Cutting Method for Inner Circumferential Face or Outer Circumferential Face of Work

Abstract

A cutting method in which, in cutting an inner circumferential face or an outer circumferential face of a work based on turning of a main shaft around a predetermined position serving as a center, control is enabled to make a cutting velocity constant. To achieve the object, a cutting method is provided for an inner circumferential face or an outer circumferential face of a work, using a cutting tool projecting from a main shaft which turns around a predetermined position serving as a center and for which a turning radius is adjustable, wherein, in the case that a turning angular velocity of the main shaft is represented as , a distance from a turning center to a tip of the cutting tool is represented as R, and a cutting velocity of the tip of the cutting tool is set to a constant value C, making the cutting velocity of the cutting tool is made constant by performing control such that changes in association with a change in the distance R so that

[00001]$={\left(C^2-{\stackrel{.}{R}}^2\right)}^{\frac{1}{2}}/R$

is formulated (where {dot over (R)} denotes a time differential of the distance R), thus providing an even cut face.

Claims

1. A cutting method for an inner circumferential face or an outer circumferential face of a work using a cutting tool projecting from a main shaft which turns around a predetermined position serving as a center and for which a turning radius is adjustable, comprising the step of: in the case that a turning angular velocity of the main shaft is represented as , a distance from a turning center to a tip of the cutting tool is represented as R, and a cutting velocity of the tip of the cutting tool is set to a constant value C, making the cutting velocity of the cutting tool constant by performing control such that changes in association with a change in the distance R so that $={\left(C^2-{\stackrel{.}{R}}^2\right)}^{\frac{1}{2}}/R$ is denoted (where {dot over (R)} denotes a time differential of the distance R).

2. The cutting method for an inner circumferential face or an outer circumferential face of a work according to claim 1, wherein a position of the turning center of the main shaft is movable in one of: an orthogonal direction and an oblique direction to a plane orthogonal to the turning central axis, and when the position of the turning center of the main shaft is movable in the oblique direction, moving a supporting position of the work on a table on which the work is placed in association with the movement in the oblique direction to maintain a state where cutting is enabled.

3. The cutting method for an inner circumferential face or an outer circumferential face of a work according to claim 2, further comprising the step of moving the position of the turning center of the main shaft in one of the orthogonal direction and the oblique direction, while the turning radius is sequentially changed.

4. The cutting method for an inner circumferential face or an outer circumferential face of a work according to claim 2, further comprising the step of moving the position of the turning center of the main shaft in one of the orthogonal direction and the oblique direction, while the turning radius is changed in a stepwise manner.

5. The cutting method for an inner circumferential face or an outer circumferential face of a work according to claim 1, wherein a position of the turning center of the main shaft is not moved in the orthogonal direction nor the oblique direction, and further comprising the step of forming a ring shape by the following steps: (1) in an inner region of the work that is close to the turning center, sequentially increasing the distance from the turning center to the tip of the cutting tool to move the tip along a helical locus, in the case that the distance reaches a maximum state, so that the maximum state is maintained to form an inner wall in a ring shape, and (2) In an outer region of the work that is away from the turning center, sequentially reducing the distance from the turning center to the tip of the cutting tool to move the tip along a helical locus, in the case that the distance reaches a minimum state, so that the minimum state is maintained to form an outer wall in a ring shape.

6. The cutting method for an inner circumferential face or an outer circumferential face of a work according to claim 1, further comprising the step of adopting a plurality of main shafts and cutting tools projecting from the respective main shafts.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0018] FIG. 1 is a block diagram of a system allowing a method of the present invention to be implemented;

[0019] FIGS. 2(a) and 2(b) are plan views denoting the state of a plane in a direction orthogonal to a turning central axis of a main shaft, FIG. 2(a) denoting that an inner circumferential face is cut, and FIG. 2(b) denoting that an outer circumferential face is cut;

[0020] FIGS. 3(a) and 3(b) denote a method of forming a normal tapered shape by moving the position of a turning center of the main shaft and sequentially changing a turning radius, FIG. 3(a) being a plan view denoting a locus of movement of a tip of a cutting tool, and FIG. 3(b) being a side view of the tapered shape formed by the sequential change;

[0021] FIGS. 4(a) and 4(b) denote a method of forming a stepped tapered shape by moving the position of the turning center of the main shaft and changing the turning radius in a stepwise manner, FIG. 4(a) being a plan view denoting a locus of movement of the tip of the cutting tool, and FIG. 4(b) being a side view of the stepped tapered shape formed by the stepwise change; and

[0022] FIGS. 5(a), 5(b), and 5(c) are perspective views denoting a process of forming a ring shape by helically moving and finally circumferentially moving the tip of the cutting tool in an inner region and an outer region of the work without moving the turning center position of the main shaft, FIG. 5(a) denoting a process of forming an inner wall in a ring shape, FIG. 5(b) denoting a process of forming an outer wall in a ring shape, and FIG. 5(c) denoting the finished ring shape.

DETAILED DESCRIPTION OF THE INVENTION

[0023] As is denoted in FIG. 1, components of the present invention include a main shaft 1 that turns, a cutting tool 2 provided at a tip side of the main shaft 1, a work 3, a table 4 that supports the work 3, and a control apparatus 5 that controls movement of the main shaft 1 and the table 4 (in FIG. 1, blank arrows indicate a moving state of the main shaft 1 associated with adjustment of a turning radius or a moving state of the main shaft 1 in the orthogonal direction or the oblique direction, curved arrows indicate a turning state by revolution of the main shaft 1 and a rotating state of the table 4, a dotted arrow from the control apparatus 5 indicates a state where signals which allow a turning angular velocity and a rotating angular velocity to be controlled are dispatched, and solid arrows indicate states where signals are dispatched which allow control of movement of the main shaft 1 associated with adjustment of the turning radius of the main shaft 1, and in the basic configuration (2), control of movement of the rotating center of the table 4 associated with movement of the turning center of the main shaft 1 in the orthogonal direction or the oblique direction and movement of the turning center of the main shaft 1 in the oblique direction).

[0024] In the present invention, elements to be controlled are parameters indicative of the turning angular velocity of the main shaft 1 with respect to the turning center, and the turning radius of the main shaft 1 (these elements correspond to the basic configuration (1)), and further the moving position and the moving velocity of the turning center in the orthogonal direction or the oblique direction with respect to a plane orthogonal to a central axis 6 for turning of the main shaft 1 (the above-described elements correspond to the basic configuration (2)). For the basic configuration (1), the number of the parameters is two, and for the basic configuration (2), the number of the parameters is three.

[0025] The main shaft 1 and the cutting tool 2 make turning motion around a predetermined central position. A tip of the cutting tool 2 cuts an inner circumferential face of the work 3 as is denoted in FIG. 2(a) or cuts an outer circumferential face of the work 3 as is denoted in FIG. 2(b). The turning radius of the main shaft 1 from the central position is adjustable, and thus, the radius of curvature of the tip of the cutting tool 2 is also adjustable, allowing a cutting curved face to be optionally selected.

[0026] That is, circumferential curved faces in FIGS. 2(a) and 2(b) merely denote typical examples based on rotation by the composition of the revolution of the main shaft 1 and the rotation of the table 4. The cutting curved face is not necessarily limited to the circumferential curved face.

[0027] Criteria based on expressions for the basic configuration (1) and corresponding to a technical demand for provision of an even cut face will be described below.

[0028] As is denoted in FIGS. 2(a) and 2(b), if the distance from the turning center to the tip of the cutting tool 2 is represented as R, and an angular position of the cutting tool 2 is represented as , and that a coordinate position of the cutting tool 2 is represented as (X, Y), then X=R cos and Y=R sin is formulated and

{dot over (X)}={dot over (R)} cos R{dot over ()} sin ,{dot over (Y)}={dot over (R)} sin +R{dot over ()} cos

is formulated (dots over reference characters indicate time differentials).

[0029] Therefore, when the cutting velocity is represented as V,

V.sup.2={dot over (X)}.sup.2+{dot over (Y)}.sup.2={dot over (R)}.sup.2+{dot over (R)}.sup.2{dot over ()}.sup.2

is formulated.

[0030] According to the above-described relational expressions, wherein, in the case that the turning angular velocity of the main shaft 1 is represented as .sub.1 and the rotating angular velocity of the table 4 is represented as .sub.2, the constant value C may be preset and controlled to formulate

[00003]$=\stackrel{.}{}={\left(C^2-{\stackrel{.}{R}}^2\right)}^{\frac{1}{2}}/R$

in association with the distance R and {dot over (R)} that is a time differential of the distance R, in order to allow the tip of the cutting tool 2 to operate at a constant cutting velocity V.

[0031] In the present invention, to form each of the inner and outer circumferential faces into any of various cutting shapes, the following embodiment may be adopted. That is, as shown in the basic configuration (2), the position of the turning center of the main shaft 1 is movable in an orthogonal direction or an oblique direction to the plane orthogonal to the turning central axis 6. When the position of the turning center of the main shaft 1 is movable in the oblique direction, a supporting position of the work 3 on the table 4 on which the work 3 is placed is also moved in association with the movement in the oblique direction to maintain a state where cutting is enabled.

[0032] When the turning center of the main shaft 1 is movable in the oblique direction as is described above, the turning central axis 6 of the main shaft 1 moves by itself. Thus, the supporting position of the work 3 on the table 4 on which the work 3 is placed is forced to move with synchronized state to the position of the turning center in order to maintain a state where the cutting tool 2 can cut the work 3.

[0033] FIGS. 3(a) and 3(b) denote that the outer circumferential face is formed into a normal tapered shape in accordance with the embodiment in which the position of the turning center of the main shaft 1 is moved in the orthogonal direction or the oblique direction, while the turning radius is sequentially changed.

[0034] When the tapered shape has circumferential curved faces at opposite ends thereof, the turning radius may be approximately constant at an initial stage and a final stage of turning as is denoted in FIGS. 3(a) and 3(b).

[0035] FIGS. 4(a) and 4(b) denote that the inner circumferential face is formed into a stepped tapered shape in accordance with the embodiment in which the position of the turning center of the main shaft 1 is moved in the orthogonal direction or the oblique direction, while the turning radius is changed in a stepwise manner.

[0036] As is apparent from FIGS. 3(a) and 3(b) and FIGS. 4(a) and 4(b), the basic configuration (2) enables the inner circumferential face or the outer circumferential face to be formed into any of various shapes.

[0037] The above-described drawings all denote that the turning center of the main shaft 1 is moved in the direction orthogonal to the plane orthogonal to the turning central axis 6, that is, in the same direction as that of the turning central axis 6. When the turning center is moved in the direction oblique to the plane, a tapered shape is obtained which generally changes in the oblique direction.

[0038] Alternatively to the embodiments denoted in FIGS. 3(a) and 3(b) and FIGS. 4(a) and 4(b), if the turning radius of the main shaft 1 is not changed, the inner circumferential face or the outer circumferential face (not denoted in the drawings) can be formed into a normal cylindrical shape (when the turning center moves in the orthogonal direction) or an oblique cylindrical shape (when the turning center moves the in the oblique direction).

[0039] FIG. 5 denotes an embodiment in which the position of the turning center of the main shaft 1 is not moved in the orthogonal direction nor the oblique direction. In the embodiment, a ring shape is formed as follows:

(1) In an inner region of the work 3 that is close to the turning center, the distance from the turning center to the tip of the cutting tool 2 is sequentially increased to move the tip along a helical locus, in the case that the distance reaches a maximum state, the maximum state is maintained to form an inner wall in a ring shape.
(2) In an outer region of the work 3 that is away from the turning center, the distance from the turning center to the tip of the cutting tool 2 is sequentially reduced to move the tip along a helical locus, in the case that the distance reaches a minimum state, the minimum state is maintained to form an outer wall in a ring shape.

[0040] In the above-described embodiment, the ring shape can be quickly obtained.

[0041] Thus, in the present invention, the work 3 is cut with a summation of the cutting velocity to allow the inner circumferential face and the outer circumferential face to be quickly formed. The need for special control for the summation is not required to achieve simple control.

Example

[0042] In an example, a plurality of main shafts 1 and cutting tools 2 projecting from the respective main shafts 1 are adopted.

[0043] In this example, the plurality of cutting tools 2 performs cutting to further increase the cutting velocity, while the properties of the individual cutting tools 2 related to the cut face are averaged to allow a more even cut face to be provided.

[0044] As is described above, the present invention enables the inner circumferential face and the outer circumferential face of the work to be cut into any of various shapes with even cut faces at a constant cutting velocity. Thus, the present invention has enormous applicability.