JP2007034653A - Path controlling method for nc milling machine - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a path-controlling method for an NC milling machine which makes a table-feeding speed cooperate with a rotation speed of a spindle, while keeping a path error minimum, to realize control for making a cutting speed constant, and makes the roughness of a cut surface of a processed product constant. <P>SOLUTION: A system represented by a stationary coordinate system (X-Y axis coordinate system) is subjected to a rotating coordinate system (D-Q axis coordinate system) conversion to decompose the system into a path error component and an advancing direction component. Then, the rotating coordinate system (D-Q axis coordinate system) is subjected to a flexible coordinate conversion, and the advancing direction component is approximately converted to a tangential line direction component. Then, a target value of a machining path on the flexible coordinates, to which the flexible coordinate conversion is made, is made to be constant, and a cutting speed, which is represented by the sum of the tangential line direction speed of a table and rotation speed of a spindle, is made to be constant. A control system, which performs the above-mentioned processes, is realized by an optimum control means. <P>COPYRIGHT: (C)2007,JPO&INPIT

Description

  The present invention relates to a path control method for an NC milling machine, and more specifically, path control for performing path control in which axes are mutually coordinated by using a rotation coordinate transformation and a stretch coordinate transformation in a system represented by a stationary coordinate system. Regarding the method.

In recent years, in a multi-axis NC machine tool that requires high-speed and high-precision performance, not only position control but also path control is becoming more important. In contrast, the present inventor has proposed vector decomposition route control as one of route control methods (Non-Patent Document 1). This converts the system represented by the XY coordinate system into a rotating coordinate system, separates it into a path error component (gain component) and a traveling direction component (phase component), and virtually converts the target path. It has been used in combination with expansion / contraction coordinate transformation, and its effectiveness has been confirmed so far in a demonstration experiment of a desktop NC milling machine in which a table of each axis is driven by a ball screw connected to a motor (Non-Patent Document 2).
Egami, Tsuburaya: "Vector decomposition path control using elastic coordinate transformation" IEEJ Transactions D, Vol.123, No.12 (2003) Kodaira, Sano, Sato, Egami: “Path control of desktop NC milling machine”, Proceedings of the Conference of the Institute of Systems, Control and Information Engineers, No.4011 (2003)

  However, in the NC milling machine, not only the path but also the cutting surface roughness of the product is made constant, so that the cutting speed represented by the sum of the tangential speed of the XY table and the rotational speed of the cutting tool is kept constant. It is also important. In the conventional method, the tangential speed of the XY table and the rotational speed of the cutting tool are controlled independently to be constant, but the tangential speed of the XY table is determined by the backlash of the ball screw, Due to table friction, cutting load fluctuations, etc., the speed is not always constant, and the rotation speed of the spindle to which the cutting tool is attached also fluctuates due to cutting load fluctuations. As the load increases, the tendency to fluctuate increases. For this reason, when a speed fluctuation occurs in one of the two, this leads to a fluctuation in the cutting speed, resulting in a problem that the surface roughness of the processed product fluctuates.

  Therefore, in the present invention, the control of making the cutting speed constant is realized by coordinating the feed speed of the table and the rotational speed of the spindle while minimizing the path error. The main object is to provide a path control method for an NC milling machine capable of keeping the degree constant.

  The present invention has been made to solve the above-described problems, and is a cutting speed represented by the sum of the feed speed of the work material and the speed of the cutting edge of the cutting tool compared to the conventional vector decomposition path control. The control system is configured to maintain a constant value. That is, a new vector decomposition path control is proposed in which the NC milling table and the spindle on which the cutting tool is mounted cooperate with each other.

  This is because the system expressed in the XY coordinate system is divided into two parts, a path error component and a tangential velocity + spindle velocity component, by performing rotation coordinate transformation and expansion coordinate transformation. In addition, while keeping the path error to a minimum, the table feed speed and the spindle rotation speed are coordinated with each other, thereby realizing a control for making the cutting speed constant. Specifically, the rotational speed of the main shaft is added as a new control amount to the conventional vector decomposition path control, and the speed of the traveling direction component and the rotational speed of the main shaft are coordinated.

  Therefore, according to the present invention, a cutting tool is mounted on a rotatable main shaft, and a blade portion of the cutting tool is brought into contact with a work material (workpiece) fixed on a table so that a predetermined amount is applied to the work material. In the NC milling machine path control method that moves relatively along the machining path, the coordinate system converted from the stationary coordinate system (XY axis coordinate system) to the rotating coordinate system (DQ axis coordinate system) Then, it is decomposed into a path error component and a traveling direction component, and expansion / contraction coordinate conversion is performed on the rotating coordinate system (DQ axis coordinate system), and the traveling direction component is approximately converted to a tangential direction component. The target value of the machining path is made constant on the telescopic coordinate system converted into the telescopic coordinate system, and the position control system based on the speed configured for the tangential direction component and the rotational speed of the main shaft are configured. Combine with speed control system Cutting speed represented by the sum of the rotational speed of the tangential velocity and the main axis of the table in the control system, characterized in that the constant (Claim 1).

Here, by making the target value of the path error component virtually constant by expansion and contraction, it is possible to eliminate an error caused by the difference in time delay between the axes. Therefore, the rotational coordinate system (DQ axis coordinate system) The coordinate system of the system given in the stationary coordinate system (XY axis coordinate system) is transformed so that the current position is on the D axis, and the expansion and contraction coordinate transformation is performed on the path error component. Good (claim 2).

  The expansion / contraction coordinate conversion converts the target path to a unit circle when the processing path is a closed curve path (Claim 3), and converts the target path to a straight line when the processing path is an open curve path. (Claim 4). In such a configuration, since the target value of the target route is constant, it is possible to make the route error zero by configuring a type 1 control system in any route.

  As described above, according to the path control method of the NC milling machine according to the present invention, the feed speed of the work material and the speed of the cutting edge of the cutting tool are coordinated with each other, and the path error is maintained while keeping the cutting speed constant. Since it becomes possible to suppress to the minimum, it becomes possible to make the cutting surface roughness of a processed product constant.

The best mode of the present invention will be described below.
In performing the route control according to the present invention, the following experimental apparatus is used.

[Experimental equipment specifications]
In this research, a desk NC milling machine SG-01 manufactured by Sakai Giken was used as an experimental device. SG-01 moves in a plane direction by an XY table and moves in a vertical direction by a Z axis to which a main shaft is attached. Each table employs a sliding surface and is driven by a ball screw connected to a motor. Table 1 shows the specifications of SG-01.

  An AC servo motor manufactured by Wako Giken is used as the motor for each axis of SG-01. The CNE series is used for the X, Y, and Z axis motors, and the LNE series is used for the spindle motor. An optical rotary encoder is connected to the motor, and the resolution of the X, Y, and Z axes is 2000 Pulse / Rev for accurate positioning, and the resolution of the spindle is 1000 Pulse / Rev. Table 2 shows the specifications of each servo motor.

  Each table of SG-01 has a limit mechanism so that it cannot move beyond the operating range. The protrusion provided at the tip of the table is a mechanism for operating the microswitch attached to the operation limit position to zero the voltage applied to the motor. There are also microswitches required when each axis returns to the origin, and all are connected to the DMC-1740. A brake mechanism is provided to prevent the Z-axis from dropping due to its own weight when SG-01 is not being controlled or when the power is OFF. When controlling the Z-axis, the lock is released by energizing the electromagnetic brake. The DMC-1740 is connected via a relay device.

  SG-01 controls a servo motor using a motion control board DMC-1740 manufactured by Galil, USA. SG-01 is controlled by software SA100M that converts an NC program into a processing instruction of DMC-1740 and transfers it. The SA100M cannot be processed in the same way as a commercially available NC due to the difference in command instruction processing of the DMC-1740 and the grammar processing of the NC program, but is programmed to reproduce the same movement as much as possible.

  The NC milling machine SG-01 as a product state has a control system constituted by a dedicated control board DMC-1740. Therefore, in order to conduct a path control experiment using an arbitrary control law such as vector decomposition path control, The NC milling machine SG-01 must be modified to configure a control system with a personal computer as a new controller. Moreover, the comparison method of the machining accuracy before and after remodeling of the NC milling machine SG-01 compares the encoder pulse when machined with the NC program and the encoder pulse when machined with vector decomposition path control considering the tangential speed.

  Therefore, in order to obtain the encoder pulse of each axis being processed by the NC program, only the encoder signal is branched from the wiring between the driver and the DMC-1740, one is directly to the DMC-1740 and the other is the counter board. 1 is connected to another personal computer to which is connected, and the configuration as shown in FIG. That is, a voltage command is input from the personal computer to the D / A board, and this is output to the motor driver for each axis. Next, the encoder pulse of the rotating motor is counted by the CNT board from the driver and fed back to the control system of the personal computer. The limit switch signal of each table and the relay signal of the Z-axis brake are output from the PIO board to the personal computer.

[NC milling machine modeling]
In performing the route control of the present invention, the following model is assumed.
Here, modeling is performed on a table of each axis using an NC milling machine motor and a ball screw. Although modeling needs to be performed for each of the X, Y, and Z axes, it can be performed in the same manner in all cases, so one of them will be described as an example.

ただし、Ｍ：テーブル質量［kg］、Ｆ(t)：推力[N]、Ｄ：摩擦係数［Ns/m］、d(t)：負荷推力(外乱)[Ｎ]とする。ここで、駆動回路の電流指令値をｕ(ｔ)[A]とすると、推力Ｆ(ｔ) は次のようになる。 Modeling is performed as shown in FIG. 2, where the table position of the experimental apparatus is P (t) [m] and the velocity is v (t) [m / s]. Based on this model, the following equation of motion is obtained according to Newton's law.

However, M: Table mass [kg], F (t): Thrust [N], D: Friction coefficient [Ns / m], d (t): Load thrust (disturbance) [N]. Here, when the current command value of the drive circuit is u (t) [A], the thrust F (t) is as follows.

このとき、Ｋ_Fは推力定数［Ｎ／Ａ］と呼ばれ、各サーボモータ固有のパラメータである。ただし、Ｔ：モータトルク［Ｎｍ］、Ｋ_T：トルク定数［Ｎｍ／Ａ］、Ｐ：ボールねじのリード［ｍ］、Ｒ＝Ｐ／２π：回転から直動への変換係数［ｍ／rad］である。

At this time, K _F is called a thrust constant [N / A] and is a parameter unique to each servo motor. Where T: motor torque [Nm], K _T : torque constant [Nm / A], P: ball screw lead [m], R = P / 2π: conversion coefficient from rotation to linear motion [m / rad] It is.

Substituting Equation (3) and Equation (4) into Equation (1) gives the following.

となる。ただし、状態変数ｘ(t)および係数A_c、b_c、e_c、cは、

となる。 From the equation of motion obtained from equation (5), the state equation and output equation are:

It becomes. However, the state variable x (t) and the coefficients A _c , b _c , e _c , c are

It becomes.

[Conversion to rotating coordinate system]
Here, vector decomposition path control is considered on a two-degree-of-freedom plane, and suppose that the X-axis and Y-axis are given as follows.

  However, the X-axis and Y-axis parameters in Equations (14) and (16) do not necessarily match. Therefore, when the parameters are apparently matched and the parameters are a, b, and e, the following is obtained.

ただし、

である。 ・ X axis

However,

It is.

ただし、

である。 ・ Y axis

However,

It is.

あるいは、

と表すことができる。 Expressions (17) and (20) can be expressed as a matrix.

Or

It can be expressed as.

となる。 Also, the equations (13) and (15) are

It becomes.

ただし、θはＸ軸とＤ軸のなす角である。 Next, a rotational coordinate transformation is performed on a system represented by a stationary coordinate system (XY coordinate system) with respect to the multi-axis mechanical system described above to a DQ coordinate system rotated by an angle θ around the origin.
When converting a system given in the XY coordinate system to the DQ coordinate system, the relational expression when the position, velocity, and acceleration between the XY coordinate system and the DQ coordinate system are simply projected. Is expressed as:

Here, θ is an angle formed by the X axis and the D axis.

For the closed curve path, as shown in FIG. 3, the XY coordinate system is converted to the DQ coordinate system, and the vector from the origin to the current position is matched with the D axis to respond. Then, control is performed so that the D axis and the θ angle become P _d → R _d and θ → R _θ , respectively. Here, R _d is an intersection of the D axis and the target route, and R _θ is a target angle around the origin.

としてＸ，Ｄ軸を実軸とし、Ｙ，Ｑ軸を虚軸にとったガウス平面上において複素ベクトルで表すと、

となり、あるいは、

となる。また、式（３１）を時間で一階微分すると、

となる。 Since the relational expression between the XY coordinate system and the DQ coordinate system is Expression (26),

As a complex vector on a Gaussian plane with the X and D axes as real axes and the Y and Q axes as imaginary axes,

Or

It becomes. In addition, when Equation (31) is first-order differentiated with respect to time,

It becomes.

と表現される。同様に式（２４）も、

となる。 From Expressions (31) and (32) to Expression (25)

It is expressed. Similarly, equation (24) is

It becomes.

となる。 When Expressions (33) and (34) are expressed by respective components of the DQ coordinate system,

It becomes.

  As described above, the vector decomposition path control in which the equation of motion is separated into the gain component and the phase component by using the rotation coordinate transformation and is made non-interfering is performed by using the DQ coordinate obtained by the rotation coordinate transformation and the path on the D axis. The evaluation target is separated so that the error can be evaluated and the followability can be evaluated on the Q axis. Good path control performance can be obtained for circular and linear path target values, and disturbances, etc. Although the influence can be considerably absorbed by the phase component, sufficient performance is not necessarily obtained for the path target value of the arbitrary curve.

  This is because if the system is transformed by rotational coordinate transformation, the D axis directly affects the path error. Therefore, when the target value of the D axis changes with time, the error due to the time delay becomes the path error as it is. This is because sufficient path control cannot be performed. In other words, in the path control, the path is expressed by the response of multiple axes, so when there is a difference in the time delay between the axes, the path response is disturbed, and the axis that directly evaluates the path error. This is because the time delay is a direct path error.

  Therefore, the target value on the axis that directly evaluates the path error (on the D axis that is the path error component) can be changed freely, the target value is virtually fixed, and the error caused by time delay etc. In order to reduce, it is effective to expand / contract an arbitrary axis by a certain ratio by expansion / contraction coordinate transformation.

座標系の間で位置、速度、加速度を単純投影したときの関係式は次のように表される。

ここで、α_x、α_y はそれぞれの軸の伸縮比率であり、一般的にこの値は時変である。この伸縮座標上の位置

に対し、図４に示されるように、

となるような制御を行う。 [Conversion to telescopic coordinate system]
In telescopic coordinate transformation, as shown in FIG.

The relational expression when the position, velocity and acceleration are simply projected between the coordinate systems is expressed as follows.

Here, α _x and α _y are the expansion / contraction ratios of the respective axes, and generally this value is time-varying. Position on this stretched coordinate

On the other hand, as shown in FIG.

Control is performed as follows.

座標系の間で位置、速度、加速度を単純投影したときの関係式は、次のように表される。

[Combination of expansion / contraction coordinate transformation and rotation coordinate transformation]
Now, it is assumed that the equation of motion on the DQ coordinate is given by equations (35) to (38). DQ coordinate system and telescopic coordinate system

The relational expression when the position, velocity and acceleration are simply projected between the coordinate systems is expressed as follows.

とすることができる。同様にして、式（３６）は

となる。 Equations (39) through (35) are

It can be. Similarly, equation (36) becomes

It becomes.

となり、同様に式（３８）は、

となる。 Moreover, Formula (37) is

Similarly, equation (38) becomes

It becomes.

[Application to closed curve path]
In the DQ coordinate system closed curve path, as shown in FIG. 5, the position response is made to coincide with the D axis of the rotational coordinate system, and the D axis target value α _d ( t) When R _d (t) = 1, the following condition holds.

となり、式（４６）、（４７）を次のように定義する。

From equation (44), equations (35), (40), and (41) are respectively

Equations (46) and (47) are defined as follows.

となる。 From equations (42) and (45), the first derivative of equation (48) is

It becomes.

ただし、

である。 Therefore, when the D-axis component is expressed as a matrix,

However,

It is.

より、

となり、

となる。 Similarly, from equations (43) and (45), the first derivative of equation (47) is

Than,

And

It becomes.

ただし、

である。 Therefore, when the θ component is expressed as a matrix,

However,

It is.

  As a result, the D-axis component in equation (51) corresponds to the gain component, and the θ component in equation (55) corresponds to the phase component, which can be treated as non-interference. Can think. Here, since the equation (51) performs the expansion / contraction coordinate conversion, the D-axis error becomes a path error in the conversion region, and the target value of the D-axis control system can always be kept constant at 1. . For this reason, if a type 1 control system is configured, the steady state error can be ideally zero.

が成り立つため、Ｄ-Ｑ座標系をＤ-Ｌ座標系に近似的に変換する。そして、Ｄ軸と円周の始点からの長さｌを制御量とし、接線速度を一定にし、かつ最終的な位置も一致させるような速度ベース位置制御を構成する。この時、Ｐ_d → Ｒ_d、Ｐ_l →Ｒ_l となるような制御を行う。 By the way, in the above-described control system, the tangential speed vibrates with respect to an arbitrary target path such as an ellipse, and the surface of the processed product becomes rough. Therefore, in the present invention, as shown in FIG. 6, when Δθ≈0, Δl = P _d Δθ

Therefore, the DQ coordinate system is approximately converted to the DL coordinate system. Then, the speed base position control is configured such that the length l from the starting point of the D axis and the circumference is set as the control amount, the tangential speed is made constant, and the final position is also matched. At this time, control is performed such that P _d → R _d and P _l → R _l .

  Hereinafter, the conversion method to the DL coordinate system will be described in detail. As described above, in the vector decomposition path control, the control of the traveling direction component is given by the θ component, and even if the speed of the θ component is made constant, Since the tangential speed cannot be made constant with respect to an arbitrary target path, when the vibration of the tangential speed becomes a problem as in the path control of a machine tool, the DQ coordinate system is changed to the DL coordinate system. Approximate conversion is performed, and the tangential velocity is made constant by directly setting the tangential direction component as the control amount. The D axis is omitted because it can be handled in the same manner as the DQ coordinate system.

のとき

が成り立つ。式（５７）の両辺を時間で微分すると

となり、さらに式（５９）の両辺を時間で微分すると、式（３８）から

となる。 For the L axis, first

When

Holds. Differentiating both sides of Equation (57) with time

Further, when both sides of the equation (59) are differentiated with respect to time, the equation (38)

It becomes.

ただし、

である。 Therefore, when the tangential direction component (L-axis component) is expressed as a matrix,

However,

It is.

  The relational expression of the D-axis component expressed by the above-described expression (51) can be handled in a non-interfering manner with the relational expression of the tangential direction L component expressed by the expression (60). Constitutes a position control system, and the latter relational expression constitutes a speed-based position control system. For this reason, it is possible to realize the control that minimizes the path error while considering the tangential velocity.

[Application to open curve path]
In the open curve path, a linear target path with the radius of the unit circle of FIG. 5 as shown in FIG. 7 infinite is considered. In FIG. 7, the D axis is set so as to be orthogonal to the straight line target value represented by the dotted line, the DQ coordinate system is fixed by the angle θ at that time, and control is performed using the fixed DQ coordinate system. Do. At this time as well, the error of the D-axis component becomes a path error, and the same consideration is made by converting the stretchable coordinate to only the D-axis to convert it into a straight line.

この条件を用いて、式（３５）、（３６）、（４０）、（４１）、（４２）、（４３）にそれぞれ適用させると次のようになる。

Now, since control is performed in a coordinate system in which θ is fixed, the following condition is satisfied for the θ angle.

When this condition is applied to equations (35), (36), (40), (41), (42), and (43), the following results.

Expressions (65) and (66) are defined as follows.

となる。ただし、

である。 From equations (63) and (67), the first derivative of equation (69) is

It becomes. However,

It is.

となる。ただし、

である。 Similarly, the first derivative of equations (64) and (68) to equation (70) is

It becomes. However,

It is.

軸の目標値は常に１で一定となる。通常α_q＝１なので、式（７３），（７４）は、次のように表せる。

Thus, a closed curve path, the open curved path both perform stretching coordinate transformation since D-axis component to evaluate a path error is sufficient only in the D-axis, for example, the axial stretch ratio α _q = 1, α _d = If 1 / _Rd ,

The target value of the axis is always 1 and constant. Since α _q = 1 normally, equations (73) and (74) can be expressed as follows.

を一定化するようにωを制御する。 [Coordination between XY table and spindle (cooperation between spindle rotation speed and travel direction component)]
Next, the tangential speed of the XY table and the rotation speed of the spindle are coordinated in order to make the cutting speed that affects the cutting surface roughness of the product constant. The tangential velocity represented by the D-L coordinate transformation is expressed by the equation (60), and the spindle rotational speed ω is treated as a first-order lag element, taking into account the end mill radius r,

Ω is controlled so that is constant.

これに、使用するエンドミルの半径ｒを考慮すると、エンドミルの刃先周速度ｖ_θは以下のようになる。

Specifically, in order to make the surface roughness of the processed product constant, the rotational speed of the spindle to which the cutting tool is attached and the speed of the traveling direction component of the vector decomposition path control are coordinated. The basic formula of the spindle can be expressed as follows.

In consideration of the radius r of the end mill to be used, the peripheral speed v _θ of the end mill is as follows.

となり、（７９）式の出力は

となるため、出力方程式は、

となる。 From Equation (60) and Equation (78),

And the output of equation (79) is

Therefore, the output equation is

It becomes.

[Control system configuration]
A control law is derived in the above transformation region. Although any control system may be used as the control system, in this example, in order to use the optimal servo system, the control input is obtained by solving the optimal regulator problem using an expansion system (error system). A normal control system may be used for the path error component, and here, a control system for the tangential direction component will be described.

となる。 First, when (59) and (78) are discretized,

It becomes.

  A speed-based position control system is configured for expression (81), a speed control system is configured for expression (82), and the cutting speed is made constant in a control system in which both are combined.

とし、速度誤差ｅ_θ(k)を

とすると、

となる。 In equation (83), the target speed value of the spindle rotational speed v _θ (k) is

And the speed error e _θ (k) is

Then,

It becomes.

の目標値を

とし、それぞれの誤差ｅ_p(k),e_v(k)を

とすると、式（８４）と同様の結果が得られる。 Similarly, the tangential position l (k) and speed of the XY table

Target value of

And each error e _p (k), e _v (k)

Then, the same result as that of the equation (84) is obtained.

となり、状態変数

および

は以下のようになる。ただし、Ｔはサンプリング周期を表す。

Summarizing equations (84), (85), and (86),

And the state variable

and

Is as follows. However, T represents a sampling period.

と外乱信号

がステップ信号あるいは一定値をとるとすると、それらの値の変化する時刻以外では

であるので、式（８７）は、

となる。 The system represented by Expression (87) is an expansion system (error system) in which an error signal and a first-order difference value of a state variable are used as new state variables and input variables.
Where speed target value

And disturbance signal

, Taking a step signal or a constant value, other than the time when those values change

Therefore, the equation (87) is

It becomes.

In Equation (95), if the closed loop system can be stably controlled by adding an appropriate control input, X _D (k) → 0, and therefore e _p (k) → 0, e _v (k) → 0, if k → ∞. And can. That is, the steady error can be made zero. Moreover, even if there is a parameter variation of the control target, if the parameter variation is in a range where the closed loop is maintained, it is compensated that the steady-state error is zero.

ただし、Ｑ：半正定行列とする。 [Optimum control input]
An optimal servo system that guarantees steady robustness is constructed by stably controlling the error system represented by Equation (95). Here, an optimal regulator theory is used to obtain such control input. Appropriate pole placement.
Here, the following evaluation function is defined for the error system of Expression (87).

Where Q is a semi-definite matrix.

と選ぶと、式（９６）は以下のようになる。

For example, Q and H for the evaluation function of Expression (87)

Then, the equation (96) becomes as follows.

の重みで、これを他の重みに比べて一番大きくすることで、切削速度を一定にした制御系が構成できる。 Where q _cut is

By making this the largest weight compared to other weights, a control system with a constant cutting speed can be configured.

  In order to perform dynamic analysis of a controlled object using the above equation of motion, an equation of motion having an accurate physical parameter is required. Therefore, in this example, parameters were obtained by the sequential identification method, and the following experiment was attempted.

[Experiment Overview]
As shown in FIG. 8, the target route is an elliptical route having a major axis direction (X-axis direction) radius of 0.01 m and a minor axis direction (Y-axis direction) radius of 0.007 m. From [x, y] = [-0.01,0], control is performed with a period of 4 s in a counterclockwise direction, and the experiment is performed in two patterns with and without cutting, respectively. The cutting depth is 5mm and psychowood is used as the work material. The specification end mill was a high-speed steel square two-flute, and the target speed of the spindle was selected from the table for obtaining the optimum cutting conditions and was 0.486 [m / s].

[Experimental result]
We compared the control by the general-purpose NC controller and the control by this method, and compared from the practical aspect.
The experimental results of the general-purpose NC controller are shown in FIGS. 9 and 11, and the experimental results of this method are shown in FIGS. FIG. 13 shows the experimental results of conventional vector decomposition path control in which the tangential speed of the table and the rotational speed of the spindle are not coordinated.

  (A) shows the path error, (b) shows the cutting speed, (c) shows the tangential speed of the XY table, and (d) shows the rotational speed of the spindle. 9 and 10 show experimental results when there is no cutting, and FIGS. 11, 12, and 13 show experimental results when there is cutting.

Comparing the experimental results of the general-purpose NC controller with the experimental results of vector decomposition path control (hereinafter referred to as the proposed method) in consideration of the tangential speed and cutting speed, the following can be understood.
[Result of path error]
Comparing FIG. 9 and FIG. 10 under the condition without cutting, it can be seen that a large path error occurs at points 1, 2, and 3 at which the table is inverted. When the table is reversed, the maximum error of the general-purpose NC controller exceeds 0.01 [mm], while the proposed method suppresses the maximum error to 0.006 [mm]. Regarding the error, it can be seen that the proposed method suppresses the error as compared with the general-purpose NC controller.
11 and 12 under the condition with cutting, it can be seen that the path error is larger in both cases than in the case without cutting. It can be seen that the steady-state error of the general-purpose NC controller is about 0.01 [mm], whereas the proposed method suppresses it to 0.004 [mm].

[Results of cutting speed]
Comparing FIG. 9 and FIG. 10 under the condition without cutting, it can be seen that the cutting speed is constant in both cases. Further, when comparing FIG. 9 and FIG. 10 with respect to the table tangential speed and the spindle rotation speed, which are components of the cutting speed, both components of the general-purpose NC controller are constant. However, it can be seen that the table tangential speed of the proposed method is observed to vibrate, and the spindle rotational speed vibrates to cooperate with this.
Even in the condition with cutting, the vibration width of each speed becomes large, but the result is almost the same as the condition without cutting.

  In the conventional vector decomposition path control shown in FIG. 13 in which the table tangential speed and the spindle rotation speed are not coordinated, the path error can be suppressed smaller than the control by the NC controller, but the cutting speed varies greatly. Is recognized.

[Result of motor torque command value]
The torque command value given to the motor of the XY table is compared by both control methods. While the NC controller maintains a certain width under the condition without cutting, vibration is recognized in the proposed method. However, looking at the torque of both during cutting, it can be seen that while the proposed method vibrates, the absolute value of the torque applied to the motor is comparable.

The following can be considered from the above experimental results.
[Consideration of path error]
In the general-purpose NC controller, the path error component and the traveling direction component are mixed in each of the X axis and the Y axis, and it is considered that these are sequentially controlled. On the other hand, the proposed method performed the rotation coordinate conversion, so that the path error component can be evaluated with only one D-axis. At that time, expansion / contraction coordinate conversion is performed to eliminate the target value fluctuation on the D axis, and it is possible to cope with a type 1 servo, and the position control is performed by the optimum control. These factors are thought to be the cause of the path error suppression of the proposed method.

[Consideration of cutting speed]
In the general-purpose NC controller, it is considered that the table tangential speed, which is a component of the cutting speed, and the rotational speed of the spindle are controlled so as to independently follow a certain target value. In this case, it is clear that the cutting speed fluctuates when disturbance load fluctuation occurs in either one of them. In contrast, in the proposed method, the control system is designed so that the tangential speed of the table and the rotational speed of the spindle are coordinated with each other. Thus, it is considered that the cutting speed, which is the relative speed between the two, is constant.

[Consideration of motor torque command value]
The proposed method uses coordinate transformation to decompose a system represented by an XY coordinate system into a path error component and a traveling direction component. At this time, in order to make the control system with more importance on the path error, the weight applied to the path error component is increased and a part of the weight of the traveling direction component is decreased. In this way, the balance between the path error and the component in the traveling direction can be determined while keeping the torque command values given to the X-axis and Y-axis constant, and the torque command value is comparable to that of a general-purpose NC controller. Nevertheless, it is considered that the path error can be suppressed.

FIG. 1 is a system diagram showing an improved configuration of a desktop NC milling machine. FIG. 2 is a conceptual diagram modeling an NC milling machine. FIG. 3 is a diagram for explaining the concept of rotational coordinate conversion. FIG. 4 is a diagram for explaining the concept of the expansion / contraction coordinate transformation. FIG. 5 shows that in the closed curve path, the position response is made coincident with the D axis of the rotating coordinate system, and the D axis target value α _d (t) R _d (t) = 1 is set at the intersection of the D axis and the unit circle. It is a figure which shows a case. FIG. 6 is a diagram for explaining the concept of coordinate conversion to the DL coordinate system. FIG. 7 is a diagram showing a case where a straight line with an infinite radius of the unit circle is set as the target value in the open curve path. FIG. 8 is a diagram showing a case where the target route is an elliptical route having a radius of 0.01 m in the major axis direction (X-axis direction) and a radius of 0.007 m in the minor axis direction (Y-axis direction). FIG. 9 is a diagram showing actual measurement data of path control by a conventional general-purpose NC controller, and shows a case where there is no cutting. FIG. 10 is a diagram showing actual measurement data of the vector decomposition path control according to the present invention, and shows a case where there is no cutting. FIG. 11 is a diagram showing actual measurement data of path control by a conventional general-purpose NC controller, and shows a case where there is cutting. FIG. 12 is a diagram showing actual measurement data of vector decomposition path control according to the present invention, and shows a case where there is cutting. FIG. 13 is a diagram showing measured data of conventional vector decomposition path control in which the tangential speed of the table and the rotational speed of the spindle are not coordinated, and shows a case where there is cutting. FIG. 14 is actual measurement data showing a change in torque command voltage in path control by a conventional general-purpose NC controller. FIG. 15 is actual measurement data showing changes in the torque command voltage in the vector decomposition path control of the present invention.

Claims (4)

A cutting tool is mounted on a rotatable spindle, and the blade part of the cutting tool is brought into contact with a work material fixed on a table so as to move relative to the work material along a predetermined machining path. In the NC milling machine path control method,
The system given in the stationary coordinate system (XY axis coordinate system) is transformed into a rotating coordinate system (DQ axis coordinate system) and decomposed into a path error component and a traveling direction component,
Performing expansion / contraction coordinate conversion on the rotating coordinate system (DQ axis coordinate system), and approximately converting the traveling direction component into a tangential direction component,
A position control system based on the speed configured for the tangential direction component and a speed configured for the rotation speed of the main shaft while making the target value of the machining path constant on the expanded / contracted coordinate system converted to the expandable coordinate system A path control method for an NC milling machine, wherein a cutting speed expressed by a sum of a tangential speed of the table and a rotation speed of the spindle is made constant in a control system integrated with a control system. The rotational coordinate system (DQ axis coordinate system) is a coordinate transform of the system given by the stationary coordinate system (XY axis coordinate system) so that the current position is on the D axis, 2. The NC milling machine path control method according to claim 1, wherein the expansion / contraction coordinate transformation is performed on the path error component. 3. The NC milling machine path control method according to claim 1, wherein the expansion and contraction coordinate conversion is to convert a target path into a unit circle when the machining path is a closed curve path. 4. 3. The NC milling machine path control method according to claim 1, wherein the expansion and contraction coordinate conversion is to convert a target path into a straight line when the machining path is an open curve path.

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