RU1816531C - Method of cutting aspherical surfaces and device for its realization - Google Patents

Abstract

Usage: in machine tool industry, when processing optical surfaces: Summary of the invention: the axis of the first tool spindle is offset from the axis of the working spindle, and their rotational frequencies are referred to as 1: 3. An additional spindle is installed on the tool spindle with an offset, the rotation frequency of which is greater than the rotation speed of the tool spindle, wherein the cutter is mounted with an offset relative to the axis of the additional spindle. 2 s.p. f-ly, 5 ill.

Description

The invention relates to machine tool industry and can be used to obtain optical surfaces on materials that can be machined with ultra-precise cutting.

The purpose of the invention is to improve the quality of the surface layer of aspherical surfaces bounded by two planes perpendicular to the axis of symmetry of the aspherical surface, by eliminating the periodic incision of the cutting tool into the surface to be treated.

Fig. 1 shows a diagram of processing aspherical surfaces in a plane passing through the axis of the working and first tool spindles; figure 2 - the same in the spatial coordinate system; Fig. 3 is a diagram for calculating the ratio of rotation frequencies of the working and second tool spindles; Fig. 4 shows a device for treating zones of aspherical surfaces; figure 5 is the same, a top view. .

In FIG. 1-4, the arrow with the designation A corresponds to the translational movement of the cutting tool, the circular arrow with the designation Si corresponds to the circular feed direction of the first tool spindle with a value of Si, the circular arrow with the designation S2 corresponds to the circular feed direction of the second tool spindle with a value of $ 2. The circular arrow with the designation n corresponds to the direction of rotation of the working spindle with a frequency of n.

The device implementing the method (Figs. 3-4) comprises a working spindle 1, a workpiece 2, a cutter 3, a tool holder 4, an actuator 5, a manual drive 6, a second tool spindle 7, a manual drive 8, a first tool spindle 9, rack 10, manual drive 11, the frame of the device 12.

In this case, the part 2 is mounted on the working spindle 1 mounted on the bed 12. A stand 10 is also mounted on the bed 12, carrying the first tool spindle 9 and having a manual drive 11 to move the first tool spindle 11 so that its axis remains

(L

WITH

00

 ate

G4

parallel to the axis of the working spindle 1. On the rotation axis of the first tool spindle 9, a manual drive 8 is mounted rigidly connected to the second tool spindle 7. The manual drive 8 parallelly moves the axis of the second tool spindle 7 relative to the axis of the first tool spindle 9. On the second tool spindle 7 is mounted a manual drive 6 carrying a tool holder 4 with a tool 3 so that the main cutting edge of tool 3 is offset relative to the axis of the second tool spindle 7. In tool holder 4 p the actuator 5 necessary for moving the cutter 3 in a direction parallel to the axis of the second tool spindle 7 is positioned.

 For cutting zones of aspherical surfaces, for example, an elliptical paraboloid, bounded by two parallel planes perpendicular to the axis of symmetry of the aspherical surface (axis OA), it is necessary that when the end of the cutting edge of cutter 3 is spaced as far as possible from the axis of rotation of the working spindle 1, the axis of the working 1, the first 9 and second 7 tool spindles and the end of the cutting edge of the cutter 3 were in the ZOY plane (Figs. 1-2). In this case, the axis of the second tool spindle 7 must be spaced from the axis of the working spindle 1 by the distance R-rv The axis of the first tool spindle 9 rotates around the axis of the second tool spindle 7 in a circle of radius r. In this case, when rotating part 2, the projection of the axis of the first the tool spindle 9 forms a guide circle on the surface of the part 2. When the axis of the first tool spindle 9 is rotated with a frequency 3 times greater than the speed of the working spindle 1 (), the projection of the axis of the second spindle 7 onto the surface of the part 2 forms a producing circle that rolls without slipping along the forming circle. If () 2: 1, the projection of the axis of the second tool spindle 7 will form an ellipse with half axes on the surface of part 2: (large), (smaller). An ellipse will be formed if the rotational speed n of the working spindle 1 and the frequency and Zg of the second tool spindle 7 are referred to as 1: 3. In this case, the rotation of the axis of the second tool spindle 7 around its axis ensures the movement of the cutter 3 along the circumference of the radius of the item. The value of 2n is due to the width of the treated area, and the semi-major axis of the ellipse, which defines the smaller border of the zone, is equal to Q R + 2r-П less -. When the rotational speed of the cutter 3 is greater than the rotational speed of the axis of the second tool spindle 7. (), the cutter 3 moves along an epicycloid-like curve and fills its path limited by the zone ellipses. If the ratio of the circumference 2lg1 to the length of the ellipse with the half axes a R + 2r-n is an irrational number, then the curve formed by the movement of the cutter type 3 of the epicycloid is not closed, it has an infinite number of branches intersecting one another. Thus, any necessary supply of the cutter 3 along the formed zone can be achieved by providing the necessary density of the marks from the cutter 3 on the machined surface. If the distance d between the axes of the first 9 and second 7 tool spindles is greater than g, but while maintaining their ratio frequencies 3: 1 of the second tool 9 and working 1 spindles, an ellipse of the corresponding smaller zone boundary can be formed on the surface of part 2: aRt-r + frt-dj-tn (large), (dr) -n. In this way, any ellipse can be formed. Cutter 3 is informed of the translational movement D necessary for forming the desired profile of the treated area, consistent with Si 82 and n.

The values of the circular feeds Si, 82 of the cutter 3 and the rotational speed of the working spindle 1 determine the basis of the calculated cutting conditions, and the translational movement A of the cutter 3 is determined from the parameters of the aspherical surface.

With such a treatment of cutting an area of aspherical surfaces, the cutter 3 is always oriented tangentially to its path, which keeps the cutting angles constant and improves the accuracy of the workpiece.

For example, for processing elliptical paraboloids having, in sections, planes passing through the Y axis of parabola, and in sections of planes parallel to the XOY plane, ellipses.

In the coordinate system selected in FIGS. 1-2, an elliptical paraboloid is expressed by the equation

X2 72 1G + 1G 2 (U-p).

(1)

where a, b are the parameters of the parabolloid;

h is the height of the formed relief.

Cutter 3 moves along an epicycloid-type curve, which in the absence of

the translational movement of the cutter 3 lies in a plane parallel to ZOY. In order to form the necessary profile of the zone, it is required to ensure the translational movement of the cutter 3 so that the end of the cutting tool always belongs to the aspherical surface. To do this, we define an analytical expression of the trajectory of the end of the cutter 3 in the coordinate system associated with the rotating part 2 during the rotation of the first 9 and second 7 tool spindles. In the selected coordinate system, the trajectory of the axis of the first 9 tool spindle (M. Vygodsky. Handbook of Higher Mathematics. - M.: Nauka, 1975, p. 811) has the following:

l

X (R + r + r} cos (n + Si) t-d cos R + r + r (n + Si) t;

Z () sio (n + Si) t-d.sin R + + r (n + Si) t. (2)

Here R + r is the distance by which the axis of the first tool spindle 9 is spaced from the axis of the working spindle 1;

 d is the distance by which the axis of the second tool spindle 7 is spaced relative to the second tool spindle 9.

In order to form an ellipse on the surface of part 2, it is necessary that the (R + r), n -frequency of rotation of the working spindle 1; Si is the rotational speed of the first tool spindle 9. d is the distance between the axes of the first 9 and second 7 tool spindles. In this case, equations (2) will take the form:

 cos (4nt) -d cos (3 4nt); sin (4ny) - d sin (3 4 nt). (3)

It can be seen from equation (3) that the parameters of the ellipse formed on the surface of part 2 depend on parameter d. The ellipse (3) at a ratio of (R + r) r 2: 1 will be formed at a certain ratio of the frequency n of rotation of the working 1 and frequency S.1 of the first tool 9 spindles, equal to. The need for such a frequency ratio is due to the fact that, using the Willis theorem (the method of reversed movement - p. 160 Artobolevsky YI Theory of mechanisms and machines. - M .: Nauka, 1988, p. 160) the gear ratio from worker 1 to the second instrumental 9 spindle m relative to the carrier - link,

connecting the center of rotation of the working 1 1 and the second tool 9 spindles with a stationary carrier, is equal to:

i

W1 - (OH Wl -ftJH

(4)

However, in a motionless coordinate system {g; X},,

then Utt - + 1-U9H (1) -U9Hra + 1

15 id U9H (1) 1-U91H.

(6)

Suppose that the contacting circles formed by the working 1 and second tool 9 spindles, the contact

gearing. Moreover, the circle belonging to the working spindle 1 is characterized by the number of teeth Zi, and the circle 4 formed by the first tool spindle 9, Zg.

Then

U9if

(7)

The assumption of the contact of the circles belonging to the working 1 and the first 9 tool spindles by means of gearing is valid because the formation of a cycloid is only possible

when there is no slippage between the contacting circles. It also follows that the rotation of the working spindle 1 and the first instrumental 9 spindle should be carried out towards each other. In this case (6) takes the form

and +5

or UQH 9

Z9 + Z1

(8)

(9)

However, as was previously established, the formation of an ellipse on the surface of part 2 is possible with a ratio of radii (R + r). This ratio also determines the ratio Zg; then (9) is written

55

(10)

It follows that the ratio of the frequency n rotations of the working spindle 1 and the frequency Si of the tool spindle 9 should be

(eleven)

According to the ellipse defined by the equation - II (3), as along the guiding circle, the axis of the generating circle with a radius of n rolls, which is the axis of the second tool spindle 7, rotates with a frequency of $ 2. In this case, when the rotation speed Si of the first tool spindle 9 is less than the speed S2 of the second tool spindle 7, i.e. . the end of cutter 3 will form an epicycloid-type curve. If the ratio of the circumference to the length of the ellipse (3) is an irrational number, then the epicycloid-like curve is not closed, it has countless branches intersecting one another. In this case, the directions of rotation of the first 9 and second .7 tool spindles should be towards each other for the reason considered in the previous example. And then the entire space of the formed zone will be covered by traces of the movement of the cutter 3, intersecting each other at an angle equal to or close to the angle of 90 °. Such a submicrorelief ensures the absence of anisotroria upon reflection of the light beam from the treated surface, regardless of the spatial orientation of the light beam. The value D of the translational incisor 3 is determined from the condition that Des is the distance from the ZOX plane at the point where the incisor 3 is currently located to the aspherical surface (1). Given the movement of the first 9 and second 7 tool spindles, it is easy to determine the coordinates of the incisor 3 at any given time.

Similarly, Di can be calculated for other types of surfaces forming aspherical surfaces.

With this method of cutting, the marks after the cutter form an unclosed countless branches of epicycloids on the treated surface, resulting in a surface roughness with isotropic properties, i.e. the treated surface has the same reflectivity regardless of how the incident beam is oriented in space.

In addition, with this method of cutting, the cutting tool is constantly directed tangentially to the path of the tool, which ensures a constant chip width. This helps to reduce the level of roughness and increase the accuracy of processing.

The device operates as follows,

Part 2 is fixed on the working spindle 1 and the working spindle 1 is informed of the rotation with a frequency of n. After this, the first tool spindle 9 is informed of the rotation with a frequency of $ 2, having previously shifted its axis parallel to the axis of the working spindle 1 by the distance R + r. After that, the rotation of the second tool spindle 7 is reported with a frequency of $ 2. having previously shifted its axis parallel to the axis of the first tool spindle L by the distance d and the axis of the second tool spindle 7, the cutting edge of the cutter 3 by the distance p. In this case, before starting work, the cutter 3 is set to its initial position. Starting with processing a larger boundary, the smallest depth of cut takes place. Cutter 3 is initially brought into contact by a hand drive 6 with the surface of part 2, and then cutter 3 is informed of translational movement D consistent with the values of Si, §2 and n, and also consistent with the asphericity of the zone. The treatment of the zone continues until the surface to be treated has a uniform roughness.

Coordinated with Si, 82 and n, the movement D of the cutter 3 is pre-tabulated with the necessary accuracy, then it is entered into a storage device (not shown in Fig.), Which provides a signal to the actuator 5 with the necessary frequency. As a storage device, for example, , read only memory (ROM) type K556 OT4, PT5. These microcircuits can be programmed on a standard FDA-based programmer. The ROM output is connected to a digital analog converter controlling the actuator 5.

In view of the small (within tens of microns) linear displacements, the most appropriate embodiment of the actuator 5 for moving the cutter 3 is the execution in the form of a precision small displacement motor, for example, piezoelectric or electro-hydraulic, which ensures its high rigidity, accuracy and speed.

For rotation of tool 7 and 9 and working 1 spindles, it is advisable to use pneumatic actuators or high-torque electric drives.

Equipping the device with electric or pneumatic actuators and piezoelectric or hydraulic drives makes it possible to most easily implement the proposed method. Moreover, the proposed implementation of the method minimizes the length of the kinematic chain, which significantly increases the rigidity, accuracy and speed of the work and the actuator, which ultimately increases the accuracy of surface treatment.

Manual drives 6, 8 and 11 of the device are intended for preliminary adjustment, determined by the geometric parameters of the treated area, and can be made as screw pairs.

The control of the magnitude of the movement A of the cutter 3 can be carried out depending on the required accuracy by a photoelectric sensor or interferometer.

The control of the frequency values Si, 82, n can be carried out by fiber optic or electromagnetic frequency meters.

An advantage of the method of processing zones of aspherical surfaces by cutting and a device for its implementation are high characteristics in terms of accuracy and level of processing roughness, which make it possible to obtain fragments of aspherical metal optic surfaces with a shape error of no worse than 0.5 μm and a roughness of no more than R 0, 02 μm, while the risks from cutter 3 are made in the form of open endless branches of the epicycloid. The processing of such surfaces with the same quality of the surface layer cannot provide a prototype device ..

Claims (2)

1. A method of processing aspherical surfaces by cutting, in which the tool spindle is given rotational movement and the translational movement coordinated with it to the cutting tool, and a circular feed, coordinated with the translational movement of the cutting tool, is informed to the spindle with the component fixed to it, distinguishing that. in order to improve the quality of the surface layer of the zones of aspherical surfaces bounded by two planes perpendicular to the axis of symmetry of the aspherical surface, by excluding the periodic cutting of the cutting tool into the surface to be machined, the rotation axes of the cutting tool report rotation around an axis parallel to the axis of rotation of the part, the rotational speed of the part is three times lower than the rotational speed of the axis of rotation of the cutting tool and the directions of these rotations coincide, while the rotation radius of the cutting its tool is equal to half the width of the formed zone, and the frequency of rotation of the cutting tool is greater than the frequency of rotation of the axis of rotation of the cutting tool and the directions of their rotation coincide. 2. A device for processing aspherical surfaces by cutting, comprising a bed with a working spindle for fastening, parts, a tool spindle, a tool holder, a carrying tool and an actuator for moving the tool, which, in order to improve the quality of the surface layer of the zones of aspherical surfaces, bounded by two parallel planes perpendicular to the axis of symmetry of the aspherical surfaces, due to the exclusion of periodic cutting of the cutting tool into the work surface, the construction is equipped with a stand and an additional spindle with a housing, the tool spindle mounted on the stand fixed parallel to the eccentric axis of the working spindle, the auxiliary spindle housing mounted on the tool spindle with the possibility of rotation around the axis of the latter, and the axis of the additional spindle is eccentric and parallel to the axis of the tool spindle, and the tool holder is mounted on an additional spindle. .kr. / . Figure 1 fig.Z Fig 4