JPS63120304A - Production of involute curve - Google Patents

Abstract

PURPOSE:To shorten a working program by fixing a work at the time of cutting and keeping a fixed cutting speed of a tool in the tangent direction against the work. CONSTITUTION:A work is fixed and an involute curve to be produced is referred to as L with the center of a basic circle of the curve L defined as an original point O respectively. Then a straight line passing through the point O is defined as an X axis together with a straight line passing through the point O and vertical to the X axis defined as a Y axis, an intersecting point between the X axis and the basic circle as the start point B of a involute, the rotational angle of the involute as theta with a straight line OB defined as an original line, and the tool coordinates as (x) and (y) respectively. A numerical controller performs control in order to satisfy the relation of such an equation that secures a fixed speed v0 at a contact between a tool and the work in the tangent direction. In such a production way, it is not required to approximate the involute curve with a segment, a circular arc, a parabola, etc. As a result, a working program is extremely shortened to reduce the load of a programmer. At the same time, the program producing time is shortened and therefore the production efficiency is improved.

Description

Detailed Description of the Invention (Technical Field of the Invention) The present invention (-S, relates to a method for creating an involute curve in a workpiece using a numerically controlled machine tool) O (Prior Art and Problems) Conventional numerically controlled machine tool Creation of an involute curve (during one cutting, the workpiece is fixed, the entire involute curve is divided into several small curves, the small curves are approximated to a straight line, circular arc, parabola, etc., and the tool is moved using two linear axes according to the approximation. The method of moving and the method of rotating the workpiece during cutting as the center of the basic circle and approximating it by all straight lines, arcs, parabolas, etc. of the involute curve require all complex calculations to create the Kani program. .

(Approximately, the program length of the Canadian program becomes longer.

(→ Because speed fluctuations occur at the joints of each block of the Kani program, the machined surface of the workpiece does not have a smooth curve, and the speed fluctuations have a large impact on the acid system, which has a negative impact on the accuracy of the machine. To give.

There are problems such as, and is it a processed product? Qv) The method of moving the tool along the tangent of the base circle while rotating requires the center of the rotation axis to be aligned with the center of the base circle of the base circle, making it easier to attach the workpiece. This led to mechanical devices becoming more complex and expensive.

(Object of the Invention) The present invention (1) was made to solve the above-mentioned problems, and the purpose of the present invention is to fix the workpiece during cutting and to control the tool position using two linear axes. By keeping the speed of the tool in the tangential direction relative to the workpiece constant, an involute curve can be created without having to approximate the involute curve with a straight line, arc, parabola, etc.

(Summary of the Invention) The method for creating an involute curve of the present invention provides a method for creating an involute curve on a workpiece, when creating a complete involute curve on a workpiece. Fixed 1
-1 The origin is at the center of the base circle of the involute curve to be created, one straight line @ and the X axis that pass through this entire origin, and
The Y axis is a straight line perpendicular to the axis, and the radius of the base circle is fcr. , the intersection of the base circle and the X axis? The starting point of the involute, the straight line (X-axis) connecting the center of the base circle and the starting point, and the rolling angle of the involute as a metal wire is θ, and the differential symbol 'dt, then the tool and processing determined by the X-axis and Y-axis. The position coordinates of the point of contact with the involute curve created on the object (xSy
) k, the speed in the tangential direction of the contact point of the tool and workpiece is a constant value ■
. It is characterized by controlling so that the relationship of formula (■) holds true so that

- (Embodiment of the invention) An embodiment of the invention will be described below.Relationship between the coordinate system set in a numerically controlled machine tool in which the tool position is determined by two linear axes and the involute curve created? In the same figure, the involute curve to be created is defined as the center of the base circle of the involute curve, the center of the base circle of the involute curve is the origin 0, one straight line passing through the origin 0 is the X axis, and the origin O is 9.
A straight line perpendicular to [XIII]? Intersection of Y-axis, X-axis and the base circle Starting point of all involutes B1 Straight line 0BfX-axis)? What is the rolling angle of an involute as a primitive line? θ, tool seated image (X
, 3'). When the coordinate system is determined as shown in Figure 1, the command block to the numerical control device gives the tangential velocity v0, the radius of the base circle ``., the rolling angle θ of the starting point xys mark (Xy,), the rolling of the end point Angle θb,, xV coordinate (xb
,,yb) are given. Numerical control where Tlj: sampling period, k is the initial 1υ1 value θ at the time of sampling. -θ8, xo = x, , Yo = Y-
Expression ① is fully executed and ΔXk and Δyk are output to the X-axis and Y-axis, respectively, as position command values to the position control means. Equation (■) is a differential approximation of Equation (2).

In addition, when performing tool diameter correction, use the difference approximation formula instead of formula
θ. = 08, X0 = ". F core. θ.

Yo”” ron sinθa formula■? to calculate △Xks△Ykk and send it to the position control means.
7 position command value. What is the relationship between the involute curve created and the tool path when the tool radius is compensated to the positive side in Figure 2? Is the tool diameter corrected on the negative side as shown in Figure 3? 1. In-policy made when carried out 1. - shows the relationship between the curve and the tool path.

(Effects of the invention) As described above, the creation of the involute curve of the present invention,
According to the hole method, there is no need to approximate using all involute curve segments, circular arcs, parabolas, etc., so that the conventional Kani program, which required several tens to hundreds of blocks, can be reduced to just one block. Therefore, the burden on the programmer is reduced, and at the same time, the time required to create a program is shortened, thereby improving production efficiency. Also, in the conventional method, 1-S
In order to create a cutting program that takes into account the tool diameter, complicated calculations using a computer were required, but all tool corrections can be made with simple calculations. Furthermore, since the tangential speed of the tool and workpiece during involute curve generation is constant, the machined surface is smooth.

[Brief explanation of the drawing]

Figure 1 shows the relationship between the coordinate system in which the present invention is implemented and the involute curve created. Diagram for explanation. Figure 2 shows an example in which tool radius correction is performed outside the involute curve, and Figure 3 shows an example in which tool radius correction is performed inside the involute curve.

Claims (2)

[Claims] (1) When creating an involute curve on a workpiece, fix the workpiece and set the center of the base circle of the involute curve to be created as the origin, one straight line passing through this origin as the X-axis, and passing through the origin as the X-axis. An involute whose origin is the straight line perpendicular to the Y axis, the radius of the base circle r_0, the intersection of the base circle and the X axis as the origin of the involute, and the straight line (X axis) connecting the center of the base circle and the origin. When the rolling angle of dx/dt=A(x-θy) dy/dt=A(y+θx) A=(v_0/r_0) [l/(l+θ_2)]dθ/ so that the velocity in the tangential direction of the contact point becomes a constant value v_0.
A method for creating an involute curve, characterized by controlling so that the following relationship holds: dt=(v_0/r_0)l/θ. (2) When controlling the speed in the tangential direction of the point of contact between the tool and the involute curve to be created on the workpiece to a constant value v_0, when the radius of the tool is R_0, the curve is The tool trajectory is obtained by adding an offset vector that is always separated by an amount corresponding to the tool radius in the normal direction, and the tool position coordinates (x, y) determined by the X and Y axes are calculated using the following formula dX/dt= A(X-θY) dY/dt=A(Y+θX) A=(v_0/r_0) [l/(l+θ^2)]dθ/
dt=(v_0/r_0)l/θ dx/dt=B(dX/dt) dy/dt=B(dY/dt) B=l±R_0/{r_0θ} X, Y; Intermediate variable R_0; Tool radius B ± is determined by the correction direction. A method for creating an involute curve according to claim (1), characterized in that the tool diameter is corrected by controlling so that the following holds true.