SU1404284A1 - Method of abrasive working of spherical surfaces - Google Patents

Abstract

The invention relates to the machining of optical components and allows for an increase in dimensional tool life. On the working surface of the tool and the workpiece are concentric circles corresponding to each other in the pitch. In zones formed by concentric instrument circles, an abrasive is placed with various concentrations. The speed of the relative movement is chosen from the condition of directly proportional dependence of the average speed of the relative movement of each of the annular zones of the tool on the abrasive concentration. Such a choice of abrasive concentration and its placement allows to increase the dimensional tool life and quality of processing. 4 il.

Description

4 N3

00

four

The invention relates to the field of machining optical parts and can be used in the optical industry, as well as in the manufacture of tools intended for processing, for example, spherical surfaces of kinematic pairs of manipulators and balls of large diameter.

The aim of the invention is to improve the quality of processing by increasing the dimensional stability of the tool.

The proposed method of machining spherical surfaces consists in communicating the workpiece and the tool with an end spherical working surface of relative mixing. On the working surface of the tool, annular zones are isolated and filled with abrasive with different concentrations, which is proportional to the processing time and the average speed of the relative movement of the workpiece and the tool. The indicated speed is obtained by averaging the values of the relative displacement velocities, which are determined at the intersection points of the said annular zones of the tool and the workpiece. The annular zones on the workpiece are selected from the condition that the annular zones of the tool are tangent to their circumferences.

FIG. 1 shows the workpiece and the tool in the plane coinciding with the axis of their rotation, a section; in fig. 2 - the same, top view; in fig. 3 is a view A of FIG. 1 (along the tool axis with concentric circles on its working surface and concentric circles on the surface to be machined); in fig. 4 is a diagram of an apparatus for carrying out the proposed method.

The proposed method consists in processing the workpiece 1 with a tool with a working surface 2, on which annular zones are marked in the form of concentric circles with equal pitch. FIG. 2 shows their radii from / o max to, 1. The central angles of these circles with respect to the axis of symmetry of the tool are denoted by b, where, 1, 2, ... On the surface of workpiece 1, choose circles of radius y so that they have a common point of tangency in the plane coinciding with their axis of rotation. To this end, after selecting the values of g /, the value of the corresponding central angle of the instrument is determined by the formula

b, sin

fe

 i;

where Re is the radius of the processed sphere.

Then determine the central angle D /

on the treated surface by the formula

, (2)

where - | - the angle between the axis of symmetry (rotation) of the tool and the machined

blanks (the sign "- corresponds to the points of contact of the circles located between the axes of the workpiece and the tool;" - (- corresponds to the value A ,. Then, the values of the radii of the circles Ri on the treated surface, which relate to the circles of radius g / on the working surface of the tool in the plane coinciding with the axis of their rotation by the formula

, sinA /. (3)

As can be seen from FIG. 1 and 2, in the circles on the tool corresponds to the circles on the surface to be machined. The number of tangent points is equal to the number of circles m of radius R /. At each point of intersection of the circles, the cosine of the angle l is determined between the radius n and the projection of the radius vector R / onto the plane of the corresponding circle G; According to the formula

cosa (.-% slnll ...

2Rj-riCos-

where / g, 7, - (1-CGD /) is the height of the segment formed by the plane of the circle of radius RJ.

FIG. Figure 2 shows the angle between the vectors oz and 33 at the intersection point of the zero circle of the radius tool and the third circumference of the surface of the radius being machined. At the second intersection point of these circles, the angle is "360 °." Formula (4) is derived from a triangle, for example, Oz, Oz, C (Fig. 3). The triangle formed by the sides g /, RjCos D / 2 and max L1751pD / 2 (in Fig. 3 - the sides of the vines,

Rascos- and Go- / Zsssin-) is located in

WITH.

the plane of the corresponding circle g / (in Fig. 3 - in the plane of the circle

0 max) As can be seen from f. 2 and 3, the angle a between the Waz and VS s vectors of the 3, O points belonging to the surface to be machined and the tool coinciding with the intersection points of the selected circles.

five

associated with an angle of a 180 ° -ag.

(five)

At the same points of contact with the rotation of the tool with the speed of the soc and the workpiece with the speed of Sd in the directions indicated

in fig. 2, angle, and in others. The velocity distribution at these points, shown in FIG. 2 shows that at some point on the surface of the workpiece there is a point on the arc ac, which is separated from the axis of rotation

5 details at a distance / in which, i.e. V, -. This means that at this point there is no relative movement speed (cutting speed), i.e. the removal allowance is theoretically not present when pressure is present. This combination leads to the formation of microcracks on the treated surface. Writing down the condition of equality of the velocities of the point of contact of the circles of radii Гх h RX in the form of (3) f, Rx or taking into account

formulas (1) - (3) in the form (o „з1п ()

CL jSinA; c, after transformations, the value of the angle Lx corresponding to the zone of possible cracking is determined from the expression

tgA.

sinjcos-;

In equation (6), the sign "+" corresponds to the same direction of rotation of the workpiece and the tool, "- - - the opposite, as indicated in FIG. 2. The magnitude of the radius of the tool circumference, at which there is a point where the cutting speed (slip) is zero, is determined from the expression

r. (A, + f-).

If, then the point at which the vs V is Vfi-cosa.

No missing, located on the arc ac of the treated surface (Fig. 1, 2). This will be in the case of the opposite direction of the angular velocity of the workpiece and

tool. If, then such a point

located on the ace arc (Fig. 1, 2) closer to the periphery of the treated surface. This case corresponds to the same direction of SOCs and SOC. As can be seen from equation (6), when such a point is located on the axis of rotation of the tool, it is at point C (Fig. 3). Equations (6) and (7) allow you to select the minimum value of the internal diameter of the tool, at which there are no adverse conditions for removal of the allowance. As can be seen, its value is determined not only by geometry, but also by kinematics. Thus, after the determination, the rates of relative movement (wear) at each point // of the tool’s intersection of the tool’s working surface and the workpiece are determined by the formula

(eight)

Expression (8) makes it possible to determine the amount of wear U at each intersection point and the tangency of Utf of the circles depending on the time t of the tool’s rotation,

as Uij VcK-i - Considering that K; a) d) c- / /;

Y (, - y, then (j) u, where L is the number of tool revolutions. From the expression (-8) taking into account the previously obtained ratios, we have

//

Ui,

Th, so5a,) 2ll

(9)

five

15

Equation (9) makes it possible to determine the relative amount of wear (7.7 at each intersection point of the circles during any tool operation time determined by its number of revolutions.

The absolute amount of wear can be determined using equations (9) with regard to the intensity of wear determined by pressure. After determining the relative amount of tool wear at each intersection point, the total relative wear along each circle is determined as the sum of the wear at the intersection point and the touch of each circumference of the tool with all the radius circles on the surface to be machined using the formula

20

25

Z

 ij 1

tp

p I ij 1

Uy

2

ij

ten)

ZO

h5 ds

55

g l where Uij - relative wear at two points

touching each circle, defined taking into account that in them or. This method of calculating the geometry and wear of the working surface of the tool is relatively simple, allows you to use a computer to analyze the wear and tear of both the tool surface and the work surface and determine the speed of relative movement along the tool circumference (along the tangent to it). Formulas (4), (5) allow us to determine the angle between these vectors using only geometric parameters and the proposed method of splitting adjacent spherical surfaces.

This technique takes into account the projection of the total velocity of the relative displacement on a tangent to the path of the tool point located on a circle of radius l. In general

I / (1 /,) 2+ (vT.) -2 K GKSoza,

where

However, taking into account the fact that, that is, V ,, - Vf (for example, rpm is taken at rpm or rpm), it can be considered with a slight error.

This method of calculating the tool also resolves the issue of choosing a rational ratio of the internal diameter of the tool and improving the quality of processing by determining the law of placement of various concentrations of diamond powder on the working surface of the tool. This is the way to ensure

more uniform wear of the working surface of the tool, rather than the thickness of the diamond layer of the tablet, since the wear resistance coefficient does not change from its value. It can be changed, for example, by changing the concentration of diamond powder in anyone. After calculating the size of the inner diameter and average wear along all the middle circles of the selected annular zones of the working surface of the tool, a diamond layer is formed along them, and the concentration of diamond powder in these zones is proportional to the average speed of relative movement along each circle and the processing time measured by the number of tool turns at a certain (specified) ratio of the angular velocity of the workpiece and the tool. To achieve a greater degree of accuracy in the orientation of the diamond layer and the strength of its adhesion to the tool body, the grinders with the appropriate concentration of diamond powder are placed in cylindrical shells with a diameter corresponding to the selected annular zones, while the inner and outer walls of the cylindrical shells are made of a low-melting metal capable of bonding softened condition.

A device for carrying out the method (FIG. 4) comprises a pallet 3, which is used to install it in the furnace during sintering, cylindrical shells 4 of fusible material with housed inside of them, tool case 5, punch 6, bolt 7 with nuts 8 and 9 to fasten the centering part 10 and press the spherical surfaces of the additional 11 and main 12 inserts.

A device for implementing the method works as follows.

A main insert 12 is assembled on a pallet 3, assembled with a bolt 7 and a lower nut 9. On the bolt 7, an additional liner 11 is installed on top, then assembled (inserted into each other) cylindrical shells 4 with a mixture. After that, the tool body 5 is put on the additional liner 11, the centering part 0 is bolted on the bolt 7, it is tightened

0

„,.

0

five

the nut 8 and the top of the assembled parts wear the clip. Thereafter, the mold is placed in the working area of the heating device, a punch 6 is inserted between the sleeve and the centering part 10, and the body 5 is connected to the cylindrical shells 4, which are melted into the spiral grooves formed on the end of the tool body. Under the influence of pressure and temperature, the final formation of the diamond layer occurs.

This method of working area breakdown takes into account the geometry of the contacting surfaces, and the calculation method allows us to take into account the nature (pattern) of wear of the working surface of the tool both along the selected annular surfaces and between them and to realize high-quality mounting and precise positioning of the diamond layer on the working surface tool. At the same time, by varying the concentration of the diamond powder in accordance with the identified pattern of wear, the proposed method allows controlling the wear resistance coefficient of individual annular zones of the tool. This solves some problems of increasing the dimensional stability of the tool and improves the quality of the machined surface.

Claims (1)

Invention Formula A method of abrasive machining of spherical surfaces, in which a workpiece and an instrument with an end working surface are informed of relative movement, characterized in that, in order to improve the quality of processing by increasing the dimensional durability of the tool, concentric circles corresponding to each other are arranged on the working surface of the tool and workpiece and in zones formed by concentric instrument circles, an abrasive is placed with different concentrations, and the relative speed Nogo movement of selected conditions is directly proportional to the average velocity of the relative movement of each of the annular zones of the tool to the abrasive concentration. Wu, g.1 VU2.2 M Vl123 % FIG.