JP7532736B2 - Compensator derivation device, position error compensation device, machine tool, transfer function derivation method and program - Google Patents

Description

This disclosure relates to a compensator derivation device, a position error compensation device, a machine tool, a transfer function derivation method, and a program.

When performing high-precision machining using a machine tool, it is necessary to consider the influence of vibrations of the machine tool. Figure 7 shows an example of a gate-type machine tool. The machine tool 1 shown in Figure 7 includes a machine tool body 5, a ram 7 supported on the machine tool body 5 so as to be movable along the Z-axis direction, and an attachment 8 detachably attached to the tip of the ram 7. The machine tool body 5 includes a bed 2, a table 3 arranged on the bed 2 and movable along the X-axis direction, a gate-type column 4 arranged to straddle the table 3, and a saddle 6 movable along the Y-axis direction on the column 4. The table 3 is movable along the X-axis direction by a ball screw drive mechanism. A cross rail 9 is attached to the column 4 in the Y-axis direction, and the saddle 6 moves on the cross rail 9 so that the saddle 6 can move along the Y-axis direction. The ram 7 is attached to the saddle 6 so as to be movable along the Z-axis direction. An attachment 8 for performing cutting and the like is attached to the tip of the ram 7. For example, the machine tool 1 is equipped with a CAM (computer aided manufacturing) system and a control device, and the CAM system reads CAD (computer aided design) data of the workpiece and generates NC (numerical control) data, and the control device controls the movement of the saddle 6 and ram 7 based on the NC data.

In the machine tool 1 illustrated in FIG. 7, when a movement is performed in which the acceleration is discontinuous in the Y-Z plane (for example, the trajectory of the movement of the tip of the ram 7 is L-shaped), transient vibrations may occur in the column 4. When the column 4 vibrates, an error occurs between the tip position of the ram 7 and the target position indicated by the NC data, which affects the machining accuracy. In order to improve the machining accuracy, it is necessary to reduce the error between the tip position of the ram 7 and the target position caused by the vibration of the column 4. In order to compensate for this position error, a compensator may be provided in the control device. This compensator may be designed using a physical model expressed by a simple formula (for example, a one-dimensional equation of motion) based on the mass, moment of inertia, and stiffness of parts of the main components (for example, the column 4, the saddle 6, and a motor (not shown) that drives the movement of the saddle 6) in order to express the vibration characteristics of the machine tool 1 (for example, Patent Document 1).

JP 2011-3137 A

However, in the compensator designed as above, the number of components has been reduced and the physical model simplified, so it is not possible to take into account the effects of the posture, friction, backlash, etc. of each component, and there is a limit to how effectively it can reduce position errors.

The present disclosure therefore aims to provide a compensator derivation device, a position error compensation device, a machine tool, a transfer function derivation method, and a program that can solve the above-mentioned problems.

According to one aspect of the present disclosure, the compensator derivation device includes a data acquisition unit that acquires frequency characteristic data of a machine that vibrates, a machine transfer function derivation unit that derives a machine transfer function that is a transfer function that approximates the frequency characteristic data, and a compensator derivation unit that uses the machine transfer function to derive a compensator for compensating for a positioning error caused by vibration of the machine.

According to one aspect of the present disclosure, the position error compensation device obtains a position command for the moving mechanism, compensates the position command using the compensator calculated by the compensator derivation device, and outputs the compensated position command.

According to one aspect of the present disclosure, a machine tool includes a machine tool body, a movement mechanism supported by the machine tool body for moving a tool, and a control device that includes the above-mentioned position error compensation device and controls the movement mechanism based on the position command after compensation to the movement mechanism.

According to one aspect of the present disclosure, a transfer function derivation method includes the steps of acquiring frequency characteristic data of a machine that vibrates, deriving a machine transfer function that is a transfer function that approximates the frequency characteristic data, and deriving a compensator for compensating for a positioning error caused by vibration of the machine using the machine transfer function.

According to one aspect of the present disclosure, a program causes a computer to execute the steps of acquiring frequency characteristic data of a machine that vibrates, deriving a machine transfer function that is a transfer function that approximates the frequency characteristic data, and deriving a compensator for compensating for a positioning error caused by vibration of the machine using the machine transfer function.

The compensator derivation device, position error compensation device, machine tool, transfer function derivation method, and program disclosed herein can reduce the position error of a moving mechanism.

FIG. 4 illustrates an example of a moving mechanism according to an embodiment. FIG. 1 illustrates an example of a servo control device according to an embodiment. FIG. 2 illustrates an example of a compensator derivation device according to an embodiment. 11 is a flowchart illustrating an example of a process for calculating a compensator according to an embodiment. FIG. 4 is a diagram illustrating an example of frequency characteristic data according to an embodiment. FIG. 1 illustrates an example of a compensator design method according to an embodiment. FIG. 1 is a schematic perspective view showing an example of a gate-type machine tool. FIG. 2 is a diagram illustrating an example of a hardware configuration of a servo control device and a compensator derivation device according to an embodiment.

<Embodiment>
(Configuration of the moving mechanism)
FIG. 1 is a diagram illustrating an example of a moving mechanism according to an embodiment of the present disclosure.
1 shows a schematic configuration of a ball screw drive mechanism that controls the position of the saddle 6 in the Y-axis direction in the machine tool 1 in FIG. 7 to coincide with a command position θ. The ball screw drive converts the rotational motion of a motor 90 into linear motion by a ball screw feed unit 93 consisting of a ball screw nut 91 and a ball screw shaft 92, and moves the saddle 6 in the Y-axis direction. The motor 90 is provided with a motor encoder 94 that detects a motor speed ωM. The motor encoder 94 outputs the detected motor speed ωM to a servo control device 100. The ball screw drive mechanism is provided with a linear scale 95. The linear scale 95 detects a position _θL that indicates the position of the saddle 6 in the Y-axis direction, and outputs it to the servo control device 100.

The servo control device 100 calculates a command torque τ based on the command position θ and outputs the command torque τ to the motor 90. This rotates the motor 90, rotates the ball screw shaft 92, and moves the ball screw nut 91 and the saddle 6 fixedly connected thereto in the Y-axis direction. The position of the ram 7 may also be controlled in the Z-axis direction by a similar mechanism. When the saddle 6 moves in the Y-axis direction or the ram 7 moves in the Z-axis direction during cutting or other processing, vibrations are generated in the column 4, and these vibrations affect the accuracy of the position control of the saddle 6 and the ram 7. The servo control device 100 is equipped with a mechanical deflection compensation unit 20 (Figure 2) for compensating for positioning errors caused by vibrations in the column 4.

FIG. 2 is a diagram illustrating an example of a servo control device according to an embodiment.
The servo control device 100 has a mechanical deflection compensation unit 20 , a velocity feedforward unit 40 , a subtraction unit 41 , a multiplication unit 42 , a subtraction unit 43 , and a proportional integral calculation unit 44 .
The mechanical deflection compensation unit 20 is configured by a second-order transfer function 21 for compensation (hereinafter, this is also referred to as the "compensator 21"). In another embodiment, the compensator 21 may not be a second-order transfer function, and may be a third-order or higher transfer function. The mechanical deflection compensation unit 20 compensates the command position θ by the compensator 21, and outputs a command position θ' after compensation. The subtraction unit 41 outputs a deviation position Δθ which is a difference between the command position θ' after compensation and the position _θL of the saddle 6. The multiplication unit 42 multiplies the deviation position Δθ by a position loop gain _KP and outputs a deviation speed ΔV. The speed feedforward unit 40 is configured to calculate a compensation speed V' that compensates for position error factors such as "strain,""deflection," and "viscosity" that occur in the motor 90 and the saddle 6. The subtraction unit 43 outputs a command speed V obtained by adding the compensation speed V' output from the speed feedforward unit 40 to the deviation speed ΔV and subtracting the motor speed ωM from the result. The proportional integral calculation unit 44 performs proportional integral calculation of the command speed V and outputs a command torque τ. The proportional integral calculation unit 44 calculates the command torque τ by τ = _VKT { _KV (1 + (1/ _TVs ))} using the speed loop gain _KV , the integral time constant _TV , and the torque constant _KT . In this embodiment, the purpose is to calculate the compensator 21 for controlling the position of the saddle 6 so that the position of the tip of the ram 7 in the Y-axis direction coincides with the command position θ.

As shown in FIG. 1, the command torque τ is output to the motor 90 of the machine tool 1, but can also be output to, for example, a multibody dynamics (MBD) model 200 (hereinafter, simply referred to as the "MBD model 200") of the machine tool 1. The MBD model 200 is a three-dimensional model of the machine tool 1 constructed during multibody dynamics analysis. When a product consisting of multiple parts is defined as a multibody, the multibody analysis is a numerical analysis technique that analyzes the dynamics of a multibody that is interconnected from the part level to the product level, and the MBD model 200 is an analysis model used in this analysis. In the MBD model 200, the rigidity of the components (including machine element parts such as ball screws) that constitute the movement mechanism of the machine tool 1, the shape of the structural parts, and material properties such as density and Young's modulus are characterized as identification parameters. The MBD model 200 can simulate the operation of each component of the machine tool 1, but it is desirable to be able to express the operation in six degrees of freedom in each axial direction and around each axis in three dimensions. The MBD model 200 is constructed at the design stage of the machine tool 1, and is used to understand the machine performance, such as the mechanism operation and vibration characteristics.

For example, when the servo control device 100 inputs a command torque τ to the MBD model 200, the MBD model 200 simulates the movement of the saddle 6 in the Y-axis direction and calculates the motor speed ωM and the position _θL of the saddle 6 in the Y-axis direction when the command torque τ is output to the motor 90. By returning the motor speed ωM and position _θL calculated by the MBD model 200 to the servo control device 100, the servo control device 100 calculates the next command torque τ by the above processing and outputs the value to the MBD model 200. By repeating this, the saddle 6 can be moved to a target position on the MBD model 200. In addition, the MBD model 200 can calculate the change in the deflection position caused by the movement of the saddle 6 in the Y-axis direction and the forces acting on each component such as the cross rail 9 and the column 4.

In addition, for example, when the shape, density, Young's modulus, and stiffness of mechanical components such as ball screws that connect the components of the machine tool 1 are input to the MBD model 200 and a hammering test simulation is performed on the tip of the ram 7 on the MBD model 200, the MBD model 200 can calculate the vibration (acceleration) at the tip of the ram 7 in response to hammering. The frequency response of the machine tool 1 can be obtained by analyzing the acceleration calculated by the MBD model 200.

In this embodiment, the vibration of the machine tool 1 is simulated by the MBD model 200, and frequency characteristic data of the machine tool 1 is obtained from the frequency response at that time. Then, based on this frequency characteristic data, the compensator derivation device 10 derives a compensator 21 that can reduce position errors caused by vibration. Next, the compensator derivation device 10 will be described.

(Configuration of the Compensator Derivation Device)
FIG. 3 is a diagram illustrating an example of a compensator derivation device according to an embodiment.
As shown in FIG. 3 , the compensator derivation device 10 includes a data acquisition unit 11 , a mechanical transfer function derivation unit 12 , a compensator derivation unit 13 , an output unit 14 , and a storage unit 15 .
The data acquiring unit 11 acquires frequency characteristic data of the machine tool 1 obtained by analyzing the vibrations simulated by the MBD model 200. In this embodiment, the frequency characteristic data means data indicating the frequency characteristic of the gain (gain characteristic) and the frequency characteristic of the phase (phase characteristic).
The mechanical transfer function derivation unit 12 derives a quadratic transfer function that approximates the frequency characteristic data obtained from the analysis result of the MBD model 200 acquired by the data acquisition unit 11. This quadratic transfer function represents the relationship between the input and the output when the input is the command position θ and the output is the actual position of the saddle 6 in the Y-axis direction relative to the command position θ. In this embodiment, the parameters of the quadratic transfer function are determined so that the waveform of the mechanical transfer function when graphed approximates the waveform of the frequency characteristic data. For example, the quadratic transfer function _Gm (s) is expressed as follows: _Gm (s)=( ^As2 +Bs+1)/( ^Cs2 +Ds+1)... (0)
When the second-order transfer function is expressed by the following equation (1), the mechanical transfer function deriving unit 12 detects the peak frequency, notch frequency, peak gain, and notch gain from the frequency characteristic data, and determines the parameters A, B, C, and D of the equation (0) using the peak frequency, notch frequency, peak gain, and notch gain.

Here, ω _P is the peak frequency of the frequency characteristic data, ω _N is the notch frequency of the frequency characteristic data, ζ _P is the peak gain of the frequency characteristic data, ζ _N is the notch gain of the frequency characteristic data, and s is the Laplace operator.
In the following description, the second-order transfer function that approximates the frequency characteristic data obtained from the analysis results of the MBD model 200 is also referred to as the "mechanical transfer function."

The compensator derivation unit 13 derives a quadratic transfer function (compensator 21) for compensating for positioning errors due to machine vibrations based on the quadratic transfer function of equation (1). For example, the compensator derivation unit 13 derives the compensator 21 using the inverse of the mechanical transfer function derived by the mechanical transfer function derivation unit 12. An example of the compensator is shown in the following equation (2).

The output unit 14 outputs the compensator 21 to the mechanical deflection compensation unit 20 .
The storage unit 15 stores data necessary for calculations by the compensator 21, such as frequency characteristic data.

(Compensator calculation process)
Next, the calculation process of the compensator 21 by the compensator derivation device 10 will be described with reference to FIG. 4 and FIG.
FIG. 4 is a flowchart illustrating an example of a process for calculating a compensator according to an embodiment.
FIG. 5 is a diagram illustrating an example of frequency characteristic data according to an embodiment.
First, the data acquisition unit 11 acquires frequency characteristic data (step S1).
Now, reference is made to Fig. 5. Waveform C1 in the upper diagram of Fig. 5 is a waveform indicated by frequency characteristic (gain characteristic) data obtained by analyzing the frequency response obtained when an impact is applied to the tip of the ram 7 on the MBD model 200 (simulation of a hammering test is performed). The vertical axis of the upper diagram of Fig. 5 is gain (dB) indicating the ratio of the magnitude of vibration at the tip of the ram 7 to the impact input in the simulation of the hammering test, and the horizontal axis is frequency (Hz). The lower diagram of Fig. 5 shows an enlarged view of a part of the upper diagram of Fig. 5. The data acquisition unit 11 acquires the frequency characteristic data (waveform C1) and writes and stores it in the memory unit 15.

Next, the mechanical transfer function derivation unit 12 derives a mechanical transfer function (step S2).
The mechanical transfer function derivation unit 12 determines the parameters of the secondary transfer function _Gm (s) by, for example, performing curve fitting so that the waveform indicated by the secondary transfer function Gm(s) approximates the waveform C1 (particularly so that it approximates in a range including the peaks and notches of the waveform C1). In addition, for example, the mechanical transfer function derivation unit 12 may derive the secondary transfer function _Gm (s) that approximates the waveform C1 based on the peaks _C1P and notches _C1N of the waveform C1 shown in the lower diagram of Fig. 5. Specifically, the mechanical transfer function derivation unit 12 identifies the peaks _C1P and notches _C1N of the _waveform C1 and detects the peak frequency _ωP , peak gain _ζP , notch frequency _ωN , and notch gain _ζN . The mechanical transfer function derivation unit 12 applies the peak frequency ω _P , the peak gain ζ _P , the notch frequency ω _N , and the notch gain ζ _N to the parameters to derive a second-order transfer function Gm(s) that approximates the waveform C1. Specifically, the mechanical transfer function derivation unit 12 sets parameter A in equation (0) to (1/ω _N ² ), parameter B to (2ζ _N /ω _N ), parameter C to (1/ω _P ² ), and parameter D to (2ζ _P /ω _P ).

The waveform of the mechanical transfer function (Equation (1)) derived by the mechanical transfer function derivation unit 12 using the peak frequency ω _P , peak gain ζ _P , notch frequency ω _N , and notch gain ζ _N is shown in C2 of Fig. 5. Comparing the waveform C2 with the waveform C1, it can be seen that the waveform C2 is similar to the waveform C1 in the range including the peaks and notches. It is also possible to derive a third or higher order transfer function that more precisely approximates the waveform C1 over a wider range, but it has been confirmed through verification that the position error of the tip of the ram 7 is sufficiently compensated for by the compensator 21 calculated based on a second order transfer function. Of course, in other embodiments, the mechanical transfer function may be a transfer function other than a second order transfer function (such as a third order transfer function).

Next, the compensator derivation unit 13 derives the compensator 21 (step S3).
Specifically, the compensator derivation unit 13 calculates, as the compensator 21, the inverse of the second-order transfer function G _m (s) (mechanical transfer function) derived in step S2, 1/G _m (s) (Equation (2)).

Next, the output unit 14 outputs the compensator 21 to the mechanical deflection compensation unit 20 (step S4). The mechanical deflection compensation unit 20 receives and sets the compensator 21 shown in equation (2).

The compensation of the position error by the compensator 21 is performed as follows. When the command position θ is input, the mechanical deflection compensation unit 20 compensates for the command position θ by the compensator of equation (2) and outputs the compensated command position θ'. The servo control device 100 uses the compensated command position θ' to calculate the motor command value τ through various processes described with reference to FIG. 2, and controls the position of the saddle 6 in the Y-axis direction. It has been confirmed that the compensator 21 of this embodiment can reduce the position error in the position control of the ram 7 more than a conventional compensator designed based on a physical model of the main components.

In the above, the compensator 21 is calculated using the MBD model 200. When an actual machine tool 1 corresponding to the MBD model 200 exists, the accuracy of the MBD model 200 and the compensator 21 can be improved by the method shown in FIG.
FIG. 6 is a diagram showing an example of a compensator design method (a method for determining the compensator 21) according to an embodiment.
First, a hammering test simulation is performed on the MBD model 200 to obtain a frequency response (step S11). Next, the mechanical transfer function derivation unit 12 derives a mechanical transfer function using frequency characteristic data obtained by analyzing the frequency response (step S12). Next, the compensator derivation unit 13 derives a compensator 21 from the mechanical transfer function (step S13). Next, the compensator 21 calculated in step S13 is set in the mechanical deflection compensation unit 20, and a coupled simulation of the servo control device 100 and the mechanical deflection compensation unit 20 is performed (step S14). For example, the servo control device 100 moves the ram 7 on the MBD model 200 based on predetermined NC data, and records the tip position, tip speed, and tip acceleration of the ram 7 during that time in the storage unit of the computer on which the MBD model 200 operates at predetermined time intervals. Next, actual machine verification is performed using the machine tool 1 (actual machine) (step S15). For example, the servo control device 100 moves the ram 7 of the machine tool 1 (actual machine) based on the same NC data used in the coupled simulation in step S14, and records the tip position, tip speed, and tip acceleration of the ram 7 during that time in the storage device at predetermined time intervals. Then, the data recorded in step S14 and the data recorded in step S15 are compared and evaluated, and the identification parameters of the components included in the MBD model 200 are fine-tuned so that the MBD model 200 can accurately simulate the operation of the machine tool 1 (step S16). The processes in steps S11 to S16 are repeated until the difference between the actual measurement results by the actual machine and the analysis results by the MBD model 200 falls within an allowable range.

According to the compensator design method shown in FIG. 6, correlation analysis is performed between the vibration data measured from the machine tool 1 (actual machine) and the vibration data calculated by the MBD model 200, thereby improving the accuracy of the vibration characteristics calculated by the MBD model 200, and as a result, the accuracy of the compensator 21 is also improved. In addition, by deriving the compensator 21 from the MBD model 200 that has been fine-tuned through correlation analysis between the vibration data measured from the machine tool 1 (actual machine) and the MBD model 200, it is possible to deal with individual differences in the machine tool 1 due to manufacturing variances. With the machine tool 1 having the compensator 21 of this embodiment, high-precision machining of molds and the like can be achieved.

As described above, according to this embodiment, the frequency characteristics of the machine tool 1 can be obtained using the MBD model 200 of the machine tool 1. In the MBD model 200, the mass and moment of inertia are considered in three dimensions, and the positions at which components (parts, etc.) are connected are also reproduced based on design information, so that the reproducibility of the model can be made closer to the actual machine than a conventional one-dimensional physical model. In addition, the MBD model 200 can reproduce the movement of the ram 7, including the effects of backlash and the like that occurs between components, which is difficult to achieve through desk study. Therefore, even if an actual machine does not exist, the compensator 21 can be derived based on the MBD model 200 to obtain a highly accurate compensator 21. In addition, by using the MBD model 200, it is possible to obtain a frequency response at a position that cannot be measured by the actual machine (for example, a position where the vibration characteristics specific to the machine tool 1 can be measured more accurately), and it is possible to calculate a highly accurate compensator 21. Also, as explained using FIG. 6, by using the MBD model 200, it is possible to calculate a compensator 21 with a certain degree of accuracy before manufacturing the machine tool 1, and after manufacturing the machine tool 1, it is possible to adjust the compensator 21 to match the actual machine tool 1.

Conventional methods required theoretical consideration of the parameters of a one-dimensional physical model, but according to this embodiment, the compensator 21 can be derived based on the frequency characteristics of the machine tool 1, so there is no need to adjust the parameters of the physical model.

In addition, by approximating frequency characteristic data that includes nonlinear characteristics such as posture, friction, and backlash, and deriving a second-order transfer function (mechanical transfer function), it is possible to derive a compensator that takes nonlinear characteristics into account.

In the above explanation, frequency characteristic data is obtained from the MBD model 200 and the compensator 21 is derived, but frequency characteristic data may be obtained by performing a hammering test simulation on the machine tool 1 (actual machine) and the compensator 21 may be calculated by the process described with reference to FIG. 4. Also, an example of compensating for position error in the Y-axis movement control of the saddle 6 in the machine tool 1 has been described, but a similar compensator 21 may be used to compensate for position error in the Z-axis movement control of the ram 7.

In addition, the above description focuses on compensation of position errors in the position control of the saddle 6 of the machine tool 1, but the application of the compensator 21 of this embodiment is not limited to the machine tool 1, and can be applied to the position control of the moving mechanism in various structures equipped with the moving mechanism, such as industrial robots and ships.

FIG. 8 is a diagram illustrating an example of a hardware configuration of a servo control device and a compensator derivation device according to an embodiment.
The computer 900 includes a CPU 901 , a main memory device 902 , an auxiliary memory device 903 , an input/output interface 904 , and a communication interface 905 .
The above-described servo control device 100 and compensator derivation device 10 are implemented in a computer 900. The above-described functions are stored in the auxiliary storage device 903 in the form of a program. The CPU 901 reads the program from the auxiliary storage device 903, loads it in the main storage device 902, and executes the above-described processing in accordance with the program. The CPU 901 also reserves a storage area in the main storage device 902 in accordance with the program. The CPU 901 also reserves a storage area in the auxiliary storage device 903 for storing data being processed in accordance with the program.

In addition, a program for realizing all or part of the functions of the servo control device 100 and the compensator derivation device 10 may be recorded on a computer-readable recording medium, and the program recorded on the recording medium may be read into a computer system and executed to perform processing by each functional unit. The term "computer system" here includes hardware such as an OS and peripheral devices. In addition, if a WWW system is used, the term "computer system" also includes a homepage providing environment (or display environment). In addition, the term "computer-readable recording medium" refers to portable media such as CDs, DVDs, and USBs, and storage devices such as hard disks built into a computer system. In addition, if the program is distributed to the computer 900 via a communication line, the computer 900 that receives the program may expand the program into the main storage device 902 and execute the above processing. In addition, the above program may be for realizing part of the above-mentioned functions, and may further be capable of realizing the above-mentioned functions in combination with a program already recorded in the computer system.

Although several embodiments of the present invention have been described above, these embodiments are presented as examples and are not intended to limit the scope of the invention. These embodiments can be implemented in various other forms, and various omissions, substitutions, and modifications can be made without departing from the gist of the invention. These embodiments and their modifications are included in the scope of the invention and its equivalents as described in the claims, as well as in the scope and gist of the invention.

<Additional Notes>
The compensator derivation device 10, the position error compensation device (mechanical deflection compensation unit 20), and the transfer function derivation method and program described in each embodiment can be understood, for example, as follows.

(1) A compensator derivation device 10 according to a first aspect includes a data acquisition unit 11 that acquires frequency characteristic data of a machine (moving mechanism) that vibrates, a mechanical transfer function derivation unit 12 that derives a mechanical transfer function that is a transfer function that approximates the frequency characteristic data, and a compensator derivation unit 13 that uses the mechanical transfer function to derive a compensator for compensating for a positioning error due to vibration of the machine.
This makes it possible to derive a transfer function (compensator) for compensating for the error between the target position and the actual position of the machine due to vibrations of a structure that occur when a machine (moving mechanism) that involves vibration is operated (moved).

(2) The compensator derivation device 10 according to the second aspect is the compensator derivation device 10 of (1), in which the mechanical transfer function derivation unit 12 detects the peak frequency, notch frequency, peak gain, and notch gain of the frequency characteristic data, and sets the parameters of the transfer function using the peak frequency, notch frequency, peak gain, and notch gain to derive the transfer function.

第２、第３の態様に係る補償器導出装置１０によれば、構造物（工作機械１）の周波数特性データのピーク周波数、ノッチ周波数、ピークゲイン、ノッチゲインから直接的にパラメータを決定することができるので、少ない計算量で伝達関数を導出することができる。 (3) A compensator derivation device 10 according to a third aspect is the compensator derivation device 10 of (1) to (2), in which the mechanical transfer function derivation unit 12 derives the following transfer function when ω _P is a peak frequency of the frequency characteristic data, ω _N is a notch frequency of the frequency characteristic data, ζ _P is a peak gain of the frequency characteristic data, ζ _N is a notch gain of the frequency characteristic data, and s is a Laplace operator.

According to the compensator derivation device 10 according to the second and third aspects, parameters can be directly determined from the peak frequency, notch frequency, peak gain, and notch gain of the frequency characteristic data of the structure (machine tool 1), so that a transfer function can be derived with a small amount of calculation.

(4) A fourth aspect of the compensator derivation device 10 is the compensator derivation device 10 of (1) to (3), wherein the frequency characteristic data is a frequency characteristic of the structure simulated by a multibody dynamics (MBD) model of the structure.
This makes it possible to derive a compensator before manufacturing the structure, using an MBD model constructed at the design stage of the structure.

(5) The compensator derivation device 10 according to the fifth aspect is the compensator derivation device 10 of (4), in which the mechanical analysis model has at least the stiffness, shape, density, and Young's modulus of the components that make up the machine as identification parameters.

(6) The compensator derivation device 10 according to the sixth aspect is the compensator derivation device 10 according to any one of (1) to (5), in which the compensator derivation unit 13 derives the inverse of the transfer function as the compensator 21.

第６、第７の態様に係る補償器導出装置１０によれば、少ない計算量で補償器２１を導出することができる。 (7) A seventh aspect of the compensator derivation device 10 is the compensator derivation device 10 of any one of (1) to (6), in which the compensator number derivation unit 13 derives the following compensator when ω _P is a peak frequency of the frequency characteristic data, ω _N is a notch frequency of the frequency characteristic data, ζ _P is a peak gain of the frequency characteristic data, ζ _N is a notch gain of the frequency characteristic data, and s is a Laplace operator.

According to the compensator derivation device 10 according to the sixth and seventh aspects, the compensator 21 can be derived with a small amount of calculation.

(8) The compensator derivation device 10 according to the eighth aspect is the compensator derivation device 10 according to any one of (1) to (7), in which the mechanical transfer function is a second-order transfer function.

(9) A position error compensation device (mechanical deflection compensation unit 20) relating to a ninth aspect acquires a position command for the moving mechanism, compensates for the position command using the compensator 21 calculated by the compensator derivation device 10 described in any one of the first to eighth aspects, and outputs the compensated position command.
This makes it possible to compensate for the error between the target position and the actual position of the moving mechanism caused by vibrations of the structure that occur when the moving mechanism is moved.

(10) A machine tool 1 in a tenth aspect includes a machine tool body 5, a moving mechanism (column 4) supported by the machine tool body for moving a tool, and a control device (servo control device 100) that is equipped with the above-mentioned position error compensation device and controls the moving mechanism based on the position command after compensation to the moving mechanism.
This makes it possible to achieve high-precision machining.

(11) The method for deriving a compensator transfer function according to the eleventh aspect includes the steps of acquiring frequency characteristic data of a machine with vibration, deriving a transfer function that approximates the frequency characteristic data, and deriving a compensator for compensating for a positioning error caused by vibration of the machine using the transfer function.

(12) The program according to the twelfth aspect causes a computer 900 to execute the steps of acquiring frequency characteristic data of a machine that vibrates, deriving a machine transfer function that is a transfer function that approximates the frequency characteristic data, and deriving a compensator for compensating for a positioning error caused by vibration of the machine using the machine transfer function.

DESCRIPTION OF SYMBOLS 1: Machine tool 2: Bed 3: Table 4: Column 5: Machine tool body 6: Saddle 7: Ram 8: Attachment 9: Cross rail 10: Compensator derivation device 11: Data acquisition unit 12: Mechanical transfer function derivation unit 13: Compensator derivation unit 14: Output unit 15: Memory unit 20: Mechanical deflection compensation unit (position error compensation device)
21: Compensator 40: Speed feedforward section 41: Subtraction section 42: Multiplication section 43: Subtraction section 44: Proportional and integral calculation section 90: Motor 91: Ball screw nut 92: Ball screw shaft 93: Ball screw feed section 94: Motor encoder 95: Linear scale 100: Servo control device 200: MBD model 900: Computer 901: CPU
902: Main storage device 903: Auxiliary storage device 904: Input/output interface 905: Communication interface

Claims (8)

A data acquisition unit that acquires frequency characteristic data of a machine that vibrates;
a mechanical transfer function derivation unit that derives a mechanical transfer function that is a transfer function that approximates the frequency characteristic data;
a compensator derivation unit that derives a compensator for compensating for a positioning error caused by vibration of the machine using the mechanical transfer function;
Equipped with
the frequency characteristic data is obtained by a simulation for obtaining a frequency response from vibrations simulated by applying an impact to a multibody dynamics (MBD) model of the machine;
The mechanical transfer function derivation unit derives the mechanical transfer function from the following formula, where Gm(s) is the mechanical transfer function, ω _P is a peak frequency of the frequency characteristic data, ω _N is a notch frequency of the frequency characteristic data, ζ _P is a peak gain of the frequency characteristic data, ζ _N is a notch gain of the frequency characteristic data, and s is a Laplace operator:

The compensator is the inverse of the mechanical transfer function.
Compensator derivation device. The mechanical analysis model has at least the stiffness, shape, density and Young's modulus of components constituting the machine as identification parameters.
The compensator deriving device according to claim 1 . The compensator derivation unit derives the compensator as follows, where ω _P is a peak frequency of the frequency characteristic data, ω _N is a notch frequency of the frequency characteristic data, ζ _P is a peak gain of the frequency characteristic data, ζ _N is a notch gain of the frequency characteristic data, and s is a Laplace operator:

The compensator deriving device according to claim 1 or 2 . The mechanical transfer function is a second-order transfer function.
The compensator deriving device according to any one of claims 1 to 3 . Obtaining a position command for the machine;
The position command is compensated by the compensator calculated by the compensator derivation device according to any one of claims 1 to 4 , and the compensated position command is output to the machine.
Position error compensation device. A machine tool body,
a movement mechanism for moving a tool, which is the machine supported by the machine tool body;
A position error compensation device according to claim 5 ,
a control device that controls the moving mechanism based on the position command after compensation for the moving mechanism;
A machine tool comprising: Obtaining frequency characteristic data of a machine that vibrates;
Deriving a mechanical transfer function that is a transfer function that approximates the frequency characteristic data;
deriving a compensator for compensating for a positioning error due to vibration of the machine using the machine transfer function;
having
the frequency characteristic data is frequency characteristic data of the machine obtained by a simulation in which a frequency response is obtained from vibrations simulated by applying an impact to a mechanical analysis model of the machine,
When Gm(s) is the mechanical transfer function, ω _P is a peak frequency of the frequency characteristic data, ω _N is a notch frequency of the frequency characteristic data, ζ _P is a peak gain of the frequency characteristic data, ζ _N is a notch gain of the frequency characteristic data, and s is a Laplace operator, the mechanical transfer function is derived by the following formula:

The compensator is the inverse of the mechanical transfer function.
Transfer function derivation method. On the computer,
Obtaining frequency characteristic data of a machine that vibrates;
Deriving a mechanical transfer function that is a transfer function that approximates the frequency characteristic data;
deriving a compensator for compensating for a positioning error due to vibration of the machine using the machine transfer function;
Run the command,
the frequency characteristic data is frequency characteristic data of the machine obtained by a simulation in which a frequency response is obtained from vibrations simulated by applying an impact to a mechanical analysis model of the machine,
When Gm(s) is the mechanical transfer function, ω _P is a peak frequency of the frequency characteristic data, ω _N is a notch frequency of the frequency characteristic data, ζ _P is a peak gain of the frequency characteristic data, ζ _N is a notch gain of the frequency characteristic data, and s is a Laplace operator, the mechanical transfer function is derived by the following formula:

The compensator is the inverse of the mechanical transfer function.
program.

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