SU1604569A1 - Arrangement for grinding and polishing of parts having aspherical surfaces - Google Patents

Abstract

The invention relates to the field of machine tool construction and can be used for grinding and polishing aspherical convex surfaces of optical parts. The aim of the invention is to simplify the design and increase productivity by reducing the number of drive elements of the tool and ensuring that three rotational motions are added during operation. From actuator 1, the rotation is transmitted to the input cranks 3 and 4 of the spherical five-link mechanism, as a result of which the connecting rods 5 and 6 and, accordingly, located in the kinematic pair of their connection, the spindle 7 of the tool 8 makes movement along a definite path. Table 11 performs both rotational and reciprocating movements. Because the tool 8 has a radius that overlaps the vertical axis of the workpiece 10, the entire aspherical surface is machined. 2 Il.

Description

The invention relates to machine tool and can be used for grinding and polishing aspherical. Convex surfaces of optical parts "

The aim of the invention is to simplify the design and increase productivity by reducing the number of drive elements of the tool and ensuring the addition of three rotational movements during operation ”

In Fig. 1, a kinematic diagram of a device for grinding and polishing optical parts with aspherical surfaces is shown; in the figure "2 is a kinematic diagram of a five link spherical mechanism"

The device consists of a drive 1 mounted on a frame 2 "Drive

I is connected by input cranks 3 and 4 of a five-link spherical mechanism. ”In a kinematic pair of connected connecting rods 5 and 6, a spindle 7 is installed with a tool 8 connected to a separate electric drive 9“ All links of a spherical five-link mechanism are connected by rotational kinematic pairs ”. The workpiece 10 is mounted on a table 11, associated with the drive rotation and reciprocating movement in the vertical-longitudinal direction "

The grinding and polishing tool has an aspherical concave shape corresponding to the surface of the part, with such a radius that part of the tool always overlaps the vertical axis of the workpiece ”

The device operates as follows "

From the electric drive 1 mounted on the frame 2, the rotation transmits. connecting to the input cranks 3 and 4 of the spherical five-link mechanism, as a result of which the connecting rods 5. and 6 and correspondingly located in the kinematic pair of their connection, the tool spindle 7 moves along a certain path, while the spindle 7 with the tool 8 rotates along a circle located on the aspherical surface of the optical part 10 mounted on the table AND "Table

II performs both rotational and reciprocal motion in the vertical longitudinal direction "

The movement of the tool 8 and the rotation of the workpiece are carried out in opposite directions. Due to the fact that the tool 8 has a radius that overlaps the vertical axis of the workpiece 10, this ensures grinding and polishing of the entire aspherical surface.

The reduction of grinding and polishing time is achieved by adding three rotational movements, rotating the part, rotating the tool both about its axis and the part located on the aspherical surface ”

The accuracy of the description of the exact spherical circumference of the spindle 7 of the tool (Fig. 1), t ”e” by the centrosocial joint of the connecting rods of the spherical five-link articulated mechanism ASVDE (Fig. ₀ 2), is confirmed by the synthesis of this mechanism, carried out in the following sequence ”

First, the equation of the trajectory described by the centrosocial joint of the connecting rods of a spherical five-link articulated mechanism is derived "

For the special case when the gear ratio between the leading cranks is ^ί ₅₂ - ⁺ 1 ”and the angles οί ₀ and y) ₀ , which determine the initial position of the leading links, are equal to zero, the trajectory equation has the form

Aj B _g - A ₀ A, B, + A> _o = °, (1) where A _o = sin (cos 1 ₂ cos U cos V -cos l ₃ ) + sin 1 ₂ (cos If cos l ₅ wcos U * xcos V + sin 1 (cos l ₅ sin U cos V.-

- cos 1 ₄ );

A, = sin l ₂ sin lj [sin U cos V xx (l-cos 1 () + sin (lf-U) cos U cos VJ;

B _o = (cos l _t cos l ₅ cos U cos V + + sin 1, cos ljsin U cos V - cos 4) -

- sin ² lcsin ² V;

B ί = sin ^z l ₅ (cos 1 ₍ sin U cos V -

- sin ljcos U cos V) (cos l _t cos lj-X X cos U cos V + sin ljcos l ^ sin Ux, cos V - COS 14);

B ₂ = sin ^a l _s (cos 1, sin U cos V -

- sin l | Cos U cos V) * + sin ^ V;

1 (- 15 “the sizes of the links of the spherical five-link;

U and V are the coordinates of point C ".

In the synthesis of a spherical five-link articulated mechanism, the method of point interpolation was used. For this purpose, the equation of a spherical circle, which has the form

A cos r = sin V _o sin V + sin U sin U _o cos Vx xcos Vg + cos U cos U _o cos V cov V _c , (2) where r is the radius of the circle described on the surface of the sphere, 0 Circumference

and V _o are the given coordinates of the center of the spherical circle;

U and V are the current coordinates of a point on a spherical circle;

Thus, having equations (1) and (2), for which the coordinates U 'and V are set; of several points on a spherical circle, we can conclude that the sizes of the links follow the definition. ”Assume that r = l ₂ = 1 ^, then by a joint consideration of equations (I) and (2) we obtain four equations with four unknowns (1, 14) 0 There is sin V _o sin V, '+ sin Uj sin U _e cos V- cos V _fi + cos U; cos U ₀ cos V; cos V _o -cos Z = [sin l _a (cos l ₂ cos U; cos V, '- cos 1 ^) + sin l ₂ (cos 1, cos ljCos Ujcos V; + + sin 1 ₍ cos l _z sin U ; cos cos 1 ₄ ) J ² [sin ^ l ^ (cos 1., sin U; cos V; -sin l, cos U; x xcos V;) ² + sin ² V '[] - [sin la (cos l2cos Ujcos V; - cos 1e) + sin l2 (cos l ^ cos U, ') x xcos V; + sin I, cos l2sin UJ cos V] - cos 14)] [sin ² · l2 [sin Ujcos V; (1-cos1,) 1 + sin (1, -UJ) cos Uj'cos * sin ² ·! ^ [(Cos l, sin Щ cos V; - sin l ^ cos U; x xcos V;) (cos 1 ₍ cos l ₂ cos U; cos V] + sin l.jcos 1 ^ sin Uj-cos VJ- cos. 1 ^) ^ + + sin'l ^ [sin U · cos-V; (1-cos 1,) + sin (1, -U;) .cos U; cos V ^^ cos 1 ₍ cosl ^ x ixcos-U ₍ cos Vj. + sin I, cos l ^ cos V ;. - cos I4) - sin ² l2 sin ² V; (3)

Indeed, if we substitute the coordinate values into equation (3), suppose, four points M / U ₂ V _Z ), M ₅ (U ^ V ₃ ) and M ₄ (u, v ₄ ) ', then from (3) we obtain four equations with four unknowns, the solution of which on a computer showed that point C of the spherical five-link mechanism on the surface of the sphere can describe a spherical circle with radius r ₍ = = 1 j. = log · for the following sizes of links 1 ₍ = 1 j = 1 4 = 3 1 ₂ "

Claims (1)

Claim A device for grinding and polishing optical parts with aspherical surfaces, comprising a bed with spindles mounted on it for mounting parts and tools, and a tool spindle drive mechanism, characterized in that, in order to simplify the design and increase productivity, the tool spindle drive mechanism is designed as a five-link spherical mechanism, including two input links placed in the frame and two interconnected cranks, each of which is associated with one of the input, venev, wherein all parts of the mechanism are interconnected rotational kine40 matically in pairs, and the tool spindle is arranged in the kinematic pair of rods, with a compound of rotational movement "