# A new programming method for machining elliptic cu

2022-07-24
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A new programming method for machining elliptic curves with NC machine tools

preface

in the mechanical manufacturing industry, the parts with elliptical shape are two-dimensional contour workpieces, which are common and difficult to process. At present, the main machining methods of elliptical parts are: approximate machining on ordinary machine tools; According to the forming theorem of ellipse, a special processing device is designed for processing; Perform numerical control machining on the numerical control machine tool [3 ~ 6]. Since the programming code of general NC machine tools only has the functions of linear interpolation and circular interpolation, for the NC machining of non-circular curves such as ellipses, small straight lines or small arcs are mostly used to approximate the contour curve to complete the NC programming. For example, documents [4] to [6] respectively use 4, 8 or more smoothly connected arcs to approximate the elliptic curve, and control the maximum deviation within the allowable tolerance, Then the starting point coordinates, end point coordinates and arc radius of each arc are calculated, and then the NC machining program is compiled for machining. Since the start point and end point of each small segment of straight line or arc must be calculated according to the allowable accuracy requirements, when the workpiece contour is long and the accuracy requirements are very high, the approximation segment of straight line or arc must be divided into very fine parts, so the amount of calculation is large, which brings a lot of inconvenience to manual programming. At the same time, this method of programming according to the approximation curve or approximate drawing method has brought errors in principle, so it is impossible to process high-precision elliptical parts. In reference [3], a special ellipse interpolation program is designed by using the interpolation principle of point by point comparison method to realize the numerical control machining of elliptic curve in the economical numerical control device for elliptical ceramic forming. Although it can improve the accuracy, it is lack of universality

among the CNC machine tools widely used in the metal processing industry at home and abroad, the semi closed loop position servo system is a widely used technical scheme, as shown in Figure 1. The semi closed-loop position servo system excludes the mechanical transmission chain of the machine tool from the position closed-loop. The electrical control part of the servo system is relatively independent of the executing machinery. Because there are few non-linear factors in the closed-loop, the system is easy to set and can easily realize gap compensation, so as to improve the position control accuracy [7, 8]

Figure 1 semi closed loop position servo system

in this paper, the concept of "virtual axis" is adopted to successfully realize the NC machining of elliptic curve on the NC machine tool with semi closed loop structure. This method is not only simple to program, but also avoids the machining errors caused by various approximation methods in principle

2 "virtual axis" principle realizes NC machining of elliptic curve

assuming that the outline of the part to be machined is as shown in ellipse (1) in Figure 2, the ellipse equation is expressed as follows:

(1)

make

then formula (1) becomes:

x ′ 2 + y ′ 2 = B2 (2)

and then make x ″ =x, Then equation (1) becomes:

x ″ 2 ＋ y ″ 2 = A2 (3)

Figure 2 workpiece outline

the transformation from equation (1) to equation (2) shows that the ellipse (1) becomes a circle (2) by uniformly expanding b/a times in the x-axis direction, and conversely, the circle (2) becomes an ellipse (1) by uniformly compressing b/a times in the x-axis direction; The transformation from equation (waste plastic particles 1 are in short supply 1) to equation (3) shows that the ellipse (1) becomes a circle (3) when it is uniformly compressed b/a times in the y-axis direction, and the circle (3) becomes an ellipse (1) when it is uniformly expanded b/a times in the y-axis direction

the relevant parameters of the mechanical transmission link of the machine tool (such as speed ratio, lead screw, limit stroke, pulse equivalent, etc.) are stored in the memory of the NC system in the form of machine tool data. For the control system, changing the value of the machine tool data of a certain feed axis is equivalent to changing the structure of the corresponding part of the mechanical transmission link of the machine tool. Since the structure of the feed axis actually driven by the servo motor has not changed, That is, the feed axis corresponding to the changed machine tool data does not actually exist, so it is called "virtual axis". If the "virtual axis that can not even work normally" is programmed in the NC program, the actual feed amount of the real feed axis driven by the servo motor after the program execution is not the actual programmed value, and there is a proportional relationship between the two. For example, the lead screw of a certain feed axis of a CNC machine tool has a lead of 40mm, and now the machine tool data is changed from the original value of 40mm to 80mm, which is equivalent to a "virtual axis" with a lead of 80mm connected to the servo motor. Program in the NC program to make this axis feed 80mm, the servo motor will rotate for 1 circle (assuming the speed ratio is 1), and the real lead screw actually connected with the servo motor in the transmission chain will also rotate for 1 circle, with a lead of 40mm, so the feed rate of the workbench is 40mm, so the feed rate in the program is uniformly compressed by half, and the proportional relationship between the two is 2

if sreal is the actual connecting lead screw of the machine tool, svirtual is the virtual axis lead screw. When compiling the elliptic curve machining program, according to the equation of the elliptic curve, take

to modify the machine tool data of the corresponding part of a certain feed axis of the machine tool, which can realize the amplification or compression in the direction of this axis, complete the transformation from circle to ellipse, and realize the NC machining of elliptic parts

3 programming method

set the ellipse to be processed as shown in Figure 3 (1), the long and short axes are 1500mm and 750mm respectively, and the lead screw of the X and Y feed axes of the CNC machine tool used is 40mm. Programming according to circle (2), the X axis should be taken as the virtual axis, and the lead screw should be 80mm. The programming of NC machining is divided into the following two parts:

(1) modify the machine tool data

according to the literature [9], expand the following six groups of 10 machine tool data of the x-axis of the machine tool by 2 times:

11, md12 pulse equivalent

27, MD28 acceleration and deceleration

31 maximum speed of the feed axis

20, md21 negative and positive soft limit

6, md36 back to the reference point Initial speed

3 reference point coordinates

(2) write NC machining code

according to the definition of literature [10], The "virtual axis" method is used to process the NC code of elliptic curve as follows:

n01 G00 x Y0 M1 = 6 (rapid feed to the processing starting point)

n05 G02 G17 I F6000 (full circle processing with radius of 1500mm at the processing speed)

n10 G00 x200000 y (after processing, return)

n15 M1 = 30 (program end)

Figure 3 workpiece figure

4 conclusion

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