JP7689460B2 - Method for estimating thermal deformation of machine tool and method for correcting thermal deformation using the same - Google Patents

Description

The present invention relates to a method for estimating thermal deformation of a machine tool that estimates the amount of thermal deformation of a workpiece caused by heat during machining, and a method for correcting thermal deformation based on the amount of thermal deformation estimated using this method.

As a method for estimating the amount of thermal deformation of a workpiece caused by heat during machining, a method has been proposed in which a first temperature sensor is provided in association with the spindle, a second temperature sensor is provided in association with a ball screw mechanism that moves a moving member that moves integrally with the machining tool, and a third temperature sensor is provided to detect the ambient temperature, and the amount of thermal deformation of the workpiece is estimated using the temperatures detected by the first to third temperature sensors (see, for example, Patent Document 1).

In this thermal deformation estimation method, the amount of thermal deformation of the spindle (H1) is calculated using a spindle thermal deformation correction formula, and this amount of thermal deformation of the spindle (H1) is expressed as the sum (H1 = C1 + C2) of the amount of thermal deformation of the machine tool bed (C1) and the amount of thermal deformation of the spindle bearing means (C2).

The amount of thermal deformation of the bed (C1) is calculated using the initial temperature (T0) of the first temperature sensor, the ambient temperature (T1), and the amount of temperature change (ΔTs) of the first temperature sensor, using the following formula (1):
C1=[a1+(a2×T0)+(a3×T1)]×ΔTs...(1)
The thermal deformation amount (C2) of the bearing means of the spindle is expressed by the following formula (2) using the rotation speed (N) of the spindle, the initial temperature (T0) of the first temperature sensor, the ambient temperature (T1), and the time elapsed until convergence (t):
C2=N×[b1+(b2×T0)+(b3×T1)]×
{1-exp[(ln0.1)×t/30)]} ...(2)
b1, b2, b3: Represented by coefficients.

The amount of thermal deformation (H2) of the moving member is calculated using a moving member thermal deformation correction formula, and this amount of thermal deformation (H2) is calculated using the temperature change (ΔTb) of the second temperature sensor according to the following formula (3):
H2=Σpi×ΔTb...(3)
pi: represented by a coefficient.

The thermal deformation of the workpiece (HA) is the composite deformation (HA = H1 + H2) of the thermal deformation of the spindle (H1) and the thermal deformation of the moving member (H2). By correcting with this composite deformation (HA), the effects of heat generated during machining can be suppressed, allowing for high-precision machining.

Patent No. 4450722

The conventional method described above takes into account the thermal deformation of the spindle of the machine tool, i.e., the temperature change of the first temperature sensor, and the thermal deformation of the moving member (to which the machining tool is attached), i.e., the temperature change of the second temperature sensor. However, in reality, it is predicted that the location where the temperature change should be measured will differ depending on the model of machine tool. Therefore, it is desirable to realize a method for estimating the amount of thermal deformation that takes into account the temperature change of the location that should be measured by the machine tool.

In addition, there are various conditions for machining a workpiece, such as the diameter of the workpiece, the axial machining length of the workpiece, the machining rotation speed of the workpiece, fluctuations in the machining environment temperature, whether cutting oil is used, and the material of the workpiece, and there is a need to realize a method for estimating the amount of thermal deformation that can be applied even when these various machining conditions change.

The objective of the present invention is to provide a method for estimating thermal deformation of machine tools that takes into account a small number of temperature change measurement points suitable for estimating thermal deformation in each machine tool and can be applied to a wide range of machining conditions from a small number of experiments.

Another object of the present invention is to provide a method for correcting thermal deformation of a machine tool, which performs correction based on the amount of thermal deformation estimated using this thermal deformation estimation method.

The method for estimating thermal deformation of a machine tool of the present invention includes a test condition setting step of setting test conditions for a workpiece taking into consideration actual machining of the machine tool using an experimental design method; a spindle-to-cutter distance and temperature measurement step of measuring a spindle-to-cutter distance and temperature changes at multiple locations of the machine tool when a simulated cutting test and/or an actual cutting test based on the test conditions is performed on the workpiece; a change tendency grouping step of grouping locations showing similar trends based on change trends of the measured temperatures at the multiple locations; a measurement location narrowing down step of selecting multiple temperature trend groups from the grouped multiple temperature trend groups and narrowing down one or two measurement locations from each selected temperature trend group; an estimation equation setting step of setting a thermal deformation estimation equation with a number of terms corresponding to the number of narrowed-down measurement locations; and The method includes an experimental constant determination step of determining an experimental constant so as to minimize the sum of squares of the residual between the actual value of the change in the workpiece and the predicted amount of change in the workpiece using the thermal deformation estimation formula by substituting the amount of change in the measured temperature corresponding to each term in the formula; an experimental constant determination repetition step of repeating the estimation formula setting step and the experimental constant determination step multiple times by changing the combination of the temperature trend groups and/or the combination of the measurement points to be narrowed down in the measurement point narrowing down step; an optimal experimental constant determination step of determining, after the experimental constant determination repetition step, an optimal combination of measurement points and optimal experimental constants suitable for the thermal deformation estimation formula; and a thermal deformation amount estimation step of estimating the amount of thermal deformation of the workpiece using the thermal deformation estimation formula, the optimal combination of measurement points, and the optimal experimental constant.

In such a method for estimating thermal deformation of a machine tool, in the repeated experimental constant determination step, it is preferable to repeat the estimation equation setting step and the experimental constant determination step multiple times by changing the combination of temperature trend groups in the measurement location narrowing down step, the combination of narrowed down measurement locations, and/or the form of the thermal deformation estimation equation, and to determine an optimal thermal deformation estimation equation suitable for the machine tool, as well as an optimal combination of measurement locations suitable for this and optimal experimental constants, in the optimal experimental constant determination step. In this way, it is possible to determine an optimal thermal deformation estimation equation suitable for the machine tool, as well as an optimal combination of measurement locations and optimal experimental constants in this optimal thermal deformation estimation equation, and thereby to accurately estimate the amount of thermal deformation of the machine tool.

In addition, in the experimental constant determination repeat step, at least any two of the three or more thermal deformation estimation equations consisting of three, four, or five or more terms are set, and the estimation equation setting step and the experimental constant determination step are repeated by changing the combination of temperature trend groups and/or the combination of measurement points to be narrowed down using at least two thermal deformation estimation equations, so that the thermal deformation estimation equation can be expressed as a linear equation with an appropriate number of terms consisting of three, four, or five or more terms, and can be provided as a relatively simplified thermal deformation estimation equation.

In addition, in such a method for estimating thermal deformation of a machine tool, in the change tendency grouping step, it is preferable to make the temperature change amount on the reference side dimensionless by dividing it by the maximum temperature change amount, then multiply the temperature change of the comparison target by a coefficient, calculate the sum of squared residuals between this coefficient-integrated temperature change and the dimensionless temperature change to calculate the similarity, and group the temperature change tendencies based on the similarity. By grouping based on similarity in this way, it is possible to avoid narrowing down to include many locations where the temperature changes fluctuate in the same or similar manner.

In addition, this method for estimating thermal deformation of machine tools uses the all-pairs method as the experimental design method, and the test conditions set in the test condition setting step include the diameter of the workpiece, the machining length of the workpiece, the number of times the workpiece is machined, fluctuations in the machining environment temperature, and whether or not cutting oil is used, making it possible to provide a general-purpose thermal deformation estimation formula that takes into account general machining conditions without being limited by the number of levels of each factor.

Further, the method for correcting thermal deformation of a machine tool of the present invention includes a test condition setting step of setting test conditions for a workpiece taking into consideration actual machining of the machine tool using an experimental design method; a spindle-to-tool distance and temperature measurement step of measuring a spindle-to-tool distance and temperature changes at multiple locations of the machine tool when a simulated cutting test and/or an actual cutting test based on the test conditions is performed on the workpiece; a change tendency grouping step of grouping locations showing similar trends based on the change trends of the measured temperatures at the multiple locations; a measurement location narrowing down step of selecting multiple temperature trend groups from the grouped multiple temperature trend groups and narrowing down one or two measurement locations from each selected temperature trend group; an estimation equation setting step of setting a thermal deformation estimation equation with a number of terms corresponding to the number of narrowed-down measurement locations; and a calculation step of calculating a change in the measured temperature corresponding to each term in the thermal deformation estimation equation and calculating a change in the measured temperature corresponding to each term in the thermal deformation estimation equation. the thermal deformation estimation formula, the optimal combination of measurement points and the optimal experimental constants, which are suitable for the thermal deformation estimation formula, are determined after the experimental constant determination repetition step; a thermal deformation amount estimation step for estimating the amount of thermal deformation of the workpiece using the thermal deformation estimation formula, the optimal combination of measurement points and the optimal experimental constants; a deformation amount difference calculation step for calculating a difference in the amount of thermal deformation between the amount of thermal deformation of the workpiece in the previous machining process and the amount of thermal deformation of the workpiece in the current machining process; and a thermal deformation correction step for correcting the difference in the amount of thermal deformation calculated in the deformation amount difference calculation step.

According to the method for estimating thermal deformation of a machine tool of the present invention, test conditions for a workpiece are set by using an experimental design method, taking into account the actual machining of the machine tool (test condition setting step), and the spindle-to-tool distance and temperature changes at multiple locations of the machine tool are measured when a simulated cutting test and/or an actual cutting test based on the test conditions are performed (spindle-to-tool distance and temperature measurement step), so that data on the spindle-to-tool distance and temperature changes at multiple locations under the set test conditions can be obtained. Then, locations showing similar trends are grouped based on the change trends of the measured temperatures (change trend grouping step), multiple temperature trend groups are selected from these temperature trend groups, and one or two measurement locations are narrowed down from each selected temperature trend group (measurement location narrowing down step), so that the amount of thermal deformation can be estimated by narrowing down multiple locations with different temperature trends and taking into account the temperature changes at the different locations. In addition, a thermal deformation estimation formula with a number of terms corresponding to the number of narrowed-down measurement locations is set (estimation formula setting step), and the change in measured temperature corresponding to each term in this thermal deformation estimation formula is substituted to determine an experimental constant so that the sum of squares of the residual between the actual change in the workpiece and the predicted change in the workpiece using the thermal deformation estimation formula is minimized (experimental constant determination step). The estimation formula setting step and the experimental constant determination step are repeated multiple times by changing the combination of temperature trend groups and/or the combination of narrowed-down measurement locations (repeated experimental constant determination step). After this repeated experimental constant determination step, an optimal combination of measurement locations and optimal experimental constants suitable for the thermal deformation estimation formula are determined (optimum experimental constant determination step). The thermal deformation amount of the workpiece is estimated using this thermal deformation estimation formula, the optimal combination of measurement locations and the optimal experimental constant (thermal deformation amount estimation step). Therefore, the thermal deformation amount of the workpiece can be estimated taking into account the temperature changes at a small number of appropriate locations on the machine tool, and the thermal deformation amount can be accurately estimated with high precision using a relatively simple formula.

In addition, according to the thermal deformation correction method for machine tools of the present invention, the amount of thermal deformation of the workpiece is estimated by the above-mentioned thermal deformation estimation method, and this estimated amount of thermal deformation is used to calculate the difference between the amount of thermal deformation of the workpiece in the previous machining process and the amount of thermal deformation of the workpiece in the current machining process (deformation amount difference calculation step), and correction is made using this deformation amount difference (thermal deformation correction step), so that thermal deformation correction can be performed relatively easily and the workpiece can be machined with high precision.

1 is a front perspective view showing an example of an NC lathe to which a thermal deformation estimation method (thermal deformation correction method) according to the present invention is applied; FIG. 2 is a perspective view showing the NC lathe of FIG. 1 as viewed from the rear side. 4 is a diagram showing a flow of executing a thermal deformation estimation method applied to the NC lathe of FIG. 1 . 4 is an explanatory diagram for explaining test conditions in a test condition setting step of the thermal deformation estimating method of FIG. 3 . 5A and 5B are diagrams for explaining the similarity used when grouping temperature change trends, in which FIG. 5A shows the relationship between time and temperature change, and FIG. 5B is a diagram for explaining the calculation of the similarity. FIG. 13 is a diagram showing a flow when the thermal deformation estimation formula is applied to an NC lathe for machining.

Below, with reference to the attached drawings, an embodiment of the thermal deformation estimation method according to the present invention and a thermal deformation correction method using the same will be described by applying it to an NC lathe as an example of a machine tool. First, with reference to Figs. 1 and 2, an NC lathe will be outlined as an example of a machine tool to which the thermal deformation estimation method (thermal deformation correction method) is applied.

In Fig. 1 and Fig. 2, the NC lathe shown has a lathe body 2 installed on the floor of a factory. The lathe body 2 has a bed 3, a main shaft section 4 is provided on the left side of the bed 3, and a turret device 6 is attached to the right side of the bed 3. A main shaft 7 is rotatably supported by the main shaft section 4, a drive pulley 8 is attached to the rear end of the main shaft 7, and the output section of the main shaft drive motor 10 and the drive pulley 8 are driven and connected via a drive belt (not shown). A chuck means 12 is attached to the main shaft 7, and a workpiece (not shown) to be processed is detachably attached to the chuck means 12. Because of this configuration, when the main shaft drive motor 10 is operated, the main shaft 7 is rotated in a predetermined direction via the drive belt and drive pulley 8, and the chuck means 12 (the workpiece attached to it) is rotated integrally with the main shaft 7.

In this NC lathe, a moving member 14 is supported on the lathe body 2, a support table 16 is supported on the moving member 14, and a turret device 6 is attached to the support table 16. In this embodiment, the moving member 14 is movably supported on the lathe body 2 via a first support mechanism 18 extending in the lateral direction of the lathe body 2, i.e., in the axial direction of the main shaft 7 (Z-axis direction), and is reciprocated in the Z-axis direction via the first support mechanism 18. The support table 16 is movably supported on the moving member 14 via a second support mechanism 20 extending in the front-rear direction (X-axis direction) of the lathe body 2, and is reciprocated in the X-axis direction via the second support mechanism 20. The first support mechanism 18 includes a first drive motor 22 for moving the moving member, and the second support mechanism 20 includes a second drive motor 24 for moving the support table 16.

The turret device 6 includes a turret body 26, a turret shaft (not shown) is rotatably supported on the turret body 26, and a turret 28 is attached to the turret shaft. A turret drive motor 25 is attached to the turret body 26, and the turret drive motor 25 is drivingly connected to the turret shaft. Because of this configuration, when the turret drive motor 25 rotates in a predetermined direction (or the opposite direction to the predetermined direction), the turret 28 rotates in the predetermined direction (or the opposite direction to the predetermined direction) via the turret shaft. The turret 28 is provided with a plurality of tool attachment portions 30 spaced apart in the circumferential direction, and machining tools (not shown) for machining the workpiece are attached to these tool attachment portions 30.

In this NC lathe, when machining a workpiece, for example, the spindle 7 and the chuck means 12 (the workpiece attached thereto) are rotated in a predetermined direction by the spindle drive motor 10. The support table 16 is also moved in the X-axis direction (i.e., in a direction approaching the center of the workpiece) by the second drive motor 24, and the amount of cut during machining is set by this movement. Furthermore, the moving member 14 is moved in the Z-axis direction (i.e., the axial direction of the workpiece) by the first drive motor 22, and the machining length in the axial direction of the workpiece is set by this movement. By operating the spindle drive motor 10 and the first and second drive motors 22, 24 in this manner and acting a machining tool (not shown) attached to the turret device 6 on the workpiece (not shown) held by the chuck means 12, machining of the workpiece is performed.

In such an NC lathe, when cutting or the like is performed on a workpiece, the temperature of the NC lathe rises due to heat generated from the spindle drive motor 10, the first and second drive motors 22, 24, heat generated by the rotation of the spindle 7, heat generated in the first and second support mechanisms 18, 20, etc., and this temperature fluctuation causes thermal deformation in the workpiece, which in turn reduces the machining accuracy of the workpiece. Therefore, in the NC lathe of this embodiment, the amount of thermal deformation is estimated using the following thermal deformation estimation method, and the thermal deformation is corrected by the thermal deformation correction method using this estimated amount of thermal deformation.

Next, we will explain the thermal deformation estimation method applied to this NC lathe. In this embodiment, the thermal deformation estimation method includes various steps S1 to S7 shown in Figure 3, and these steps S1 to S7 are executed according to the flow shown in Figure 3.

In this thermal deformation estimation method, first, a test condition setting step S1 is performed. In this embodiment, the test conditions are planned by an experimental design method using an orthogonal array, an all pair method, etc. The factors and levels of the test conditions to which the experimental design method is applied are combined, for example, as shown in Table 1.

図４を参照して、表１における加工径（Ｄ）（ｍｍ）は、被加工物の加工終了時の加工径であり、加工長さ（Ｌ）（ｍｍ）は、主軸の軸方向の加工範囲であり、加工回数（Ｎ）は、１サイクル中の荒加工の回数である。また、周囲温度（Ｔ）における「温度上昇」とは、試験開始前までは２０℃に、試験開始後から３時間までは２５℃に、それ以降は３０℃に保って加工を行うことであり、「温度一定」とは、常時２０℃保って加工を行うことであり、また「温度低下」とは試験開始前までは３０℃に、試験開始から３時間までは２５℃に、それ以降は２０℃に保って加工を行うことである。この試験条件における加工径（Ｄ）、加工長さ（Ｌ）、加工回数（Ｎ）及び周囲温度（Ｔ）については、ＮＣ旋盤の機種などにより、適宜の値に設定することができる。

Referring to Fig. 4, the machining diameter (D) (mm) in Table 1 is the machining diameter at the end of machining of the workpiece, the machining length (L) (mm) is the machining range in the axial direction of the spindle, and the number of machining operations (N) is the number of rough machining operations in one cycle. In addition, the "temperature increase" in the ambient temperature (T) means machining is performed while maintaining the temperature at 20°C before the start of the test, at 25°C for 3 hours from the start of the test, and at 30°C thereafter, while the "constant temperature" means machining is performed while maintaining the temperature at 20°C all the time, and the "temperature decrease" means machining is performed while maintaining the temperature at 30°C before the start of the test, at 25°C for 3 hours from the start of the test, and at 20°C thereafter. The machining diameter (D), machining length (L), number of machining operations (N), and ambient temperature (T) under these test conditions can be set to appropriate values depending on the type of NC lathe, etc.

The number of times of machining refers to the number of times rough machining is performed. After this rough machining, one finishing machining is performed, and after this finishing machining, the spindle blade distance C between the tip of the machining tool K and the outer peripheral surface of the workpiece P is measured.

Then, the factors and levels in Table 1 are applied to the L9 orthogonal array as shown in Table 2, and the test conditions are determined as shown in Table 2, for example. The test time (the test time for test numbers L1 to L9) is set to, for example, about 6 to 10 hours (e.g., 8 hours) assuming a typical test time, and processing stoppages for maintenance work, etc. may be provided during this test period, for example, about 10 minutes 1 hour after the start of the test, about 60 minutes 3 hours after the start of the test, and about 20 minutes 5 hours after the start of the test.

このようして実験計画法を用いて試験条件を設定すると、次に、主軸刃物間距離及び温度測定ステップＳ２が実行される。ＮＣ旋盤の複数箇所（この実施形態では、２２箇所であって、第１～第２２箇所Ｃｈ１～Ｃｈ２２）に対応して温度変化を測定するために第１～第２２温度検知センサＳＥ１～ＳＥ２２が取り付けられる。第１～第２２温度検知センサＳＥ１～ＳＥ２２としては、例えば、一般的に使用されているＴ型熱電対を用いることができ、このＴ型熱電対によって、ＮＣ旋盤の複数の第１～第２２箇所Ｃｈ１～Ｃｈ２２の温度状態を検知する。

After the test conditions are set using the experimental design method in this way, step S2 of measuring the spindle-to-cutter distance and temperature is then executed. First to 22nd temperature detection sensors SE1 to SE22 are attached to measure temperature changes corresponding to multiple locations on the NC lathe (22 locations in this embodiment, 1st to 22nd locations Ch1 to Ch22). For example, commonly used T-type thermocouples can be used as the first to 22nd temperature detection sensors SE1 to SE22, and these T-type thermocouples detect the temperature states of the multiple 1st to 22nd locations Ch1 to Ch22 on the NC lathe.

For example, the first to 22nd temperature detection sensors SE1 to SE22 are provided at the first to 22nd locations Ch1 to Ch22 of the NC lathe, and the relationship between the first to 22nd locations Ch1 to Ch22 (locations where the first to 22nd temperature detection sensors SE1 to SE22 are provided) and the parts of the NC lathe is as shown in Table 3. Some of the first to 22nd locations Ch1 to Ch22 that can be illustrated are shown in Figures 1 and 2. Note that the locations where the temperatures are measured can be set as appropriate, and some of the first to 22nd locations Ch1 to Ch22 can be changed or some of these locations can be omitted, or other locations can be added to the first to 22nd locations Ch1 to Ch22.

この実施形態においては、ＮＣ旋盤は簡易的な空調室に設置して試験を行い、表３におけるＣｈ１８（環境温度）とは、この簡易的な空調室の温度であり、またＣｈ１９（空調室外気）とは、この簡易的な空調室の外側の温度である。

In this embodiment, the NC lathe is installed in a simple air-conditioned room and the test is performed. Ch18 (ambient temperature) in Table 3 is the temperature of this simple air-conditioned room, and Ch19 (outside the air-conditioned room) is the temperature outside the simple air-conditioned room.

In this spindle-to-blade distance and temperature measurement step S2, tests are performed for the test numbers in Table 2, and the temperatures of locations 1 to 22 Ch1 to Ch22 are measured at the end of one cycle of test machining for each workpiece, and the spindle-to-blade distance C during test machining is measured. These measured temperatures and spindle-to-blade distance C are then stored in a computer storage device (not shown) or the like.

The test in the spindle-to-cutter distance and temperature measurement step S2 may be an actual cutting test in which the workpiece P is actually cut, or an actual cutting and simulated cutting test may be performed by combining the actual cutting test with a simulated cutting test in which the cutting tool is moved in the same manner as when the workpiece P is processed (a test in which the workpiece is not actually cut). In this case, for example, in the simulated cutting test, a dummy workpiece is used as the workpiece, and the cutting tool is moved in the same manner as in the actual cutting test to perform the simulated test. In addition, in the actual cutting test, the actual cutting test is performed by combining the use of cutting fluid and the absence of cutting fluid, and by combining the presence and absence of cutting fluid in this way, the amount of thermal deformation in cutting, including cutting with cutting fluid and cutting without cutting fluid, can be estimated.

In the actual cutting test and the simulated cutting test, the cutting tool K is moved, for example, from the origin O in FIG. 4 in the X-axis direction and then moved in the Z-axis direction. In the actual cutting test, the cutting tool K acts on the workpiece P to perform actual cutting. In the simulated cutting test, the cutting tool K is moved without acting on a dummy workpiece (not shown) to perform simulated cutting. After one cycle of the actual cutting test and the simulated cutting test is completed, the cutting tool K is returned to the origin. In this returned state, the temperatures of the 1st to 22nd locations Ch1 to Ch22 are detected by the 1st to 22nd temperature detection sensors SE1 to SE22, and the spindle-to-blade distance (C) (see FIG. 4) is measured.

In this way, the temperature change trends of the temperature changes at the 1st to 22nd locations Ch1 to Ch22 of the NC lathe (i.e., changes in the temperatures detected by the 1st to 22nd temperature detection sensors SE1 to SE22) are grouped (change trend grouping step S3), and the measurement locations are narrowed down from the multiple grouped groups (measurement location narrowing down step S4).

In the change tendency grouping step S3, a parameter called similarity is defined, and using this parameter, the smaller the similarity value, the more similar the temperature change tendency is, and grouping is performed. When calculating this similarity, two temperature measurement points to be compared are selected under certain test conditions (in this embodiment, the test with the test number in Table 2), and in this embodiment, any two of the 1st to 22nd points Ch1 to Ch22 are selected, and one of the two selected measurement points is used as the reference object and the other is used as the comparison object to calculate the similarity.

To explain this similarity with reference to Figure 5, for example, as shown in Figure 5(a), the temperature of measurement location A of the reference object (e.g., first location Ch1) changes as shown by the solid line ΔT1, and the temperature of measurement location B of the comparison object (e.g., second location Ch2) changes as shown by the dashed line ΔT2.

To calculate this similarity, first, as shown in FIG. 5(b), the temperature change (ΔT1) at measurement location A (first location Ch1) of the reference object is divided by its maximum temperature change (ΔTmax) to make the temperature change at measurement location A (reference location) dimensionless.

Next, the temperature change at the measurement point B (second location Ch2) to be compared is multiplied by a coefficient α (°C ^-1 ), and the sum of squared residuals between this value and the temperature change at the measurement point A, which has been made dimensionless, is calculated. The sum of these sums of squared residuals for all the tests under consideration (in this embodiment, all the tests with the test numbers in Table 2) is defined as the similarity between measurement point A (first location Ch1) and measurement point B (second location Ch2), and the similarity is calculated. The coefficient α is a value determined so as to minimize the similarity.

The results of this similarity for all combinations of measurement locations, i.e. locations 1 to 22 (Ch1 to Ch22), are shown in Table 4.

このような定義の類似度は、比較に用いた二つの測定箇所（基準対象の測定箇所と比較対象の測定箇所）の温度変化量の残差二乗和の和であるために、この類似度が小さいほど、その二箇所の測定箇所の温度変化傾向の相関が高くなり、このようにしてすべての測定箇所について類似化傾向を判断する。

Since the similarity defined in this manner is the sum of the residual sums of squares of the temperature changes between the two measurement points used in the comparison (the measurement point of the reference subject and the measurement point of the comparison subject), the smaller this similarity is, the higher the correlation between the temperature change trends of the two measurement points. In this way, the similarity tendency is determined for all measurement points.

When grouping temperature change trends, the similarity between two measurement points, excluding points where the same temperature is measured, is extracted in ascending order of value, and groups are created by removing duplicate combinations. A threshold is set for this grouping, and grouping is performed based on this threshold. Note that an appropriate value can be set for this threshold.

When the temperature change trends at locations 1 to 22 (Ch1 to Ch22) are grouped based on similarity as described above, they are classified into 1st to 9th groups (G1 to G9), as shown in Table 5, for example.

そして、この温度変化傾向のグループ、この実施形態では第１～第９グループＧ１～Ｇ９から測定箇所の絞り込みが行われる（測定箇所絞込みステップＳ４）。この絞込みにおいては、設定する熱変形推定式の項数に対応する数の測定箇所を選択し、例えば、４項の熱変形推定式を設定するときには４箇所の測定箇所を選択し、例えば３項（又は５項）の熱変形式を設定するときには３箇所（又は５箇所）の測定箇所を選択するようになる。

Then, the measurement locations are narrowed down from the temperature change tendency groups, which in this embodiment are the first to ninth groups G1 to G9 (measurement location narrowing down step S4). In this narrowing down, the number of measurement locations is selected corresponding to the number of terms in the thermal deformation estimation formula to be set. For example, when a four-term thermal deformation estimation formula is set, four measurement locations are selected, and when a three-term (or five-term) thermal deformation formula is set, three (or five) measurement locations are selected.

In this narrowing down, one or two measurement locations are narrowed down from one group. When three or more measurement locations are narrowed down from one group, the emphasis is on the temperature change of the specific group selected, and the temperature change of the entire NC lathe is not taken into consideration, which is undesirable. In addition, in this narrowing down, it is desirable to include the second group G2, which includes the greatest number of measurement locations (10 in this case). By including this second group G2, the temperature change of the representative measurement locations of the NC lathe is taken into consideration, making it possible to more accurately estimate the amount of thermal deformation of the workpiece P.

In consideration of the above, in this embodiment, the second group G2 containing the most measurement points (in this case, 10), the third group G3 containing the second most measurement points (in this case, 5), and the remaining seven groups (groups containing one measurement point), for example, the fifth and seventh groups G5 and G7, are selected. Note that for the remaining seven groups, any two groups may be selected from groups containing measurement points that measured temperatures related to the NC lathe (i.e., measurement points other than the 19th measurement point Ch19), and for example, the fourth and sixth groups G4 and G6 may be selected instead of the fifth and seventh groups G5 and G7.

Then, one measurement location is narrowed down from the selected group (second group G2, third group G3, fifth group G5, and seventh group G7). In this embodiment, for the second group G2, the sixth measurement location Ch6 is narrowed down from the ten measurement locations, for the third group G3, the twelfth measurement location Ch12 is narrowed down from the five measurement locations, for the fifth group 5G, the eighth measurement location Ch8 is narrowed down, and for the seventh group G7, the fourteenth measurement location Ch14 is narrowed down, and in this manner, a combination of measurement locations is selected.

The second group G2 includes 10 measurement points that show the same or similar temperature change trends, so instead of the sixth measurement point Ch6, any one of the remaining nine measurement points, for example, the second measurement point Ch2, the twenty-second measurement point Ch22, the fifth measurement point Ch5, the eleventh measurement point Ch11, the eighteenth measurement point Ch18, the twentieth measurement point Ch20, the twenty-first measurement point Ch21, the ninth measurement point Ch9, and the fifteenth measurement point Ch15, may be selected as a combination of measurement points.

Furthermore, for the third group G3, similarly to the second group G2, instead of the 12th measurement point Ch12, a combination of measurement points may be selected by narrowing down the combination to, for example, any one of the third measurement point Ch3, the seventh measurement point Ch7, the 13th measurement point Ch13, and the 16th measurement point Ch16.

After narrowing down the measurement locations to four in this manner, a thermal deformation estimation equation is then set to obtain the amount of thermal deformation ΔD (i.e., the amount of change in machining diameter) of the workpiece P caused by the thermal deformation of the lathe body 2 (bed 3) (estimation equation setting step S5). In this embodiment, since the measurement locations are narrowed down to four, a thermal deformation estimation equation with the number of terms corresponding to the number of measurement locations, i.e., a four-term thermal deformation estimation equation, is set. In this case, the predicted amount ΔD1 of the amount of change in machining diameter of the workpiece P caused by the thermal deformation of the lathe body 2 (bed 3) is calculated using the following equation (1):
ΔD1=a1×ΔT1+a2×ΔT2+a3×ΔT3+a4×ΔT4...(1)
In this formula (1), ai (i=1 to 4) is an empirical constant, and ΔTi (i=1 to 4) is the amount of temperature change at each measurement point.

For example, when the number of measurement points is narrowed down to three, the thermal deformation estimation formula (i.e., the predicted amount of change in the machining diameter of the workpiece P caused by the thermal deformation of the lathe body 2) is expressed by the following formula (2):
ΔD2=a1×ΔT1+a2×ΔT2+a3×ΔT3...(2)
It can be expressed as:

Next, the measured temperature (specifically, the measured temperature change) is substituted into the above formula (1), and the experimental constants a1 to a4 are determined so that the sum of squared residuals between the actual value of the change in the machining diameter of the workpiece P and the predicted change in the machining diameter of the workpiece P using the above formula (1) ΔD1 is minimized (experimental constant determination step S6). In this embodiment, for the temperature change ΔT1, for example, the temperature change of the sixth measurement point Ch6 of the second group G2 is substituted, for the temperature change ΔT2, for example, the temperature change of the twelfth measurement point Ch12 of the third group G3 is substituted, for the temperature change ΔT3, for example, the temperature change of the eighth measurement point Ch8 of the fifth group G5 is substituted, and for the temperature change ΔT4, for example, the temperature change of the fourteenth measurement point Ch14 of the seventh group G7 is substituted. The calculation of the sum of squared residuals can be performed, for example, by a simple numerical solution.

Then, the empirical constants a1 to a4 of the thermal deformation estimation formula are determined using the calculation results (empirical constant determination step S7). The empirical constants determined in this way are, for example, as shown in Table 6.

この表６に示す実験定数ａ１～ａ４を用いることにより、上記式（１）は、次の式（３）、
ΔＤ１＝５．３７×ΔＴ１＋０．５０×ΔＴ２－４．８３×ΔＴ３＋
０．２６×ΔＴ４ ・・・（３）
と表すことができ、このようにして上述したＮＣ旋盤を用いたときの旋盤本体２（ベッド３）の熱変形による被加工物Ｐの加工径変化予測量ΔＤ１（ΔＤ３）を演算する熱変形推定式を決定することができる。

By using the experimental constants a1 to a4 shown in Table 6, the above formula (1) can be expressed as the following formula (3):
ΔD1=5.37×ΔT1+0.50×ΔT2-4.83×ΔT3+
0.26 × ΔT4 (3)
In this way, it is possible to determine a thermal deformation estimation equation for calculating a predicted amount of change ΔD1 (ΔD3) in the machining diameter of the workpiece P due to the thermal deformation of the lathe body 2 (bed 3) when the above-mentioned NC lathe is used.

In order to determine more optimal experimental constants, the combination of temperature tendency groups and/or the combination of narrowed-down measurement points in the measurement point narrowing-down step S4 are changed and the estimation formula setting step S5 and the experimental constant determination step S6 are repeated multiple times (for example, about 10 to 30 times) (repeated experimental constant determination step S7). In the second round, for example, for the second group G2, the second measurement point Ch2 is narrowed down, for example, for the third group G3, the seventh measurement point Ch7 is narrowed down, for example, for the fourth group G4, the fourth measurement point Ch4 is narrowed down, and for example, for the sixth group G6, the tenth measurement point Ch10 is narrowed down, thus changing the combination of measurement points (measurement point narrowing-down step S4). After narrowing down the measurement points to four points for the second round in this way, the thermal deformation amount ΔD (i.e., the amount of change in machining diameter) of the workpiece P caused by the thermal deformation of the lathe body 2 (bed 3) is then obtained (estimation formula setting step S5). In this case, the predicted change in machining diameter of the workpiece P caused by the thermal deformation of the lathe body 2 (bed 3) is calculated by the following formula (1):
ΔD1=a1×ΔT1+a2×ΔT2+a3×ΔT3+a4×ΔT4...(1)
The measured temperature (specifically, the measured temperature change) is substituted into this formula (1), and the experimental constants a1 to a4 are determined so that the residual sum of squares between the actual value of the machining diameter change of the workpiece P and the predicted machining diameter change ΔD1 of the workpiece P using the above formula (1) is minimized. In the second case, for example, the temperature change of the second measurement point Ch2 of the second group G2 is substituted for the temperature change ΔT1, for example, the temperature change of the seventh measurement point Ch7 of the third group G3 is substituted for the temperature change ΔT2, for example, the temperature change of the fourth measurement point Ch4 of the fourth group G4 is substituted for the temperature change ΔT3, and for example, the temperature change of the tenth measurement point Ch10 of the sixth group G6 is substituted for the temperature change ΔT4. The calculation of the residual sum of squares can also be performed using a simple numerical solution, as described above. Then, using the calculation results, the second experimental constants a1 to a4 are determined (experimental constant determination step S6).

In this way, the combination of temperature trend groups and/or the combination of narrowed-down measurement locations in the measurement location narrowing-down step S4 are changed, and the estimation formula setting step S5 and the experimental constant determination step S6 are repeated multiple times to perform the experimental constant determination repetition step S7. Note that the number of repetitions in this experimental constant determination repetition step S7 can be set to an appropriate number, and may be performed for all combinations of temperature trend groups and narrowed-down measurement locations.

Then, an optimal experimental constant determination step S8 is performed to determine the optimal combination of measurement points and optimal experimental constants suitable for the thermal deformation estimation formula. To determine this optimal experimental constant, the thermal deformation amount ΔD (i.e., the amount of change in machining diameter) of the workpiece P is calculated using a thermal deformation estimation formula into which experimental constants determined for each of multiple combinations are substituted, and the thermal deformation estimation formula that is closest to the amount of thermal deformation of the workpiece due to actual machining is determined from these calculated thermal deformation estimation formulas, and the experimental constants in this thermal deformation estimation formula become the optimal experimental constants.

When the optimal experimental constants are determined in this manner, the optimal measurement locations are also determined, and a thermal deformation estimation formula that applies these optimal experimental constants is also determined. This thermal deformation estimation formula, the optimal combination of measurement locations, and the optimal experimental constants can be used to accurately estimate the amount of thermal deformation of the workpiece P (thermal deformation amount estimation step S9). When using this thermal deformation estimation formula (3), it is not necessary to provide the first to second temperature detection sensors SE1 to SE22 at the first to second measurement locations Ch1 to Ch22 described above, and it is sufficient to provide temperature detection sensors at the measurement locations narrowed down when determining this thermal deformation estimation formula (3).

For example, if the measurement points of the temperature fluctuation adopted in the thermal deformation estimation formula determined as the optimal experimental constant are, for example, the sixth measurement point Ch6, the twelfth measurement point Ch12, the eighth measurement point Ch8, and the fourteenth measurement point Ch14, then it is sufficient to provide a sixth temperature detection sensor SE6 corresponding to the sixth measurement point Ch6, a twelfth temperature detection sensor SE12 corresponding to the twelfth measurement point Ch12, an eighth temperature detection sensor SE8 corresponding to the eighth measurement point Ch8, and a fourteenth temperature detection sensor SE14 corresponding to the fourteenth measurement point Ch14. After this thermal deformation estimation formula (3) is determined, the predicted amount of change in the machining diameter of the workpiece P can be accurately calculated with a relatively simple configuration.

The thermal deformation estimation formula (3) obtained in this way can be applied to the thermal deformation correction of the workpiece P. When actually applying it to an NC lathe for processing, for example, it can be performed as follows, following the flow shown in Figure 6. First, one cycle of a predetermined processing (for example, cutting processing) is performed on the workpiece (processing step S11).

When this processing cycle is completed, the temperatures at the four measurement points (in this case, for example, the sixth measurement point Ch6, the twelfth measurement point Ch12, the eighth measurement point Ch8, and the fourteenth measurement point Ch14) are measured by temperature detection sensors (in this case, the sixth temperature detection sensor SE6, the twelfth temperature detection sensor SE12, the eighth temperature detection sensor SE8, and the fourteenth temperature detection sensor SE14) (temperature measurement step S12).

Next, the measured temperatures at the four measurement locations are used to calculate the predicted amount of thermal deformation of the workpiece (predicted amount calculation step S13). When using thermal deformation estimation formula (3), the temperature change amounts (ΔT1 to ΔT4) at the four measurement locations are calculated, and these temperature change amounts (ΔT1 to ΔT4) are substituted into the thermal deformation formula (3) to perform calculations, thus calculating the predicted amount of thermal deformation in the current processing cycle. The current predicted amount of thermal deformation (estimated amount of thermal deformation) is registered in a storage device or the like, as it will be used in the next processing cycle.

Then, the difference between the predicted amount of thermal deformation in the previous machining cycle and the predicted amount of thermal deformation in the current machining cycle is calculated (predicted amount difference calculation step S14), and the thermal deformation is corrected so that this predicted difference is reflected in the next machining cycle (thermal deformation correction step S15). That is, this predicted amount difference is added to the machining conditions for machining the workpiece, and thermal deformation correction is performed in this way. Then, in the next machining cycle, the machining cycle is performed under the machining conditions after thermal deformation correction, and machining (cutting) of the workpiece is performed while repeatedly performing thermal deformation correction in this way. By machining in this way, high-precision machining with minimal thermal deformation is possible.

In the above embodiment, an example was described in which thermal deformation correction is performed for each cycle of processing the workpiece, but such thermal deformation correction may be performed for multiple cycles of the workpiece (for example, an appropriate number of cycles, for example, three cycles).

We verified whether the thermal deformation estimation formula determined as described above could actually be applied to, for example, an NC lathe, and obtained the results shown in Tables 7 and 8.

表７は、切削油を使用しない場合における結果を示し、表８は、切削油を使用した場合における結果を示し、切削油を使用した場合及び使用しない場合の双方において、上記熱変形推定式を用いることにより熱補正の効果が得られることが確認できた。

Table 7 shows the results when cutting oil is not used, and Table 8 shows the results when cutting oil is used. It was confirmed that the effect of thermal correction can be obtained by using the above thermal deformation estimation formula both when cutting oil is used and when it is not used.

The above describes one embodiment of the thermal deformation estimation method and thermal deformation correction method for a machine tool according to the present invention, but the present invention is not limited to this embodiment, and various modifications and alterations are possible without departing from the scope of the present invention.

For example, in the above-described embodiment, in the experimental constant determination repeat step S7, the combination of temperature trend groups and/or the combination of narrowed-down measurement locations are changed to determine the optimal combination of measurement locations and optimal experimental constants for the thermal deformation estimation formula. However, instead of this configuration, in the experimental constant determination repeat step S7, the combination of temperature trend groups, the combination of measurement locations and/or the form of the thermal deformation estimation formula may be changed to determine the optimal thermal deformation estimation formula suitable for the machine tool and the optimal combination of measurement locations and optimal experimental constants suitable for this. When this is done, the amount of thermal deformation (change in machining diameter) of the workpiece can be estimated with higher accuracy.

In this case, in the experimental constant determination repeat step, it is preferable to set at least two of the three or more thermal deformation estimation equations consisting of three, four, or five or more terms, and to repeat the estimation equation setting step and the experimental constant determination step by changing the combination of temperature trend groups and/or the combination of measurement points to be narrowed down using at least two thermal deformation estimation equations, to determine the thermal deformation estimation equation with the optimal number of terms, the optimal combination of measurement points, and the optimal experimental constants.

For example, in the above-described embodiment, in the step of measuring the spindle-to-cutter distance and temperature in the thermal deformation estimation method, the spindle-to-cutter distance and the temperature change at the measurement point are measured by an actual cutting test alone or a combination of an actual cutting test and a simulated cutting test. However, the present invention is not limited to this configuration, and the simulated cutting test can also be performed alone. In this case, the spindle-to-cutter distance is measured using a dummy workpiece.

2 lathe body 3 bed 4 spindle section 6 turret device 7 spindle 14 moving member 16 support table 18 first support mechanism 20 second support mechanism 26 turret body Ch1 to Ch22 measuring points K machining tool P workpiece SE1 to SE22 temperature detection sensors

Claims (6)

a test condition setting step for setting test conditions for a workpiece taking into consideration actual machining of the machine tool using an experimental design method; a spindle-to-cutter distance and temperature measurement step for measuring the spindle-to-cutter distance and temperature changes at multiple locations of the machine tool when a simulated cutting test and/or an actual cutting test based on the test conditions is performed on the workpiece; a change tendency grouping step for grouping locations showing similar trends based on the change tendency of the measured temperatures at the multiple locations; a measurement location narrowing down step for selecting multiple temperature trend groups from the grouped multiple temperature tendency groups and narrowing down one or two measurement locations from each selected temperature trend group; an estimation equation setting step for setting a thermal deformation estimation equation with a number of terms corresponding to the number of narrowed-down measurement locations; a step of repeating the estimation formula setting step and the experimental constant determination step a plurality of times by changing the combination of the temperature trend groups and/or the combination of the measurement points to be narrowed down in the measurement point narrowing down step, and a step of determining an optimal combination of measurement points and an optimal experimental constant suitable for the thermal deformation estimation formula after the experimental constant determination repetition step; and a step of estimating the amount of thermal deformation of the workpiece using the thermal deformation estimation formula, the optimal combination of measurement points, and the optimal experimental constant. The thermal deformation estimation method according to claim 1, characterized in that in the empirical constant determination repeat step, the estimation formula setting step and the empirical constant determination step are repeated multiple times by changing the combination of the temperature trend groups in the measurement location narrowing down step, the combination of narrowed down measurement locations, and/or the form of the thermal deformation estimation formula, and in the optimal experimental constant determination step, an optimal thermal deformation estimation formula suitable for the machine tool, an optimal combination of measurement locations suitable for this, and the optimal experimental constant are determined. The thermal deformation estimation method for a machine tool according to claim 2, characterized in that in the empirical constant determination repeat step, at least two of three or more thermal deformation estimation equations each having three, four, or five or more terms are set, and the estimation equation setting step and the empirical constant determination step are repeated by changing the combination of the temperature tendency groups and/or the combination of the narrowed-down measurement points using at least two thermal deformation estimation equations. A method for estimating thermal deformation of a machine tool as described in any one of claims 1 to 3, characterized in that in the change tendency grouping step, the temperature change amount on the reference side is divided by the maximum temperature change amount to make the temperature change amount on the reference side dimensionless, and then a coefficient is multiplied by the temperature change to be compared, and the sum of squared residuals between this coefficient-integrated temperature change and the dimensionless temperature change is calculated to calculate a similarity, and the temperature change tendencies are grouped based on the similarity. The method for estimating thermal deformation of a machine tool according to claim 1, characterized in that the machine tool is an NC lathe, the experimental design method is an all-pair method, and the test conditions set in the test condition setting step include the diameter of the workpiece, the machining length of the workpiece, the number of times the workpiece is machined, fluctuations in the machining environment temperature, and the use or non-use of cutting oil. a test condition setting step of setting test conditions for a workpiece taking into consideration actual machining of a machine tool using an experimental design method; a spindle-to-cutter distance and temperature measurement step of measuring a spindle-to-cutter distance and temperature changes at a plurality of locations of the machine tool when a simulated cutting test and/or an actual cutting test based on the test conditions is performed on the workpiece; a change tendency grouping step of grouping locations showing similar trends based on the change trends of the measured temperatures at the plurality of locations; a measurement location narrowing down step of selecting a plurality of temperature tendency groups from the plurality of grouped temperature tendency groups and narrowing down one or two measurement locations from each selected temperature tendency group; an estimation equation setting step of setting a thermal deformation estimation equation having a number of terms corresponding to the number of narrowed-down measurement locations; and a residual between an actual value of the change in the workpiece and a predicted amount of change in the workpiece using the thermal deformation estimation equation by substituting an amount of change in the measured temperature corresponding to each term in the thermal deformation estimation equation. a thermal deformation estimation step for estimating an amount of thermal deformation of the workpiece using the thermal deformation estimation formula, the optimal combination of measurement points, and the optimal experimental constant; a deformation amount difference calculation step for calculating a difference in the amount of thermal deformation of the workpiece in a previous machining process and a thermal deformation amount of the workpiece in a current machining process; and a thermal deformation correction step for correcting the difference in the amount of thermal deformation calculated in the deformation amount difference calculation step.

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