WO2023228253A1 - 熱変位モデル学習装置、熱変位推定装置、加工システム、および加工方法 - Google Patents

熱変位モデル学習装置、熱変位推定装置、加工システム、および加工方法 Download PDF

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Publication number
WO2023228253A1
WO2023228253A1 PCT/JP2022/021128 JP2022021128W WO2023228253A1 WO 2023228253 A1 WO2023228253 A1 WO 2023228253A1 JP 2022021128 W JP2022021128 W JP 2022021128W WO 2023228253 A1 WO2023228253 A1 WO 2023228253A1
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WIPO (PCT)
Prior art keywords
thermal displacement
data
machine tool
learning
time
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Ceased
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PCT/JP2022/021128
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English (en)
French (fr)
Japanese (ja)
Inventor
遼輔 池田
一樹 高幣
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Mitsubishi Electric Corp
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Mitsubishi Electric Corp
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Priority to JP2022554937A priority Critical patent/JP7221459B1/ja
Priority to CN202280096195.7A priority patent/CN119213374A/zh
Priority to DE112022007265.2T priority patent/DE112022007265T5/de
Priority to PCT/JP2022/021128 priority patent/WO2023228253A1/ja
Publication of WO2023228253A1 publication Critical patent/WO2023228253A1/ja
Anticipated expiration legal-status Critical
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    • GPHYSICS
    • G05CONTROLLING; REGULATING
    • G05BCONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B19/00Program-control systems
    • G05B19/02Program-control systems electric
    • G05B19/18Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of program data in numerical form
    • G05B19/404Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of program data in numerical form characterised by control arrangements for compensation, e.g. for backlash, overshoot, tool offset, tool wear, temperature, machine construction errors, load, inertia
    • BPERFORMING OPERATIONS; TRANSPORTING
    • B23MACHINE TOOLS; METAL-WORKING NOT OTHERWISE PROVIDED FOR
    • B23QDETAILS, COMPONENTS, OR ACCESSORIES FOR MACHINE TOOLS, e.g. ARRANGEMENTS FOR COPYING OR CONTROLLING; MACHINE TOOLS IN GENERAL CHARACTERISED BY THE CONSTRUCTION OF PARTICULAR DETAILS OR COMPONENTS; COMBINATIONS OR ASSOCIATIONS OF METAL-WORKING MACHINES, NOT DIRECTED TO A PARTICULAR RESULT
    • B23Q11/00Accessories fitted to machine tools for keeping tools or parts of the machine in good working condition or for cooling work; Safety devices specially combined with or arranged in, or specially adapted for use in connection with, machine tools
    • B23Q11/0003Arrangements for preventing undesired thermal effects on tools or parts of the machine
    • B23Q11/0007Arrangements for preventing undesired thermal effects on tools or parts of the machine by compensating occurring thermal dilations
    • GPHYSICS
    • G05CONTROLLING; REGULATING
    • G05BCONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B2219/00Program-control systems
    • G05B2219/30Nc systems
    • G05B2219/49Nc machine tool, till multiple
    • G05B2219/49219Compensation temperature, thermal displacement

Definitions

  • the present disclosure relates to a thermal displacement model learning device, a thermal displacement estimation device, a machining system, and a machining method for correcting thermal displacement of a machine tool.
  • a machine tool is a processing device that removes and processes a workpiece, called a workpiece, into a desired shape by driving a feed axis and changing the relative position of the workpiece and a tool.
  • Machine tools such as milling machines and lathes, attach a tool or workpiece to a spindle, and perform machining while rotating the spindle.
  • a machine tool includes an actuator for driving a feed axis and a main axis, and a servo amplifier for generating electric power for driving the actuator.
  • a machine tool equipped with an actuator measures the position of a feed axis using a position detector, and performs positioning by controlling the position so that the actual position matches the commanded position.
  • heat is generated within the machine tool.
  • actuators and servo amplifiers generate heat when converting electric power into motive power.
  • heat is generated due to material deformation, friction, etc.
  • the friction that occurs when the feed shaft is operated also generates heat.
  • the temperature of the mechanical structures of the machine tool increases and thermal expansion occurs. This deformation of the structure due to thermal expansion is called thermal displacement.
  • the temperature of a structure may not change uniformly, and in this case, different thermal displacements occur depending on the location within the structure, which may cause displacement other than simple expansion and contraction, such as collapse, distortion, or twisting of the structure. . It is known that such thermal displacement reduces the positioning accuracy of the machine tool, causing an error in the relative position between the tool and the workpiece, which may reduce machining accuracy.
  • Patent Document 1 describes a technology that makes it possible to estimate the amount of thermal displacement from the measurement data through machine learning using measurement data acquired during machining of a machine tool and actual measured values of the amount of thermal displacement.
  • the machine learning device disclosed in Patent Document 1 includes a measurement data acquisition unit that acquires a measurement data group, a thermal displacement amount acquisition unit that acquires an actual measured value of the amount of thermal displacement, and a device that inputs the measurement data group.
  • Thermal displacement is calculated based on a group of measured data by performing machine learning using the training data.
  • a calculation formula learning unit that sets a quantity prediction calculation formula.
  • the storage unit stores the measurement data group as teacher data for a predetermined period of time.
  • the accuracy of estimating the amount of thermal displacement generated in the machine tool decreases.
  • the time it takes for heat from a certain heat source to cause thermal displacement is affected by the positional relationship with other heat sources, the surrounding environment, etc. Therefore, if the storage period is too short, measurement data that affects thermal displacement may not be included in the stored teacher data during learning, and the accuracy of estimating the amount of thermal displacement may decrease.
  • the memorization period is too long, the accuracy of estimating the amount of thermal displacement may decrease due to erroneous learning of measurement data that is included in the data and has a small contribution to thermal displacement. be.
  • the present disclosure has been made in view of the above, and aims to provide a thermal displacement model learning device that can improve the accuracy of estimating the amount of thermal displacement.
  • the thermal displacement model learning device of the present disclosure provides input data that includes at least temperature data representing the time-series temperature of the machine tool, and input data that includes the time-series thermal displacement of the machine tool.
  • a learning data acquisition unit that acquires learning data in which thermal displacement data representing a quantity is associated with time;
  • a dataset generation unit that generates a dataset in which a part of the learning data is extracted from the learning data;
  • a learning unit that uses the data set to generate a learned thermal displacement model for estimating the amount of thermal displacement from input data of a machine tool;
  • the two data sets are characterized in that the data sets are generated such that the time lengths of the extracted time intervals are different from each other.
  • a diagram showing the configuration of a processing system according to Embodiment 1 A diagram showing the functional configuration of a machine tool according to Embodiment 1 A diagram showing an example of the installation position of a temperature sensor in the machine tool according to the first embodiment.
  • An explanatory diagram of an example of changes in the operating status of a machine tool A diagram showing the functional configuration of the thermal displacement model learning device according to the first embodiment
  • Explanatory diagram of the first example of the dataset generation method Explanatory diagram of the second example of the dataset generation method
  • Explanatory diagram of the third example of the dataset generation method Explanatory diagram of learning method of thermal displacement model Diagram of neural network Flowchart for explaining the operation of the thermal displacement model learning device shown in FIG.
  • FIG. 12 A diagram showing the configuration of a processing system according to Embodiment 2 A diagram showing the functional configuration of a machine tool according to Embodiment 2 A diagram showing a functional configuration of a thermal displacement estimating device according to a second embodiment Flowchart for explaining the operation of the processing system shown in FIG. 12 Diagram showing an example of hardware configuration A diagram showing a functional configuration of a thermal displacement model learning device according to a modification of the second embodiment A diagram showing the configuration of a processing system according to Embodiment 3 A diagram showing the configuration of a processing system according to Embodiment 4
  • thermal displacement model learning device a thermal displacement estimation device, a machining system, and a machining method according to embodiments of the present disclosure will be described in detail based on the drawings.
  • FIG. 1 is a diagram showing the configuration of a processing system 100-1 according to the first embodiment.
  • the machining system 100-1 includes a machine tool 1 and a thermal displacement model learning device 2.
  • the machine tool 1 is a processing device that removes and processes a workpiece using a tool.
  • the thermal displacement model learning device 2 learns a thermal displacement model for estimating the amount of thermal displacement from input data, based on thermal displacement data, temperature data, and machine state data acquired from the machine tool 1.
  • FIG. 2 is a diagram showing the functional configuration of the machine tool 1 according to the first embodiment.
  • the machine tool 1 includes a feed shaft 11 on which a tool T for processing a workpiece W is installed, a feed shaft 11 that changes the relative position between the tool T and the workpiece W, and a feed shaft motor 12 that is an actuator that drives the feed shaft 11.
  • a main shaft 13 that rotates the tool T or workpiece W
  • a main shaft motor 14 that is an actuator that drives the main shaft 13, a control device 15 that controls the machine tool 1, and a cooling device that suppresses heat generation when the actuator is driven.
  • It has a peripheral device 16, a temperature sensor TS for measuring the temperature of the machine tool 1, and a displacement sensor DS for measuring the relative position between the tool T and the workpiece W.
  • the displacement sensor DS is installed in the machine tool 1 so as to be able to detect the relative position of the tool T and workpiece W.
  • the displacement sensor DS measures the relative position and outputs the measured relative position to the thermal displacement model learning device 2 as thermal displacement data.
  • the displacement sensor DS may be any sensor that can detect displacement in at least one axial direction, and for example, a triangulation type laser sensor or a TOF (Time Of Flight) type laser sensor can be used. Note that a configuration may be adopted in which a plurality of orthogonal displacement sensors are installed to detect displacements in a plurality of axial directions.
  • the temperature sensor TS is installed on the machine tool 1.
  • the temperature sensor TS detects temperature and outputs the detected temperature to the thermal displacement model learning device 2 as temperature data.
  • the processing system 100-1 includes a plurality of temperature sensors TS. It is desirable to install the temperature sensor TS at a location where temperature changes are estimated to be large or where thermal displacement is estimated to have a large effect. Moreover, it is desirable that the temperature sensor TS is also installed outside the machine tool 1 so that the temperature sensor TS can measure the temperature of the space in which the machine tool 1 is installed.
  • FIG. 3 is a diagram showing an example of the installation position of the temperature sensor TS in the machine tool 1 according to the first embodiment.
  • the machine tool 1 shown in FIG. 3 is a milling machine type processing device, in which a Y-axis feed shaft motor 12 and a table TA are installed on a bed 17, and a workpiece W is placed on the table TA. Further, in the machine tool 1, X-axis and Z-axis feed shaft motors 12, a main shaft 13, and a main shaft motor 14 are installed on a column 18.
  • the black circles in FIG. 3 indicate an example of the installation position of the temperature sensor TS.
  • the temperature sensor TS is preferably installed at a location where the temperature change is estimated to be large and a location where it is estimated to have a large influence on thermal displacement.
  • a location where the temperature change is estimated to be large is drive mechanisms such as the feed shaft motor 12 for driving the X, Y, and Z axes and the main shaft motor 14 for rotating the main shaft 13.
  • locations that are estimated to have a large effect on thermal displacement include structures of the machine tool 1 such as the bed 17, column 18, and feed screw 19.
  • the temperature sensor TS is preferably installed at the apex of the structure, at a point between a plurality of apexes, or inside the structure.
  • the peripheral device 16 is a cooling device, and is installed to cool the machine tool 1 and prevent thermal displacement.
  • the peripheral equipment 16 performs heat exchange between the structure of the machine tool 1 , the workpiece W, and the tool T, and the outside air outside the machine tool 1 .
  • the peripheral equipment 16 includes a coolant device that injects cutting oil to cool the workpiece W, a pump that circulates a refrigerant that cools a heat exchange pipe installed in the machine tool 1, and the like.
  • the peripheral device 16 outputs operation information of the peripheral device 16 to the control device 15.
  • the operation information of the peripheral device 16 includes at least an operating state indicating whether or not the peripheral device 16 is in operation.
  • the operation information of the peripheral device 16 may include power consumption, power of the peripheral device 16, etc. in addition to the operating state.
  • the operating state included in the operating information of the peripheral device 16 can be expressed numerically. For example, an operating state of "1" represents a “state in which the peripheral device 16 is operating", and an operating state of "0" represents a "state in which the peripheral device 16 is stopped”.
  • a machining program is a series of commands given to the control device 15 so that the feed axis 11, main spindle 13, and peripheral equipment 16 of the machine tool 1 perform desired operations.
  • the machining program can include information representing a position command for the feed shaft 11, a speed command for the feed shaft 11, a rotation speed command for the main shaft 13, an operation and stop command for the peripheral device 16, and the like.
  • the control device 15 reads the machining program and analyzes the commands written in the machining program. Further, the control device 15 generates a command position and a command speed for the feed shaft 11 in order to cause the feed shaft 11 to perform a desired operation, and provides an operation amount to the feed shaft motor 12. Further, the control device 15 generates a command speed for the main shaft 13 to cause the main shaft 13 to perform a desired operation, and provides an operation amount to the main shaft motor 14 .
  • the control device 15 outputs machine state data representing the operating state of the machine tool 1 to the thermal displacement model learning device 2.
  • the machine state data is data representing the operating state of the machine tool 1, and indicates, for example, the operating state of the peripheral device 16 that adjusts the temperature of the machine tool 1, and the operating state of the actuator provided in the machine tool 1.
  • the machine state data includes at least one type of information among a command position for the feed shaft 11, a command speed for the feed shaft 11, a command speed for the main shaft 13, and operation information of the peripheral device 16.
  • the control device 15 is configured so that the difference between the actual position detected by the position detector and the commanded position, or between the actual speed and the commanded speed becomes 0. Feedback control may also be performed.
  • the machine state data can include information on one or more of the actual position of the feed shaft 11, the actual speed of the feed shaft 11, and the actual speed of the main shaft 13.
  • thermal displacement a machining error between the tool T and the workpiece W caused by thermal changes in the machine tool 1 is referred to as thermal displacement.
  • FIG. 4 is an explanatory diagram of an example of a change in the operating state of the machine tool 1.
  • FIG. 4 shows changes in the operating state of the machine tool 1 from when the power is turned on and the machine tool 1 is operated according to a machining program until the power is turned off.
  • FIG. 4 shows an example of how the operating states of the main spindle 13, feed axis 11, and peripheral equipment 16, which are the components of the machine tool 1, and the machining program execution state change over time.
  • the horizontal axis in FIG. 4 represents time, and t0 to t9 represent time. Details from time t0 to time t9 will be described later.
  • the machining program execution state indicates whether the machine tool 1 is running the program or stopped.
  • Program operation means that the machine tool 1 operates according to instructions written in a machining program.
  • the machine tool 1 performs a programmed operation for performing a certain machining process, and when the programmed operation is completed, an operator performs work such as replacing the workpiece W. After that, the work is performed in a flow such as program operation for the next machining.
  • the power to the machine tool 1 is turned on at time t0, and the power to the machine tool 1 is turned off at time t9.
  • the period from time t0 to time t1 represents a standby state until operation according to the machining program is started. Further, the period from time t8 to time t9 represents the period from the end of the operation according to the machining program until the power of the machine tool 1 is cut off.
  • machining program execution state program operation according to machining program #1 is performed between time t1 and time t5, and program operation according to machining program #2 is performed between time t6 and time t8.
  • main spindle speed which is the rotational speed of the main spindle 13
  • the feed rate which is the speed of the feed shaft 11
  • the operating state of the peripheral equipment 16 change over time.
  • spindle speed indicates the rotational speed of the main shaft 13.
  • S1000 a state in which the main shaft 13 is rotating at 1000 revolutions per minute
  • the spindle motor 14 has a rotation speed of 1000 revolutions per minute between time t1 and time t4, and a rotation speed of 3000 revolutions per minute between time t4 and time t5. From time t6 to time t8, each rotates at a rotation speed of 3000 revolutions per minute.
  • the spindle speed changes according to the commands of the machining program, the amount of heat generated by the spindle 13 also changes according to the machining program.
  • Feeing speed in FIG. 4 indicates the moving speed of the feeding shaft 11.
  • a state in which the feed shaft 11 moves 100 mm per minute is expressed as "F100".
  • the feed shaft motor 12 operates at a rotation speed of 100 mm per minute to operate the feed shaft 11 between time t1 and time t3, and at a rotation speed of 300 mm per minute between time t3 and time t5. 11, and from time t6 to time t8, each rotates at a rotation speed that operates the 300 mm feed shaft 11.
  • the feed shaft 11 operates, heat is generated from the feed shaft motor 12 and the structure of the feed shaft 11. The higher the feed speed, the greater the amount of heat generated. Since the feed rate changes according to the instructions of the machining program, the amount of heat generated by the feed shaft 11 also changes according to the machining program.
  • the "operating state of peripheral equipment" in FIG. 4 indicates whether the peripheral equipment 16 for cooling the machine tool 1 is in operation or stopped.
  • the peripheral equipment 16 does not always operate during machining, but operates and stops according to instructions written in the machining program.
  • the peripheral device 16 is in operation between time t2 and time t5
  • the peripheral device 16 is stopped between time t5 and time t7
  • the peripheral device 16 is in operation between time t7 and time t8.
  • Peripheral equipment 16 operates.
  • heat is transferred from the machine tool 1 to the external environment of the machine tool 1, and the machine tool 1 is cooled down. Since the operating state of the peripheral device 16 changes according to the commands of the machining program, the cooling state of the peripheral device 16 also changes according to the machining program.
  • the heat generated by the feed shaft 11 and the main shaft 13 and the cooling state by the peripheral equipment 16 are not constant, so the amount of thermal displacement of the machine tool 1 also changes over time depending on the machining program. Change.
  • time t5 and time t6 there are times, such as between time t5 and time t6, during which operation according to the machining program is not performed.
  • the machine tool 1 may be stopped due to setup work, such as when a worker is loading and unloading the workpiece W or cleaning the inside of the machine tool 1. be.
  • setup work such as when a worker is loading and unloading the workpiece W or cleaning the inside of the machine tool 1.
  • each section in which the operating state of the machine tool 1 differs is defined as an operating operation unit.
  • the time length of the driving operation unit is variable because it changes depending on the timing of the command written in the machining program.
  • FIG. 4 shows an example in which the machine tool 1 runs two different types of machining programs, it is sufficient to execute the machining programs at least once, and the types of machining programs and the number of executions are not limited to this example. .
  • the machine tool 1 may be powered off and then powered on again to run the machining program.
  • the time period from when the power is turned off to when it is turned on again is defined as one driving operation unit.
  • FIG. 5 is a diagram showing the functional configuration of the thermal displacement model learning device 2 according to the first embodiment.
  • the thermal displacement model learning device 2 uses data output by the machine tool 1 during operation to learn a thermal displacement model for estimating the amount of thermal displacement from input data including at least temperature data.
  • the thermal displacement model learning device 2 includes a learning data acquisition section 21, a dataset generation section 22, a learning section 23, and a model storage section 24.
  • the learning data acquisition unit 21 acquires thermal displacement data, temperature data, and machine state data output by the machine tool 1, and generates learning data by temporally synchronizing the acquired data.
  • the temperature data and machine condition data are examples of information included in the input data.
  • the input data includes at least temperature data.
  • the learning data is time-series data in which thermal displacement data, temperature data, and machine state data are arranged at a constant time period.
  • the constant time period represents a sampling period preset in the learning data acquisition unit 21.
  • the learning data acquisition unit 21 receives data of a time section corresponding to at least one driving operation unit from the machine tool 1, and generates learning data.
  • the learning data acquisition unit 21 outputs the generated learning data to the dataset generation unit 22.
  • the data set generation unit 22 detects a specific time based on the operating state of the machine tool 1, and extracts thermal displacement data, temperature data, and machine state data from the learning data using the detected time as a reference. Then, the extracted data are compiled into one set of data sets, and the plural sets of data sets are output to the learning section 23.
  • the specific time detected by the data set generation unit 22 will be referred to as an extraction reference time.
  • the extraction reference time will be explained using FIG. 4.
  • the data set generation unit 22 detects each time from time t1 to time t8 as a time when the operating state of the machine tool 1 changes. In addition, in FIG.
  • the extraction reference time is the time when any of the spindle speed, feed rate, change in the operating state of the peripheral equipment 16, and start and end of the machining program changes. is not limited to these examples.
  • the timing of calling and ending a subprogram, the timing of replacing the tool T, etc. can also be considered as changes in the operating state of the machine tool 1.
  • the data set generation unit 22 may be configured to read this information. Note that the data set generation unit 22 may temporally interpolate the two extraction reference times to additionally set a new extraction reference time.
  • the data set generation unit 22 extracts a part of the learning data from the learning data using the extraction reference time as a reference to generate a data set.
  • FIG. 6 is an explanatory diagram of the first example of the data set generation method.
  • a first example of a method in which the dataset generation unit 22 generates a dataset from learning data will be described using FIG. 6.
  • FIG. 6 shows data sets #a1 to #an extracted from the learning data when the extraction reference time t1 is the initial reference time for data extraction.
  • Input data #a1 to #an are temperature data and machine state data whose initial time is extraction reference time t1.
  • the time interval of input data #ai is temporally extended backward by a predetermined time extension width T1 from the end of the time interval of input data #ai-1. ing.
  • the time length of input data #a2 is longer than the time length of input data #a1 by time extension width T1. Further, the time length of the input data #a3 is longer than the time length of the input data #a2 by the time extension width T1. That is, if the time width of input data #a1 is T, then the time width of input data #ai is "T+(i-1)T1".
  • Input data #a1 to #an are data of a time interval of each time width "T+(i-1)T1" starting from the extraction reference time t1.
  • Teacher data #a1 to #an are thermal displacement data at the respective terminal times of input data #a1 to #an. As shown in FIG.
  • the data set generation unit 22 generates a plurality of sets of data sets #a1 to #an from one extraction reference time t1. Through the above processing, the dataset generation unit 22 generates datasets such that the time lengths of the extracted time sections of the plurality of datasets #a1 to #an generated from one extraction reference time t1 are different. be able to. The data set generation unit 22 performs the above processing for each of the plurality of extraction reference times included in the learning data. Note that, as in data set #an, the end time may exceed t2, which is the next extraction reference time after extraction reference time t1.
  • FIG. 7 is an explanatory diagram of a second example of the data set generation method. A second example of how the dataset generation unit 22 generates a dataset from learning data will be described using FIG. 7.
  • FIG. 7 shows data sets #b1 to #bn extracted from the learning data when the extraction reference time t2 is the end reference time of data extraction.
  • Input data #b1 to #bn are temperature data and machine state data whose termination time is the extraction reference time t2.
  • the time interval of input data #bi is temporally extended backward by a predetermined time extension width T1 from the start of the time interval of input data #bi-1. ing.
  • the time width of input data #bi is "T+(i-1)T1", where T is the time width of input data #b1.
  • the input data #b1 to #bn are data of a time interval of each time width "T+(i-1)T1" ending at the extraction reference time t2.
  • Teacher data #b1 to #bn are thermal displacement data at the respective terminal times of input data #b1 to #bn.
  • the data set generation unit 22 generates a plurality of data sets #b1 to #bn from one extraction reference time t2.
  • the dataset generation unit 22 generates datasets such that the time lengths of the extracted time sections of the plurality of datasets #b1 to #bn generated from one extraction reference time t2 are different. be able to.
  • the data set generation unit 22 performs the above processing for each of the plurality of extraction reference times included in the learning data. Note that, as in data set #bn, the initial time may go back to a time past t1, which is the extraction reference time before the extraction reference time t2.
  • FIG. 8 is an explanatory diagram of a third example of the data set generation method.
  • the dataset generation unit 22 generates datasets such that the data sets included in all datasets uniformly include the entire acquired data. Specifically, the data set generation unit 22 generates a data set by dividing the period from extraction reference time t1 to extraction reference time t2 next to extraction reference time t1 into n pieces at equal intervals. n is a natural number.
  • FIG. 8 shows data sets #c1 to #cn extracted from learning data between the final extraction reference time t2 and the extraction reference time t1, which is the initial reference time for data extraction.
  • Input data #c1 is temperature data and machine state data whose initial time is extraction reference time t1 and whose terminal time is time t1+(t2-t1)/n.
  • input data #c2 is temperature data and machine state data whose initial time is time t1+(t2-t1)/n and whose terminal time is time t1+2 ⁇ (t2-t1)/n.
  • Input data #ci is temperature data and machine state data whose initial time is time t1+(i-1) ⁇ (t2-t1)/n and whose terminal time is time t1+i ⁇ (t2-t1)/n.
  • Teacher data #c1 to #cn are thermal displacement data at the respective terminal times of input data #c1 to #cn.
  • the data set generation unit 22 can generate a data set such that the period from the extraction reference time t1 to the time t2 is uniformly included in the input data without overlap.
  • the data set generation unit 22 executes the above process for each of the plurality of extraction reference times included in the learning data.
  • the time lengths of the extracted time sections are uniform for the data sets #c1 to #cn generated between the extraction reference times t1 and t2.
  • the time length between adjacent extraction reference times is not uniform, and the time length of the time interval extracted when the data set generation unit 22 generates a data set is different from the time length between two adjacent extraction reference times. It is determined depending on the length of time between the extraction reference times. Therefore, by performing the above processing for each of all extraction reference times, a plurality of data sets with different time lengths of extracted time sections are generated as a whole.
  • the teacher data #a1 to #an, #b1 to #bn, #c1 to #cn are the input data #a1 to #an, #b1 ⁇ #bn, #c1 ⁇ #cn
  • the thermal displacement data is for one time corresponding to the terminal time, but the time length of the teacher data is not limited to one time, and may be time series data.
  • the teacher data #a1 to #an, #b1 to #bn, #c1 to #cn are time series having the same time length as the input data #a1 to #an, #b1 to #bn, #c1 to #cn. It may be data.
  • time interval #a1 corresponding to input data #a1 is selected n times from input data #a1 to input data #an and is adopted as input data.
  • the number of times the extended section #a2 is used as input data is (n-1) times, and the number of times that the extended section #an is used as input data is only one time.
  • time interval #b1 corresponding to input data #b1 is selected n times from input data #b1 to input data #bn and adopted as input data.
  • the number of times the extended section #b2 is used as input data is (n-1) times, and the number of times that the extended section #bn is used as input data is only one time. That is, in a plurality of input data generated using one extraction reference time as a temporal reference, there are sections where the number of extractions is large and sections where the number of extractions is small.
  • the dataset generation unit 22 equalizes the number of times each time interval and extended interval are extracted over the entire learning data. Specifically, when all datasets generated using each extraction reference time are combined and the variation in the number of extractions in a time interval is greater than or equal to a tolerance value, the dataset generation unit 22 performs histogram equalization. Execute processing.
  • the dataset generation unit 22 can equalize the bias in the number of data extractions over the entire learning data.
  • the entire set of data sets generated by the data set generation unit 22 does not extract only a specific section from the learning data, but instead consists of multiple data that uniformly reflect the driving conditions included in the learning data. Can generate sets. Note that although the explanation has been given here regarding equalizing the number of extractions by focusing on input data, it is also possible to equalize the number of extractions by focusing on teacher data.
  • the time length of the extracted time interval differs based on the extraction reference time when the operating state of the machine tool 1 changed.
  • Multiple datasets can be generated.
  • data sets are generated such that the data sets included in all data sets uniformly include the entire acquired data.
  • the learning unit 23 which will be described below, learns the thermal displacement model, it can uniformly target the entire learning data, and over-fitting where the model matches only some data. This further has the effect of suppressing the thermal displacement model and improving the generalization performance of the thermal displacement model.
  • FIG. 9 is an explanatory diagram of a learning method for a thermal displacement model.
  • the learning unit 23 has a function of learning a thermal displacement model for estimating the amount of thermal displacement from the input data using the input data and teacher data included in the dataset generated by the dataset generating unit 22.
  • the learning unit 23 has a thermal displacement model therein that outputs the amount of thermal displacement in time series when the input data included in the data set is inputted in time series.
  • the learning unit 23 optimizes the internal parameters of the thermal displacement model so that the difference between the estimated value of the amount of thermal displacement, which is the output of the thermal displacement model, and the teacher data included in the data set is minimized. Thereby, the learning unit 23 identifies a thermal displacement model that can estimate the amount of thermal displacement from the input data, and outputs it as a learned thermal displacement model.
  • the thermal displacement model learning device 2 is characterized in that the data set output by the data set generation unit 22 has a variable length. That is, in at least two of the plurality of data sets output by the data set generation unit 22, the time lengths of the extracted time intervals are different from each other. Therefore, the learning unit 23 uses a thermal displacement model corresponding to variable length input data.
  • the learning unit 23 learns the amount of thermal displacement by, for example, so-called supervised learning according to a neural network.
  • supervised learning refers to a method in which learning data, which is a data set of input and result, is given to a learning device to learn features in the learning data and infer results from the input.
  • an example will be described in which the learning unit 23 learns a thermal displacement model using an RNN (Recurrent Neural Network).
  • RNN is a neural network having a structure in which the output of an intermediate layer is recursively input to the layer that outputs the result.
  • the learning unit 23 can use, for example, a neural network having the structure shown in FIG. FIG. 10 is an explanatory diagram of a neural network.
  • the neural network shown in Figure 10 is an RNN in which the input layer consists of n inputs from x1 to xn, the middle layer consists of m nodes from h1 to hm, and the output layer consists of one output of y1.
  • the upper diagram in FIG. 10 shows the state of the neural network at time t ⁇ 1
  • the lower diagram in FIG. 10 shows the state of the neural network at time t.
  • the intermediate layer at time t outputs a weighted sum of the value calculated from the input to the input layer at time t and the term calculated from the value input from the intermediate layer at time t-1 to the output layer.
  • x t is the vector that bundles the input layers x1 to xn at time t
  • h t is the vector that bundles the middle layers h1 to hm at time t
  • h t is expressed by the following formula (1). be able to.
  • Equation (1) when the dimension of the vector x t is n and the dimension of the vector h t is m, W becomes an n ⁇ m-dimensional linear transformation matrix.
  • R represents an M ⁇ M-dimensional linear transformation matrix
  • b represents a bias vector
  • g represents an activation function.
  • the learning unit 23 uses the diachronic error backpropagation method to adjust the weighting of the neural network so that the output thermal displacement amount matches the thermal displacement data.
  • FIG. 10 shows an example of a neural network in which the input layer is n-dimensional, the intermediate layer is m-dimensional, and the output layer is one-dimensional, the dimensions of each layer are not limited to this example and can be any dimension. I can do it. Further, although FIG. 10 shows an example of a neural network having one intermediate layer, the number of intermediate layers may be plural.
  • the learning unit 23 uses methods such as "dropout” to randomly remove neurons during learning, and “early stopping” to monitor errors and stop learning early. May be used.
  • a thermal displacement model can be constructed and learned using other known RNNs such as LSTM (Long Short Term Memory) or GRU (Gated Recurrent Unit). You may do so.
  • the learning unit 23 may perform learning by regression analysis using an autoregressive model.
  • FIG. 11 is a flowchart for explaining the operation of the thermal displacement model learning device 2 shown in FIG. 5.
  • the thermal displacement model learning device 2 can generate a learned thermal displacement model by executing the process shown in FIG.
  • the learning data acquisition unit 21 of the thermal displacement model learning device 2 acquires thermal displacement data, temperature data, and machine state data from the machine tool 1 (step S101).
  • the learning data acquisition unit 21 generates learning data by associating the acquired thermal displacement data, temperature data, and machine state data with respect to time (step S102).
  • the dataset generation unit 22 generates a plurality of datasets from the learning data (step S103).
  • the learning unit 23 uses the dataset to optimize internal parameters of the thermal displacement model so that when input data included in the dataset is input, the amount of thermal displacement outputted matches the teacher data included in the dataset. By doing this, the thermal displacement model is learned (step S104).
  • the dataset generation unit 22 generates multiple types of variable length datasets, and extracts mutually from at least two datasets among the multiple datasets.
  • a thermal displacement model is trained using data sets with different time lengths.
  • the thermal displacement model learning device 2 can perform thermal displacement model learning using a data set generated using a time interval with an appropriate time length for the thermal displacement occurring in the machine tool 1. , it becomes possible to improve the estimation accuracy of the amount of thermal displacement.
  • the thermal displacement model learning device 2 can improve the accuracy of estimating the amount of thermal displacement without depending on the operation duration of the machine tool 1.
  • the machine tool 1 operates according to machining programs whose time lengths are variable depending on the finished shapes of various workpieces W, and whose operation patterns are different.
  • the data set used for learning must be obtained from a machining program and the time length must be variable.
  • the data set used by the learning unit 23 to learn the thermal displacement model is generated based on the time when the operating state of the machine tool 1 that is operated based on the machining program changes. Therefore, the thermal displacement model learning device 2 in the first embodiment can perform learning of a thermal displacement model using a data set whose temporal reference is a change in the operating state of the machine tool 1 during actual machining. Therefore, the thermal displacement model can learn input-output relationships that reflect the operating conditions of the machine tool.
  • the data set generation unit 22 when using the first example and second example of the data set generation method described above, the data set generation unit 22 generates a data set for a time that is a multiple of the predetermined time extension width T1 from the time defined as the extraction reference time.
  • a dataset can be generated by extracting data with a wide range from the training data.
  • the thermal displacement model is a temporally recursive model
  • the thermal displacement model learning device 2 can perform learning using not only the temperature data and machine state data at the moment when thermal displacement is calculated, but also the influence of changes in these data over time.
  • FIG. 12 is a diagram showing the configuration of a processing system 100-2 according to the second embodiment.
  • a machining system 100-2 according to the second embodiment includes a machine tool 1A, a thermal displacement model learning device 2, and a thermal displacement estimation device 3.
  • Machining system 100-2 has a thermal displacement estimation device 3 in addition to the configuration of machining system 100-1 according to Embodiment 1, and has machine tool 1A instead of machine tool 1 of machining system 100-1. .
  • the processing performed by the thermal displacement model learning device 2 is the same as in Embodiment 1 except for outputting the learned thermal displacement model to the thermal displacement estimating device 3, so a description thereof will be omitted here.
  • the thermal displacement estimating device 3 acquires the trained thermal displacement model generated by the thermal displacement model learning device 2 and input data for inference including at least temperature data representing the time series temperature of the machine tool 1A to be inferred. do.
  • the thermal displacement estimating device 3 uses a thermal displacement model to generate an estimated value of the amount of thermal displacement of the machine tool 1A to be inferred from the input data.
  • the thermal displacement estimating device 3 outputs the estimated value of the amount of thermal displacement to the machine tool 1A.
  • the machine tool 1A has a function of outputting temperature data and machine state data to the thermal displacement estimating device 3, and based on the estimated value of the amount of thermal displacement output by the thermal displacement estimating device 3, It also has a function to correct thermal displacement.
  • FIG. 13 is a diagram showing the functional configuration of the machine tool 1A according to the second embodiment.
  • the configuration of the machine tool 1A is the same as that of the machine tool 1 except that it includes a control device 15A instead of the control device 15 of the machine tool 1.
  • the control device 15A corrects the operation amount of at least one of the main shaft motor 14 that drives the main shaft 13 and the feed shaft motor 12 that drives the feed shaft 11 based on the estimated value of the amount of thermal displacement output by the thermal displacement estimation device 3. By doing so, the thermal displacement is corrected.
  • the machine tool 1A performs removal machining using the corrected operation amount.
  • FIG. 14 is a diagram showing the functional configuration of the thermal displacement estimation device 3 according to the second embodiment.
  • the thermal displacement estimating device 3 includes an inference data acquisition section 31 , a thermal displacement model acquisition section 32 , and an inference section 33 .
  • the inference data acquisition unit 31 acquires temperature data and machine state data from the machine tool 1A to be inferred, and synchronizes the obtained temperature data and machine state data in time to the inference unit 33 as inference data. Output.
  • the inference data includes at least temperature data, and is generated so that the learned thermal displacement model has the same combination of data as the input data used during learning. Furthermore, the inference data is sequentially output at the same time period as the learning data generated by the thermal displacement model learning device 2.
  • the thermal displacement model acquisition unit 32 acquires a learned thermal displacement model used for inference from the model storage unit 24 of the thermal displacement model learning device 2.
  • the thermal displacement model acquisition section 32 outputs the acquired thermal displacement model to the inference section 33.
  • the inference unit 33 uses the learned thermal displacement model to output an estimated value of the amount of thermal displacement from the input data included in the inference data.
  • the inference unit 33 outputs the estimated value of the amount of thermal displacement to the machine tool 1A.
  • the inference unit 33 inputs the machine state data included in the inference data into the learned thermal displacement model in the same data structure and time period as during learning, thereby calculating the amount of thermal displacement in the same time period as the input.
  • An estimated value can be calculated.
  • the inference unit 33 outputs the calculated estimated value of the amount of thermal displacement to the control device 15A of the machine tool 1A at the same cycle as the input interval of the inference data.
  • the control device 15A of the machine tool 1A receives the estimated value of the amount of thermal displacement outputted by the inference unit 33, and corrects, for example, the position command of the feed shaft 11 so as to offset the thermal displacement indicated by the estimated value of the amount of thermal displacement. do. Then, the feed shaft motor 12, which is the actuator of the feed shaft 11, is operated using the corrected position command. Correction of the position command is updated at every input interval of inference data.
  • FIG. 15 is a flowchart for explaining the operation of the processing system 100-2 shown in FIG. 12.
  • the thermal displacement model learning device 2 of the processing system 100-2 performs thermal displacement model generation processing (step S121). Note that the process in step S121 corresponds to the process in steps S101 to S104 shown in FIG. These processes are performed before processing for correcting thermal displacement is performed.
  • the machine tool 1A starts a programmed operation for machining for which thermal displacement is to be corrected (step S122).
  • the processing from step S123 onwards is performed while the processing for which the thermal displacement is to be corrected is being performed.
  • the inference data acquisition unit 31 receives temperature data and machine state data that are sequentially output during machining of the machine tool 1A, and generates inference data from the received data (step S123).
  • the inference data has a data structure similar to the input data of the thermal displacement model generated in step S121.
  • the generated inference data is sequentially output to the inference unit 33 at the same time period as the learning data generated by the thermal displacement model learning device 2.
  • the inference unit 33 estimates the amount of thermal displacement from the inference data using the thermal displacement model (step S124).
  • the estimated value of the amount of thermal displacement is calculated at the same time period as the inference data generated in step S123, and is output to the control device 15A of the machine tool 1A.
  • the control device 15A of the machine tool 1A corrects the position command and performs machining by correcting the operation amount to the actuator using the estimated value of the amount of thermal displacement (step S125).
  • the machine tool 1A determines whether the program operation of the machining for which thermal displacement is to be corrected has ended (step S126). If the program operation has not ended (step S126: No), the process returns to step S123, and the machining system 100-2 repeats the processes from step S123 to step S126. If the programmed operation has ended (step S126: Yes), the machining system 100-2 ends the process.
  • the processing system 100-2 includes the thermal displacement estimating device 3 that estimates the amount of thermal displacement using a learned thermal displacement model. Furthermore, the machine tool 1A corrects the operation amount of the actuator of the machine tool 1A based on the estimated value of the amount of thermal displacement so as to offset the thermal displacement indicated by the estimated value.
  • the inference unit 33 can sequentially calculate the estimated value of the amount of thermal displacement for the sequentially input inference data and output the estimated value to the machine tool 1A. Therefore, no matter how long the machining program executed by the machine tool 1A takes, it is possible to estimate the amount of thermal displacement. Furthermore, since the estimated value of the amount of thermal displacement is calculated from a thermal displacement model that is a temporally recursive model, not only the temperature data and mechanical state data at the moment when the estimated value of the amount of thermal displacement is calculated, but also these data are used. It is possible to estimate the amount of thermal displacement, including the influence of changes in the data over time. Therefore, the machine tool 1A can accurately correct thermal displacement without depending on the elapsed time from the start of operation.
  • step S126 shown in FIG. 15 it is determined whether or not the power to the machine tool 1A is cut off, and the processing system 100-2 performs step S123 until the power to the machine tool 1A is cut off. You may return to continue processing. In this case, it is possible to continue correcting thermal displacement even when the program operation is performed multiple times in succession.
  • the thermal displacement model learning device 2 of Embodiment 1 and Embodiment 2 is realized by, for example, a computer system.
  • the thermal displacement model learning device 2 may be realized by one computer system, or may be realized by multiple computer systems.
  • the thermal displacement model learning device 2 may be realized by a cloud system.
  • a cloud system it is possible to arbitrarily set up the separation between computer system hardware and devices such as servers for each function.
  • one computer system may function as multiple devices, or multiple computer systems may function as one device.
  • FIG. 16 is a diagram showing an example of the hardware configuration. As shown in FIG. 16, this computer system includes a control section 101, an input section 102, a storage section 103, a display section 104, a communication section 105, and an output section 106, which are connected via a system bus 107. There is.
  • the control unit 101 is, for example, a CPU (Central Processing Unit).
  • the control unit 101 executes a thermal displacement model learning program in which each process performed by the thermal displacement model learning device 2 of this embodiment is described.
  • the input unit 102 includes, for example, a keyboard, a mouse, etc., and is used by a user of the computer system to input various information.
  • the storage unit 103 includes various memories such as RAM (Random Access Memory) and ROM (Read Only Memory), and storage devices such as hard disks, and stores programs to be executed by the control unit 101 and necessary information obtained in the process of processing. Store data etc.
  • the storage unit 103 is also used as a temporary storage area for programs.
  • the display unit 104 is composed of an LCD (Liquid Crystal Display) or the like, and displays various screens to the user of the computer system.
  • the communication unit 105 is a communication circuit or the like that performs communication processing.
  • the communication unit 105 may be configured with a plurality of communication circuits each corresponding to a plurality of communication methods.
  • the output unit 106 is an output interface that outputs data to an external device such as a printer or an external storage device.
  • FIG. 16 is an example, and the configuration of the computer system is not limited to the example of FIG. 16.
  • the computer system may not include the output unit 106.
  • all of these computer systems do not need to be the computer systems shown in FIG. 16.
  • some computer systems may not include at least one of the display section 104, output section 106, and input section 102 shown in FIG.
  • a computer system having the above-mentioned configuration includes, for example, a thermal displacement model learning program stored in a CD-ROM or DVD-ROM set in a CD (Compact Disc)-ROM drive or DVD (Digital Versatile Disc)-ROM drive (not shown). is installed in the storage unit 103. Then, when the thermal displacement model learning program is executed, the thermal displacement model learning program read from the storage unit 103 is stored in an area of the storage unit 103 that serves as the main storage device. In this state, the control unit 101 executes processing as the thermal displacement model learning device 2 of the first and second embodiments according to the thermal displacement model learning program stored in the storage unit 103.
  • a CD-ROM or DVD-ROM is used as a recording medium to provide a program that describes the processing in the thermal displacement model learning device 2.
  • a program provided via a transmission medium such as the Internet via the communication unit 105 may be used.
  • the thermal displacement model learning program of Embodiment 1 and Embodiment 2 provides a computer with input data including at least temperature data representing the time-series temperature of the machine tool 1 and the time-series thermal displacement amount of the machine tool 1.
  • a step of acquiring learning data in which the thermal displacement data to be expressed is associated with time, a step of generating a data set by extracting a part of the learning data from the learning data, and using the data set, the machine tool 1A generating a learned thermal displacement model for estimating the amount of thermal displacement from the input data of.
  • the data sets are generated such that the time lengths of the extracted time intervals are different from each other in at least two data sets among the plurality of data sets.
  • the learning data acquisition section 21 shown in FIG. 5 is realized by the communication section 105 shown in FIG. 16, and the model storage section 24 shown in FIG. 5 is a part of the storage section 103 shown in FIG.
  • the data set generation unit 22 and the learning unit 23 shown in FIG. 5 are realized by the control unit 101 shown in FIG.
  • the thermal displacement estimation device 3 is also realized by one or more computer systems.
  • a program for the thermal displacement estimating device 3 to perform the operations described in the second embodiment is provided by a storage medium, a transmission medium, etc., and installed in a computer system, similarly to the thermal displacement model learning program described above. Thereby, the above-described operation of the thermal displacement estimating device 3 is realized.
  • the inference data acquisition section 31 and the thermal displacement model acquisition section 32 shown in FIG. 14 are realized by the communication section 105 shown in FIG. 16, and the inference section 33 shown in FIG. 14 is realized by the control section 101 shown in FIG. Realized.
  • the division of functions in each device shown in FIGS. 5 and 14 is an example, and if the processing systems 100-1 and 100-2 can perform the operations described above, the division of functions in each device is as shown in FIG. and is not limited to the example shown in FIG.
  • the thermal displacement model learning device 2 and the thermal displacement estimation device 3 may be integrated so that the thermal displacement model learning device 2 also has the function of the thermal displacement estimation device 3. good.
  • FIG. 17 is a diagram showing the functional configuration of a thermal displacement model learning device 2A according to a modification of the second embodiment.
  • the thermal displacement model learning device 2A has the functions of the thermal displacement estimation device 3 in addition to the functions of the thermal displacement model learning device 2.
  • the functions of each component have already been explained in FIG. 14, so the explanation will be omitted here.
  • the functions of the thermal displacement model acquisition section 32 are realized by exchanging data within the computer system.
  • FIG. 18 is a diagram showing the configuration of a processing system 100-3 according to the third embodiment.
  • the machining system 100-3 includes a plurality of machine tools 1 and a thermal displacement model learning device 2B provided on a server.
  • the thermal displacement model learning device 2B performs thermal displacement model learning based on thermal displacement data, temperature data, and machine state data received from a plurality of machine tools 1.
  • the functions of the machine tool 1 are the same as those of the first embodiment, and the functions of the thermal displacement model learning device 2B are the same as those of the first embodiment except that the thermal displacement models of a plurality of machine tools 1 are learned for each machine tool 1. It is similar to
  • FIG. 19 is a diagram showing the configuration of a processing system 100-4 according to the fourth embodiment.
  • the machining system 100-4 includes a plurality of machine tools 1 and 1A, a thermal displacement model learning device 2B provided on a server, and a thermal displacement estimation device 3B.
  • the machine tool 1 is a processing device to be learned, and the embodiments are different from each other except that characteristic information, which is information indicating characteristics of the machine tool 1 including at least the model number of the machine tool 1, is output to the thermal displacement model learning device 2B.
  • characteristic information which is information indicating characteristics of the machine tool 1 including at least the model number of the machine tool 1
  • the machine tool 1A is a processing device to be estimated, and is similar to the second embodiment except that it outputs characteristic information, which is information indicating the characteristics of the machine tool 1A, including at least the model number of the machine tool 1A, to the thermal displacement estimating device 3B. This is the same as machine tool 1A.
  • the thermal displacement model learning device 2B is the same as the thermal displacement model learning device 2B of Embodiment 3 except that it receives feature information from the machine tools 1, and generates learning data based on data received from a plurality of machine tools 1. and a model storage unit 24B that stores each of a plurality of thermal displacement models in association with characteristic information of the machine tool 1 from which the learning data is acquired.
  • the thermal displacement estimation device 3B has a thermal displacement model acquisition section 32B instead of the thermal displacement model acquisition section 32 of the thermal displacement estimation device 3.
  • the thermal displacement model acquisition unit 32B selects a thermal displacement model to be used by the inference unit 33 from among the plurality of thermal displacement models stored in the model storage unit 24B, based on the characteristic information received from the inference target machine tool 1A. It has a model selection section 321 for selection.
  • the characteristic information includes at least the model number, and in addition to the model number, can include information indicating the state of the machine tool 1, 1A, such as the environment of the factory where the machine tool 1, 1A is installed, installation conditions, etc.
  • the model selection unit 321 is a thermal displacement model generated based on data obtained from a machine tool 1 having the same model number as the inference target machine tool 1A and having a state similar to the inference target machine tool 1A. can be selected. As a result, even if there is no thermal displacement model generated from the data of the machine tool 1A itself to be inferred, it is possible to use a machine tool 1 that has the same model number as the machine tool 1A and is used in a similar environment. Using the thermal displacement model generated from the data of No. 1, it becomes possible to obtain an estimated value of the amount of thermal displacement.
  • the thermal displacement model acquisition part 32B acquires multiple types of thermal displacement models from the model storage part 24B, and the inference part 33 , a configuration may be adopted in which an estimated value to be output is selected from among a plurality of thermal displacement estimated values calculated using a plurality of types of thermal displacement models, based on the characteristic information.
  • the functions of the thermal displacement model learning device 2 and the thermal displacement estimation device 3 may be built into the machine tool 1.
  • the thermal displacement model learning device 2B is used in the same area. Learning data may be acquired from multiple machine tools 1, or the thermal displacement model may be learned using learning data collected from multiple machine tools 1 that operate independently in different areas. . Furthermore, it is also possible to add or remove the machine tool 1 from which learning data is to be collected midway through the process. Furthermore, the thermal displacement model learning device 2 that has learned the thermal displacement model for a certain machine tool 1 is applied to another machine tool 1 to relearn and update the thermal displacement model for the other machine tool 1. You may also do so.

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