be generated by simpler calculation processing using less information on the shape of cutting tool  101  than the calculation data CD indicating the load Fx and the load Fy. Further, as described above, processing unit  140  can calculate the degree of difference D 1  as an indicator indicating the difference between the geometric shape of the calculation data CD indicating the cutting-area vector Vd and the geometric shape of the measurement data MD. Therefore, with the configuration in which processing apparatus  201  obtains the calculation data CD indicating the cutting area vector Vd and performs the determination process based on the two-dimensional shape SCD indicated by the calculation data CD and the two-dimensional shape SMD indicated by the measurement data MD, it is possible to provide a system that performs the determination process with a simple configuration. 
     In processing apparatus  201  according to the embodiment of the present disclosure, processing unit  140  is configured to perform the abnormality determination process and the condition determination process, but is not limited thereto. Processing unit  140  may be configured not to perform any one of the abnormality determination process and the condition determination process. 
     In processing apparatus  201  according to the embodiment of the present disclosure, processing unit  140  is configured to perform the determination process based on the two-dimensional shape SCD indicated by the different calculation data CD for each cutting condition, but is not limited thereto. Processing unit  140  may be configured to perform the determination process based on the two-dimensional shape SCD indicated by the calculation data CD common to the plurality of cutting conditions. 
     Further, in processing apparatus  201  according to the embodiment of the present disclosure, processing unit  140  is configured to perform the abnormality determination process based on pieces of the comparison information CR 1 , CR 2 , and CR 3  in the target period T 1  and the comparison information CR 1  in the target period T 2 , but is not limited thereto. Processing unit  140  may be configured to perform the abnormality determination process without using at least one of pieces of the comparison information CR 2  and CR 3  in the target period T 1  and the comparison information CR 1  in the target period T 2 . 
     In processing apparatus  201  according to the embodiment of the present disclosure, generation unit  120  is configured to generate the measurement data MD including two-dimensional data corresponding to a plurality of measurement time points in a period required for cutting tool  101  to rotate a plurality of times, but is not limited thereto. Generation unit  120  may be configured to generate the measurement data MD including two-dimensional data corresponding to a plurality of measurement time points in a period required for cutting tool  101  to make one rotation. 
     In processing apparatus  201  according to the embodiment of the present disclosure, generation unit  120  is configured to generate the measurement data MD in which the rotation angle of two pieces of two-dimensional data adjacent to each other around rotation axis  17  is 5° or less, but is not limited thereto. Generation unit  120  may be configured to generate measurement data MD in which a rotation angle of two two-dimensional data adjacent to each other around rotation axis  17  is larger than 5°. 
     In processing apparatus  201  according to the embodiment of the present disclosure, calculation data obtaining unit  130  is configured to obtain the calculation data CD in which the rotation angle of two pieces of two-dimensional data adjacent to each other around rotation axis  17  is 2° or less, but is not limited thereto. Calculation data obtaining unit  130  may be configured to obtain calculation data CD in which a rotation angle of two pieces of two-dimensional data adjacent to each other around rotation axis  17  is larger than 2°. 
     In processing apparatus  201  according to the embodiment of the present disclosure, processing unit  140  is configured to perform a process of displaying the display screen DS including the graphs G 1 , G 2 , and G 3  on display unit  160 , but is not limited thereto. Processing unit  140  may be configured to perform a process of displaying the display screen DS that does not include at least one of the graphs G 1 , G 2 , and G 3  on display unit  160 . 
     In processing apparatus  201  according to the embodiment of the present disclosure, shape information obtaining unit  151  is configured to obtain shape information from the CAM, but is not limited thereto. For example, shape information obtaining unit  151  may be configured to receive shape information from the user. Further, for example, shape information obtaining unit  151  may be configured to receive the model number of cutting tool  101  from the user and acquire the shape information corresponding to the received model number from storage unit  170 . 
     In processing apparatus  201  according to the embodiment of the present disclosure, condition information obtaining unit  152  is configured to obtain condition information from the CAM, but is not limited thereto. For example, condition information obtaining unit  152  may be configured to receive condition information from the user. 
     In addition, processing system  301  according to the embodiment of the present disclosure is configured to include processing apparatus  201  separately from cutting tool  101 , but is not limited thereto. Processing apparatus  201  may be provided in cutting tool  101 , or may be provided in a machine tool. Processing apparatus  201  is configured to perform the determination process and the display process, but is not limited thereto. Processing apparatus  201  may be configured not to perform any one of the determination process and the display process. 
     In processing apparatus  201  according to the embodiment of the present disclosure, processing unit  140  is configured to perform a process of displaying the two-dimensional shape SMD indicated by the measurement data MD and the two-dimensional shape SCD indicated by the calculation data CD, but is not limited thereto. Processing unit  140  may be configured to perform the process of displaying the two-dimensional shape SMD and not perform the process of displaying the two-dimensional shape SCD. 
     Further, in processing apparatus  201  according to the embodiment of the present disclosure, processing unit  140  is configured to perform the determination process based on the two-dimensional shape SMD indicated by the measurement data MD and the two-dimensional shape SCD indicated by the calculation data CD, but is not limited thereto. Processing unit  140  may be configured to perform the determination process based on the two-dimensional shape SMD indicated by the measurement data MD without using the calculation data CD. In this case, processing apparatus  201  may not include at least one of calculation data obtaining unit  130 , shape information obtaining unit  151 , and condition information obtaining unit  152 . 
     For example, processing unit  140  may perform the determination process based on a degree of rotational symmetry of the two-dimensional shape SMD. More specifically, processing unit  140  generates n comparison images GMDC by rotating the white region in the binary image GMD generated based on the measurement data MD by a rotation angle Δθ° around the center of the binary image GMD. Then, processing unit  140  calculates a degree of difference D 3  between the binary image GMD and the comparison image GMDC as the degree of rotational symmetry indicating the degree of rotational symmetry of the two-dimensional shape SMD, and performs the determination process based on the calculated degree of difference D 3 . Here, n is an integer equal to or larger than 1. Δθ° is preferably 2° or less, and more preferably 1° or less. 
       FIG.  31    is a diagram showing an example of a method for calculating a degree of rotational symmetry of a two-dimensional shape by the processing unit in the processing apparatus according to the modification of the embodiment of the present disclosure.  FIG.  31    shows a comparative image GMDC_ 1  in which the rotation angle θ of the white region in the binary image GMD is 1°, a comparative image GMDC_ 45  in which the rotation angle θ of the white region in the binary image GMD is 45°, a comparative image GMDC_ 90  in which the rotation angle θ of the white region in the binary image GMD is 90°, and a comparative image GMDC  360  in which the rotation angle θ of the white region in the binary image GMD is 360°. Referring to  FIG.  31   , for example, processing unit  140  rotates the white area in the binary image GMD by 1° around the center of the binary image GMD to generate  360  comparison images GMDC. Then, processing unit  140  calculates areas of portions in which colors do not match in the binary image GMD and the comparison image GMDC as the degree of difference D 3  between the binary image GMD and the comparison image GMDC in the same manner as the method of calculating the degree of difference D 1 . 
       FIG.  32    is a diagram showing a relationship between a degree of difference and a rotation angle calculated by the processing unit in the processing apparatus according to the modification of the embodiment of the present disclosure.  FIG.  32    shows a graph G 4  in which the horizontal axis represents the rotation angle θ [degree] and the vertical axis represents the degree of difference D 3 . In  FIG.  32   , the solid line indicates a degree of difference D 3 A which is the degree of difference D 3  in a state where no loss of insert  14  has occurred, and the broken line indicates a degree of difference D 3 B which is the degree of difference D 3  in a state where loss of insert  14  has occurred. Referring to  FIG.  32   , the degree of difference D 3  has four minimum values corresponding to “4” which is the number of cutting edges of cutting tool  101 . Specifically, the degree of difference D 3  has a minimum value when the rotation angle θ is 90°, 180°, 270°, and 360° respectively. This is because the two-dimensional shape SMD is theoretically X-fold symmetric when the number of blades of cutting tool  101  is X. 
     Processing unit  140  performs a determination process based on the minimum value of the degree of difference D 3 . Here, as the minimum value of the degree of difference D 3  is larger, the degree of rotational symmetry of the two-dimensional shape SMD is lower, and as the minimum value of the degree of difference D 3  is smaller, the degree of rotational symmetry of the two-dimensional shape SMD is higher. For example, the degree of rotational symmetry of the two-dimensional shape SMD decreases due to occurrence of an abnormality such as loss of insert  14 . 
     For example, processing unit  140  compares the three minimum values other than the minimum value when the rotation angle θ is 360° in the degree of difference D 3  with a predetermined threshold value Th 3 , and detects various abnormalities based on the comparison result. More specifically, processing unit  140  determines that an abnormality has occurred in cutting when at least one of the three minimum values is larger than the threshold value Th 3 , and determines that no abnormality has occurred in cutting when the three minimum values are equal to or less than the threshold value Th 3 . 
     Specifically, processing unit  140  compares the three minimum values excluding the minimum value when the rotation angle θ is 360° in the degree of difference D 3 A with the threshold value Th 3 , and determines that no abnormality has occurred in cutting because the three minimum values are equal to or less than the threshold value Th 3 . Further, processing unit  140  compares the three minimum values excluding the minimum value when the rotation angle θ is 360° in the degree of difference D 3 B with the threshold value Th 3 , and determines that an abnormality has occurred in cutting because the minimum value when the rotation angle θ is 180° among the three minimum values is larger than the threshold value Th 3 . 
     Processing unit  140  may be configured to detect various abnormalities based on a temporal change in the three minimum values other than the minimum value when the rotation angle θ is 360° in the degree of difference D 3 . More specifically, processing unit  140  calculates a difference D 1  between a minimum value of a degree of difference D 3 C calculated based on the measurement data MD 1  of a certain target period T 1 C and a minimum value of a degree of difference D 3 D calculated based on the measurement data MD 1  in a target period T 1 D different from the target period T 1 C, and detects various abnormalities based on a result of comparing the calculated difference D 1  and a predetermined threshold value Th 4 . 
     In addition, processing unit  140  may be configured to calculate a difference D 2  between the maximum value of the three minimum values excluding the minimum value when the rotation angle θ is 360° in the degree of difference D 3  and the minimum value of the three minimum values, and detect various abnormalities based on a comparison result between the calculated difference D 2  with a predetermined threshold value Th 5 . 
       FIG.  33    is a diagram showing an example of a display screen displayed on the display unit in the processing apparatus according to the modification of the embodiment of the present disclosure. Referring to  FIG.  33   , processing unit  140  performs a process of displaying a display screen DS 2  including the graph G 4  indicating the relationship between the calculated degree of difference D 3  and the rotation angle θ on display unit  160 . For example, processing unit  140  performs a process of estimating the number of blades of cutting tool  101  based on the number of the minimum values of the degree of difference D 3 , and displaying the display screen DS further including the estimation result of the number of blades on display unit  160 . 
       FIG.  34    is a flowchart defining an example of an operation procedure when the processing apparatus in the cutting system according to the modification of the embodiment of the present disclosure performs an abnormality determination process. Referring to  FIG.  34   , first, processing apparatus  201  waits for a generation timing according to the generation cycle P (NO in step S 502 ), and when the generation timing arrives (YES in step S 502 ), generates measurement data MD 1  composed of a plurality of pieces of two-dimensional data in the target period T 1  based on a plurality of sensor measurement values sx, sy, and sr in the target period T 1  (step S 504 ). 
     Next, processing apparatus  201  calculates the degree of difference D 3  based on the measurement data MD 1  (step S 506 ). 
     Next, processing apparatus  201  compares the three minimum values other than the minimum value when the rotation angle θ is 360° in the degree of difference D 3  with the threshold value Th 3  (step S 508 ). 
     Next, processing apparatus  201  performs the abnormality determination process based on a result of comparing the three minimum values and the threshold value Th 3  (step S 510 ). 
     Processing apparatus  201  performs a process of displaying the display screen DS 2  including the two-dimensional shape SMD 1  indicated by the measurement data MD 1  in the target period T 1 , the estimation result of the number of blades, and the graph G 4  indicating the relationship between the degree of difference D 3  and the rotation angle θ on display unit  160  (step S 512 ). 
     Next, processing apparatus  201  waits for a new generation timing (NO in step S 502 ). 
     The above-described embodiments are to be considered in all respects as illustrative and not restrictive. The scope of the present invention is defined not by the above description but by the claims, and is intended to include meanings equivalent to the claims and all modifications within the scope. 
     The foregoing description includes the following additional features. 
     [Additional Note 1] 
     A processing system comprising: 
     a cutting tool for milling; 
     a plurality of sensors; and 
     a processing unit, 
     the plurality of sensors each being configured to measure a physical quantity that indicates a state related to loads on the cutting tool during cutting, 
     the processing unit being configured to generate, based on measurement results from the respective sensors at a plurality of measurement time points, measurement data that is related to the loads in two directions on a plane perpendicular to a rotation axis of the cutting tool and that includes two-dimensional data at each of the measurement time points, to obtain calculation data that is calculated based on a shape of the cutting tool and that includes a plurality of pieces of two-dimensional data, at a plurality of time points, related to the loads in the two directions on the plane perpendicular to the rotation axis, and to perform a determination process concerning cutting in which the cutting tool is used, based on a two-dimensional shape indicated by the generated measurement data and a two-dimensional shape indicated by the obtained calculation data, and 
     the processing unit being configured to obtain the calculation data that includes a plurality of pieces of two-dimensional data that indicates a cutting area vector on a plane perpendicular to the rotation axis. 
     REFERENCE SIGNS LIST 
     
         
           10  shaft part 
           11  shank part 
           12  blade fitting part 
           13  blade fixing part 
           14  insert 
           17  rotation axis 
           18  cutting force exertion plane 
           20  strain sensor 
           22  battery 
           23  wireless communication device 
           24  housing 
           101  cutting tool 
           110  wireless communication unit 
           120  generation unit 
           130  calculation data obtaining unit 
           140  processing unit 
           151  shape information obtaining unit 
           152  condition information obtaining unit 
           160  display unit 
           170  storage unit 
           201  processing apparatus 
           210  tool holder 
           220  main shaft 
           301  processing system