JPS5922241B2 - Circular interpolation method - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION Technical Field of the Invention The present invention relates to a circular interpolation method, particularly to a circular interpolation method with small errors in numerical control.

Prior Art and Problems Various methods have already been proposed for cutting by moving a tool using continuous path numerical control.

For example, when moving along an arc, DDA (Digi
It is known to perform circular interpolation using the talDifferentialAnaly2er) method. Figure 1 is D
It is a diagram explaining the principle of the DA method, and registers REGI, RE
The coordinate values (xn, yn) at time tn are set in G2, and each time an addition command of frequency f is added, register REG
The contents of I, REG2 are added to registers REG3 and REG4, and the overflow pulse of register REG3 is
The overflow pulse of the register REG4 becomes the command pulse for the X-axis.

Furthermore, the value of the overflow pulse of the register REG4 is subtracted from the register REGI, and the value of the overflow pulse of the register REG3 is subtracted from the register REG2 until the next addition command arrives. Incidentally, since the frequency f of the addition command is a value proportional to the feed speed command, as the feed speed increases, the frequency f also increases, and the addition process must be performed in a short period.

Therefore, if it is implemented in hardware, a circuit that can operate at high speed is required, and if it is implemented in software, the calculations will not be able to keep up. Therefore, in the past, the period of addition is made as long as possible by approximately performing addition a plurality of times.

FIG. 2 is an explanatory diagram of such a system, in which the register REGI stores the coordinate values (xn, yn) at time tn.
, ΔT-f (ΔT is the interrupt period, f
The value multiplied by the originally required addition frequency) is added to registers REG3 and REG4 every 1/ΔT, and the coordinate value at time Tn+1 (Xn+1, 2m is the bit of registers REG1 to REG4). number, D
x. dy is the command value for the X-axis and Y-axis. According to such a method, ΔT- which must be executed during the period of ΔT
Since f additions are performed in one time, it can be implemented even by software.

However, the same coordinate value Xn at time Tn. y
This results in adding n multiple times, so when the value of Dt becomes large to a certain extent, ΣXn+2=Xn+1-Yn+PiDt
=Xn+1-(Yn Therefore, if we eliminate the term Yn in the same way, we can obtain the difference equation from equations 1 and 2.

The characteristic equations of equations 3 and 4 are: and Its roots are *Yn+1) is shown by the following formula.

? As shown in FIG. 3, there is a drawback that the error gradually increases from the arc a to the broken line b.

The reason why such a drawback occurs will be explained below. (1)
, from equation (2), that is, if we eliminate the term Yn, we get:

・Dt)Dt=2xn+1-Xn-XO・Dt2 From this, γ=j〒]璹翇 and θ=Tan-1dt.

The X coordinate value of the starting point with the origin at the center of the arc (n=o) is
. ．． Y coordinate value Y (n=o). Then, if n=O, . XO=A yO=C n=1, X1=γ(XOcOsθ+BsinO=XO-YO-D
tyl:γ(YOcOsθ'{)SinO::YO+X
However, r=j1+Dt2=”! , COsθ k=T8nθ Therefore, however, it becomes.

As can be seen from equations 5 and 6, as n increases, the radius increases, and therefore the error gradually increases as indicated by broken line b in FIG.

Purpose of the Invention The present invention improves the conventional drawbacks shown in FIG.
The object of the present invention is to perform circular interpolation so that tracking movement can be performed on a circular arc with high precision even when the movement is difficult.

Embodiment of the invention FIG. 4 is a block diagram of the main part of an embodiment of the invention.
Gll~REGl4, REG2l~ 5REG24
, REGY1, REGY2, REGX1, REGX2 are registers, MLTl to MLT8 are multipliers, ADl to AD
8 is an adder, DVl, D2 are dividers, SUBl, SUB
2 is a subtractor.

Register REGll~REGl4, REG2l~ 2R
EG24, multiplier MLT5 to MLT8, adder AD3 to
The interpolation circuit shown in FIG. 2 is constructed in duplicate by AD9 and subtractors SUB1 and SUB2. Multiplier MLT5
~MLT8, adders AD3 to AD8, subtractor SUBl,
The command pulses W1 to W6 applied to SUB2 instruct the start of multiplication, addition, and subtraction, respectively, and are generated by a timing generator (not shown), and are pulsed W1→W2→W3→W4.
→W5→W6→W1 occurs in the order. Note that each cycle of W1 to W6 is ΔT. In FIG. 4, registers REGll and REG2l initially store X coordinate values x'n and x at time Tn, and registers REGl2 and REG2
2 stores the Y coordinate value y negative, Yt+1 at time TO.

The following calculations are performed at each timing of command pulses W1 to W6. (W1) Register RE that stores Y coordinate value y, etc. at time Tn
The output y'n of Gl2 multiplied by ΔT-f is obtained by the following equation.

(W4) X coordinate value X at time Tn+1 updated in (W3)
'n+1 output of register REGll)C/n
+, is multiplied by ΔT-f, and X'n+1 (ΔT-f) is output to the adder AD3.

Y coordinate value y at time Tn+, updated in (W3)
'n+1 output Yt+1 of register REG22 that stores n+1
is multiplied by ΔT-f, and y'n+1(ΔT-f) is output to the adder AD6.

(W5) Adder AD3 adds (W
I found it in 4)! .

+, (ΔT−f) are added. As a result, register R
The output Dj of EGl3 is as follows.

Adder AD6 adds (W
y′n+1 (ΔT−f) obtained in step 4) is added.

As a result, the output 1dl of the register REG24 is as follows.

(W6) The adder AD7 adds the output x'n+, ·Dt of the register REGl3 found in (W5) to the content y'n of the register REGl2 that stores the Y coordinate value 8 at time Tn, and The coordinate value y'n+1 is determined by the following equation.

From the contents X7l of the register 21 that stores the coordinate value x, (
The output y+1·Dt of the register 24 determined by W5) is subtracted, and the X coordinate value x+1 at time Tn+1 is determined by the following equation. Hereinafter, the coordinate value calculation processing according to the above equations (3) and (5) will be referred to as the first calculation processing, and the coordinate value calculation processing according to the above equations (4) and (6) will be referred to as the second calculation processing.

In the first calculation process, the new coordinate value X of the first axis (X axis)
When calculating 'i+1, the first axis and the second axis (Y axis)
The old coordinate value Xi. Using yi and the new coordinate value y′ of the second axis
In determining I+1, the old coordinate value Yi of the second axis and the new coordinate value X'i+1 of the first axis determined previously are used.

In the second calculation process, the new coordinate value y of the second axis (Y axis)
In calculating "i+1," the old coordinate values y"I. of the first and second axes are used. Using y″i and the new coordinate value of the first axis X″i+
1, the old coordinate value X″i of the first axis and the previously determined new coordinate value yl+1 of the second axis are used.

Set the arc of a predetermined radius R to its starting point (coordinate value is X).

, YO) in a certain direction, for example, counterclockwise, the first curve C1 obtained by connecting the points represented by the coordinate values sequentially determined by the first calculation process and the second calculation process. Therefore, the second curve C2 obtained by connecting the points represented by the sequentially determined coordinate values does not coincide with the circular arc to be interpolated, and becomes an ellipse that slightly protrudes from the circular arc. That is, as shown in FIGS. 5 and 6, the first curve C1
The long axis of the second curve C2 is a straight line that makes an angle of 45° with respect to the positive direction of the X-axis, and the long axis of the second curve C2 is a straight line that makes an angle of 135° with the positive direction of the X-axis (perpendicular to the above straight line). The arc C to be interpolated (tracked) exists between these two ellipses Cl and C2 when viewed from the center 0. Therefore, in the present invention, from the first coordinate values successively found by the first calculation process and the second coordinate values successively found by the second calculation process,
The purpose is to find the coordinate values of a point on the arc to be interpolated.

That is, registers REGl2, REGl4 and REG2l,
An operation is performed between REG23 using Dt determined by the interpolation speed, etc., and signals -Dx' and Dy/' due to overflow of registers REG14 and REG23 are applied to multipliers MLT2 and MLT3, and register REG1
l and REG22 are respectively added and subtracted.

Next, registers REGll, REG13 and REG22,
Calculations using Dt are performed between REG24,
Signals Dy/, -Dx'' due to the overflow of registers REGl3 and REG24 are applied to multipliers MLTl and MLT4, and added to and subtracted from registers REGl2 and REG2l, respectively.Whether to add or subtract is determined by the quadrant of the circular arc. Multiplier MLTl~
MLT4 receives signals -Dx', Dy due to overflow.
', -Dx'', Dy/' are generated as representing a certain numerical value, so they are used to multiply by an arbitrary ratio.If the constant representing the ratio is A.b, the above signal is respectively a・-Dx7, a-Dy7, b・-Dx'', b-
Becomes Dyl.

Then, in adders ADl and AD2, a-Dy'+b
-Dy. a. The calculations -Dx'+b and -Dx/' are performed, and in the dividers DVl and DV2, 1/a+
The calculation of b is performed. Therefore, the coordinate values (Xn+1, Yn+1) on the arc at time Ti+1 are as follows, and the signals Dx and dy resulting from these calculations are the sending pulses S,
Registers REGXl, REGX2, REG according to s'
The interpolation circuit using Yl and REGY2 results in X and Y axis distributed pulses Xa and Ya.

The above operation is shown in coordinates as shown in Figure 7.
If the arc is a, the locus of the first coordinate value is b, and the locus of the second coordinate value is c. Therefore, the constants A,
If each b is set to 1, the percentage of the sum indicates the coordinate value on the approximate arc a.

That is, according to the circular interpolation method of the present invention, circular interpolation with small errors can be performed even when Dt is large. The aforementioned calculations can be performed by the configuration shown in FIG. 4, but they can also be performed by an electronic computer.

It goes without saying that circular interpolation can be performed not only between the X and Y axes, but also between the X and Z axes and between the Y and Z axes.
As explained above, the present invention provides the above-mentioned (3) to (6)
The first coordinate value (X'n+1, y'n+1) at time Tn+1 and the second
The coordinate values (X/r1+1, y/n+1) of
The first coordinate value (XSl, yξ) and second coordinate value (Xt.yt) at
O+1, Yn+1) are calculated by the calculation means that performs the calculations shown in equations (7) and (8) above, and circular interpolation is performed, so the first coordinate value and the second coordinate value are The average value corresponds to a locus on a circular arc, and highly accurate circular interpolation can be performed.

Therefore, it has the advantage that machining accuracy by numerical control can be significantly improved.

[Brief explanation of drawings]

Figures 1 and 2 are block diagrams of a conventional circular interpolation circuit.
FIG. 3 is an explanatory diagram of its operation, FIG. 4 is a block diagram of an embodiment of the present invention, and FIGS. 5 to 7 are explanatory diagrams of its operation.

Claims (1)

[Claims] 1 In a method of performing circular interpolation between the first axis and the second axis, the coordinate value (x_n
, y_n), the first coordinate value (x'_n, y'_n
) and a second coordinate value (x″_n, y″_n); the first coordinate value (x′_n_+_1, y′_n_+_
1) and the second coordinate value (x″_n_+_1, y″_n_+
_1) and x, where dt is a constant determined by the interpolation speed, etc.
'_n_+_1=x'_n-y'_n・dty'_n_
+_1=y′_n+z′_n_+_1・dty″_n_
+_1=y″_n+x″_n・dtx″_n_+_1=
An arithmetic means that calculates x″_n−y″_n_+_1・dt, and a time t_n_+ based on the arithmetic result of the arithmetic means.
Coordinate values on the arc at _1 (x_n_+_1, y_n
__+_1), a and b are constants, x_n_+_1=
(a・x′_n_+_1+b・x″_n_+_1)/(
a+b)y_n_+_1=(a・y'_n_+_1+b
A circular interpolation method characterized by comprising a calculation means for calculating y″_n_+_1)/(a+b), and performing circular interpolation based on the calculation result of the calculation means.