SU1678551A1 - Method of hole machining - Google Patents

Abstract

The invention relates to metal cutting and can be used in the processing of holes. The aim of the invention is to increase the efficiency of the cutting process by controlling vibrations. For carrying out the method, an instrument with at least four cutting inserts installed in pairs in the radial and axial planes is used. The tool vibrations in the radial plane are controlled by varying the distance H between the cutting plates in the axial direction, and the axial vibrations are controlled by changing the central angle between the plates in the radial plane. To dampen vibrations, the cutting blades are axially displaced by a distance H (2K + 1). where S is the axial feed mm / rev, K is an integer in the range of 23-949, and the central angle between the plates in the radial plane is 0 тг (2 | + 1) 1 + + (30 п) (Ox - the frequency of axial vibrations, Hz, n is the frequency of rotation of the tool, rpm, i is an integer ranging from 6 to 150. To excite vibrations, the cutting plates are shifted axially to the distance H S K. and the central angle between the plates equal to 1 + (30o) x: n) 4 s. f f-ly, 5 ill. cl

Description

The invention relates to the field of metal cutting and can be used in the processing of holes.

The purpose of the invention is to increase the efficiency of the cutting process by controlling vibrations.

FIG. 1 shows a tool for carrying out the method of machining holes, a general view; in fig. 2 - the case of bore holes with two cutting blades, the tops of which are located in the same axial plane; in fig. 3 - the case of a bore hole with two cutting blades, the tops of which are located in a plane perpendicular to the axial plane; in fig. 4 and 5 - scan of the cutting surface

cutter located in a plane perpendicular to the axial plane

For carrying out the method, an instrument is used comprising a housing 1, in the slots of which, radial and axially adjustable cassettes 2 with cutting plates 3-6 are installed. The plates are fastened with claws 7 and fastening screws 8. When the bore is drilled with two cutting plates that are axially displaced one relative to the other by distance H (Fig. 2), the first plate works with a depth ti, and the second is ta. The tool or part is rotated at an angular velocity of Sho, the tool moves along an axis at a feed rate of S.

about VI

00

cl

The oscillations caused by the operation of the plate 3 begin from point O and are caused by any random push, geometry, segregation of the material of the workpiece, a falling characteristic of the cutting force. As a result of the resulting radial oscillations, the tool forms a wavy surface whose profile corresponds to the sweep of the system oscillations in time. The second plate 4, starting from point O, should remove chips of periodically varying width. The cutting force P and, consequently, its component Ru, is periodically modulated by a frequency equal to the oscillation frequency of the system. We establish the mutual influence of the oscillations that arise and their effect on the overall vibrations of the instrument,

Let the oscillatory system have a mass m, a rigidity K, a damping constant C.

The position of the cutting edge of the tool relative to the average position in the first pass is denoted by yi, in the second - through ya, taken in the upward direction for positive.

Cutting depth at each time point when removing the first chips

ti ti -yi. When removing the second chip

X21 t2-y2 + yi.

The cutting force is expressed in terms of the depth factor V. which determines the degree of impact of the cutting process on the oscillating system and is equal to the ratio of the increment of force d P acting on the oscillating system, cutting edge.

In our case

g

dP

cozy),

“;

 main angle in the plan. Cutting force is

P y. Component

RU rti cos / 5, Type designation

g g

we have

Ruryt1.

The equation of the oscillating mass for movement in the y direction, when operating the first plate, has the form

myi + Cyi + Kyi Rusr-gu yi. (2)

Constant force Rusr does not affect the nature of oscillations, therefore

myi + cyi + (K + ry) yi 0.

(3)

As is known, the solution / equation (3) 15 has the form

Y1 sin (ovt + pyO, (4) 20

Cty v (lT + gu) / t - (C / 2m y.

Thus, equation (4) describes the shape of the wavy surface after the first pass.

The variable depth of cut in the second pass is equal to

t2 U1 - U2.

The cutting force varies depending on the x coordinate according to

RU2 ry (yi-y2).

The equation of motion of the oscillatory system in the second pass is

40tU2 + Su2 + Ku2 (yi - Y2) gu;

tu2 gu

+ Cy2 + (K + gu) y2 gu yi 2j sin (ttyt).

(five)

Therefore, the form of the oscillatory motion equation in the y direction when the second plate is in operation is determined by the fact that its left side coincides with the left side of the motion equation for the first plate, and the right side contains the integral of this equation multiplied by r. We introduce the notation

D 2jryAy e / m; Р С / т:

q (K + ry) / m. Then equation (5) takes the form

Y2 + Ru2 + RU2 D sin (aij t + 1 /,). (6) As is well known, the general solution of an inhomogeneous equation is represented as the sum of some particular solution of this equation and the general solution of the corresponding homogeneous equation. As shown, the general solution of a homogeneous equation is

Y2 2jAy e sin (My t +)

The particular solution of the inhomogeneous equation is sought in the form

at

Y2 M cos / 3t + N.

In the latter expression, the oscillation frequency / 3 is equal to the oscillation frequency of the external force Py2. As mentioned, the cause of the appearance of a periodic external force is the regenerative trace on the treated surface, whose profile corresponds to the sweep of the oscillations of the first plate in time. As established by solving equation (3), the frequency of these oscillations is equal to fty. Thus, the force Py2 is periodically modulated by the frequency o) y, equal to the frequency of oscillations of the first plate.

/ 3-ov

Taking into account the last expression of U2 M cos My t + N sin My t. (7)

Determining the values of M and N by substituting the expression (7) into the original differential equation, we find a particular solution of the inhomogeneous equation, which has the form

 - - I sln (y +

The total integral of equation (6) is

Y2 Y2 + Y2

-2jAe 1 sin (Myt + py2) +

Dsln (Myt + UU) V (g-a $ y +

Designating

Dv

we have

Y2

mV (g-ft # y + P a $ sin (+ py2) +

+ 2 j Av e; l Dy sin (djy t + yv). (9)

The wavy surface equations for the first (4) and second (8) plates are derived under the condition that they operate independently of each other. However, in this case, both plates are rigidly fixed in the same housing, and. therefore, the resulting oscillatory motion of the tool body with the plates follows the superposition principle and is equal to the sum of the vibrations excited by the first and second plates, i.e.

15

y yi + (sin ("jyt + +) + sin (My t +) + Dy sin X

x (ftvt +)). (10)

In the last expression the phase angles

 and depends on the choice of the starting point.

the reference point, and the angle уОу - on the ratio of the amplitudes M and N. By shifting the origin to the beginning of the first sinusoid, we get

-I

y 2jAye At (sin (Myt +

+ 1 / -V) + sin ft t + Dy sin (rty t +)),

(eleven)

where i / V W2 is the phase shift between the oscillations of the first and second plates.

On the other hand, the phase angle YV can be represented as

W to.

where to the time of the first plate until the second is embedded ;,

Sho - angular speed of rotation. In turn

45

50

to L / V,

where L is the cutting path;

V is linear velocity.

These values are expressed as follows.

L nx2 L: Do / 2; V Ofe Do / 2,

where nx is the number of revolutions that the workpiece performs until the second plate is inserted;

Oo - diameter processing.

Speed

nx H / S

where H is the distance between the plates, mm:

S - feed, mm / rev

Substituting these values into equation (11), we get

W

0) 0 H 2 n D0 / 2 S W0 Do / 2

 2 ng H / S.

(12)

Taking expression (12) into account, the total oscillations of the instrument are described by the equation

y 2JAye t (sin (wyt + - |) +

ABOUT

+ Sin toy t + Dy sin (ft) y t + py)). (13)

Consider the conditions under which expression (13) vanishes, i.e. no tool vibrations. Obviously, in the presence of primary oscillations, the value of A is always different from zero. Therefore, in order to clarify the vibration quenching conditions, we equate the expression in brackets to zero and solve it with respect to i /) y. Preliminary calculations show that the value of Dy is two orders of magnitude smaller than the amplitudes of the first two sinusoids; therefore, in further calculations, with a large degree of accuracy,

Dy sin (ft t + (fa) can be neglected. Thus

sin 0) y t + sin (Wyt + 2 tg H / S) 0; sin% t - sin (Wyt + 2 Jt H / S) 0;

6 where

2 n H / S (2 K + 1).

where K is an integer ranging from 23 to 949.

We finally have

H / S (2K + 1) / 2.

Thus, in order to increase the vibration resistance of the system by damping the vibrations, the cutting plates must be axially displaced one relative to another by the distance related to the feed rate by the relation (14),

In the event that the phase angle of the band is equal to zero or a multiple of 2 liters, the oscillations will be in phase and as a result of the addition, the overall vibrations will increase. This phenomenon, under certain conditions, can be used as a source of additional useful vibrations, which intensify the cutting process.

additional vibrations can be recorded as

2lN / 5 K. or

5H / S K. (15)

Thus, in order to create radial oscillations that increase the efficiency of the cutting process, the cutting blades must be axially offset one relative to the other by the distance related to the feed rate by relation (15).

Consider the case of processing by dividing the feed when the load on the tool is distributed between the cutting edges located along the diameter of the tool, while the tips of the cutting edges are in the same diametrical plane and the central angle between them

20 is 0 (FIG. 3). Suppose that the oscillations of the first plate are due to any random reasons, as a result of which a wavy surface is formed, which can cause regenerative

25 effects, i.e. be a source of secondary vibrations.

In this case, the second cutting plate removes chips of periodically varying thickness, which causes the tool to oscillate in the axial direction. This phenomenon can cause resonance oscillations if at each instant of time the oscillation vectors of the first and second plates have the same direction. Otherwise, i.e. when the oscillations have opposite directions, as a result of the addition, the overall vibrations of the tool may be reduced. Consider the conditions of occurrence

40 secondary regenerative oscillations and their effect on the overall vibrations of the instrument. The position of the cutting edge of the plate 3 relative to the middle position (i.e. the cutting plane) is denoted by xi.

45 cutting edges of the plate 5 - through X2.

Slice thickness at each time when removing the first chip

50

ai ai -xl

when removing the second chip a2l a2-x2 + xi.

where ai and aa are the nominal shear thicknesses of plates 3 and 5, respectively.

By analogy with the considered case, the tool oscillations along the X axis can be described by the equation

mxi + C / 1 f (K + rx) xi-0 (16) fV) +. DxSln ()) (20) "Similar to equation (13), the condition is vibra- Obviously, the oscillation-damping equation is determined by the expression of the motion along the X axis caused variable slice thickness, similar to equation 5tAt (21 4-1 1 (211 vibrating mass in the direction of the Y axis,

when oscillations are caused by a variable that is within

depth of cut. Therefore, by analogy of cells 6 to 150

by equation (3) the solution of equation (16) is jrnnnn

  l The angular distance between the two cuts with visible edges can be written as follows.

xi 2jAxe At sln (Mxt + 0 i). (17)

0 QJict0 + Vb. (22)

whereA C / 2t; 15

where to is the time it takes for the instrument to complete V (| 4-rx) / m –L2. It sews a part of the turnover corresponding to the central angle in. Expression (17) is an equation. On the other hand

sweep the cutting surface after the first plate.

The variable thickness of the second plate is equal to

howl plate.d p

Variable cutting thickness at work30

where n is the frequency of rotation of the tool. 32I xi - H2Ots From the last expression we have

Cutting force varies according to you-30 volts / g

to razheniyu

Px2 rx (xi - ha). Substituted the value to to the formula (22),

The equation of oscillatory motion to GET when the second plate is in operation has the form

0 300od / n + VV.

mx2 + cx2 + 1x2 (xi - x2) rx;

From here

mx2 + cx2 + 0 + Gx) x2 rxxi. (18) 35

uh's (- 30 (Mx / n).

The form of the equation of oscillatory motion in the direction of the X axis when the second one is working. Having read expression (21), we have plates the same as equation (6) describing the oscillations of the second plate at od / -1 30 °, , „„. change the depth of cut. Therefore, the solution of equation (18) can be written as

Thus, to dampen vibrations

X2 2 j Ah e (sin (oh t + 0x5) + at the Dissolving of the cutting blades diametrically, 45 45 instrument meters constructive and techno + Dx sin (wx t)). Logical parameters should be

ppm) are related by (23).

As stated, increased vibration

As well as with variable depth of cut. occurs if the phase angle of equations (17) and (19) describe the shape of the 5Qi / s equal to 0 or a multiple of 2 liters of the cutting surface

that the plates work independently each other / i. "" "

friend However, the total vibrations of the instruments - j) - 2 l: I.U4)

The elements are a consequence of the addition of the oscillations caused by the first and second 55, thus, to increase the effect plates. Therefore, the oscillation of the instrumentation of the cutting process by creating along the X axis can be described by the equation of the axial oscillations of the tool

The blades are placed along the diameter of the tools 2) Ahe (sin (Yx t + sin ((Uxt + m, with the design parameters related by relation (24)).

Claims (5)

1. A method of machining holes, in which a tool with several cutting plates displaced one relative to the other in the axial direction is reported to rotate and move an axial feed, characterized in that, in order to increase the efficiency of the cutting process by controlling vibrations, a tool with at least at least four cutting plates installed in pairs in the axial and perpendicular planes, while controlling the vibrations of the instrument in the plane perpendicular to the axial, change The cutting between the cutting plates in the axial direction, and the vibration control in the axial direction is carried out by changing the central angle between the plates in a plane, perpendicular to the axial direction. 2. A method according to claim 1, characterized in that a tool is used in which the cutting inserts are axially offset by distance H 2 K + 1 where H is the axial distance between blades, 30 mm, mm; S - axial feed, mm / rev; 6 8 ftsts.11 0 five 0 five K is an integer ranging from 23 to 949. 3. A method according to claim 1, characterized in that a tool is used in which the cutting inserts are axially offset by a distance H S K. 4. Method pop. 1, characterized in that a tool is used whose central angle between the cutting plates in a plane perpendicular to the axial plane is equal to p gr (2i + 1) 1, ZOo where in - the central angle between the plates, rad; (M is the frequency of axial vibrations, Hz; n is the tool rotation frequency, rpm; I is an integer ranging from 6 to 150. 5. A method according to claim 1, characterized in that the tool is used, in which the central angle between the cutting plates in the plane perpendicular to the axial plane is equal to 2 1 1 + 30 a YAP Surface to be treated Surface®ag- b cutting Finished surface # W2 UV Pu..5