JP3482079B2 - Rotationally symmetric aspherical surface processing method - Google Patents

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method for processing a rotationally symmetric aspherical surface by using a grinding machine capable of obliquely intersecting the axial direction of a work spindle and the axial direction of a grindstone spindle.

[0002]

2. Description of the Related Art Conventionally, a rotationally symmetric aspherical surface has been processed by using a grinding processing apparatus shown in FIG. This grinding apparatus includes a spindle device S that rotates a workpiece W around a rotation axis l, and a soroban ball that rotates around a rotation axis that is twisted with respect to the rotation axis l of the spindle device S. And a grinding wheel G of a mold. If such a grinding machine is used, the grindstone G is applied to the workpiece W, and the grindstone G is freely moved within a specific plane including the rotation axis l. Can be ground.

[0003]

However, in such a conventional grinding process using a grinding device dedicated to aspherical surface processing, since the contact between the workpiece W and the grindstone G is close to a point contact, It was inefficient and took a long time to process.

Further, since the curve of the workpiece W in the radial direction is determined by the movement locus of the grindstone G, its processing accuracy depends on the movement accuracy of the rotating shaft of the grindstone G, and the surface roughness is improved. Was difficult.

In view of the above points, an object of the present invention is to provide a grinding machine used for ordinary spherical surface machining, that is,
To enable rotationally symmetric aspherical grinding using a grinding device capable of obliquely intersecting the axial direction of the work spindle and the axial direction of the grindstone spindle, and to bring the surface of the workpiece W and the grindstone into line contact. According to the present invention, there is provided a rotationally symmetric aspherical surface processing method capable of improving the processing efficiency and the surface roughness of the rotationally symmetric aspherical surface to be processed.

[0006]

The invention according to claim 1 is
In order to solve the above problems, a method of processing a rotationally symmetric aspherical surface by using a grinding machine capable of obliquely intersecting the axial direction of a work spindle to which a workpiece is attached and the axial direction of a grindstone spindle to which a grindstone is attached Then, the surface of the work piece is divided into a plurality of concentric circular zones, and the surface of each circular zone has a radius of curvature that minimizes the error from the corresponding portion of the rotationally symmetric aspherical surface to be machined. It is characterized by being processed as a spherical surface.

By doing so, a rotationally symmetric aspherical surface can be processed as a set of spherical surfaces divided into concentric circular zones. Therefore, when processing each ring zone, by adjusting the position where the grindstone is applied to the surface of the workpiece and the axial direction of the grindstone spindle, it is possible to perform the same processing as in the case of normal spherical surface processing. it can. Therefore, since the grindstone comes into line contact with the surface of the workpiece, the processing efficiency is improved and the surface roughness is also improved.

The invention according to claim 2 is specified by the grindstone in claim 1 having an annular point of action centered on the axis of the grindstone spindle. The invention according to claim 3 is specified by the grindstone in claim 2 being a cup grindstone.

According to a fourth aspect of the present invention, in the case of the division of the first aspect, the surface of the workpiece is concentrically formed based on preset data for specifying the boundary position of each ring zone. It is specified by dividing into a plurality of zones.

According to a fifth aspect of the present invention, when the surface of each ring zone in claim 4 is processed, the inside and outside of the ring zone are determined based on the data specifying the boundary position of each ring zone. It is specified by including each boundary position and processing it as a spherical surface having its one point on the axis of the work spindle as its center of curvature.

According to a sixth aspect of the present invention, in the case of the division according to the first aspect, a plurality of concentric circles are formed on the surface of the workpiece based on preset data specifying the width of each ring. It is specified by dividing into zones.

According to a seventh aspect of the present invention, when the surface of each ring zone according to the sixth aspect is machined, it has a preset radius of curvature and a point on the axis of the work spindle is the center of the curvature. It is specified by processing it as a spherical surface.

According to an eighth aspect of the present invention, when the surface of each ring zone according to the second aspect is processed, in a plane including the axis of the work spindle and the axis of the grindstone spindle,
It is specified by applying the working point of the grindstone to the boundary position inside the ring zone.

According to a ninth aspect of the present invention, when processing the surface of each ring zone in the eighth aspect, the distance between the intersection of the axis of the work spindle and the axis of the grindstone spindle and the point of action of the grindstone. Is specified by inclining the axial direction of the work spindle and the axial direction of the grindstone spindle with respect to each other so that is coincident with the radius of curvature of the spherical surface.

[0015]

BEST MODE FOR CARRYING OUT THE INVENTION Embodiments of the present invention will be described below with reference to the drawings.

[0016]

[First Embodiment] First, a first embodiment of the present invention will be described. <Structure of Grinding Machine> First, the structure of the grinding machine used in the rotationally symmetric aspherical surface machining method according to the first embodiment of the present invention will be described with reference to FIG.

In FIG. 1, the grinding apparatus comprises a work part A and a grindstone part B. This work part A
Is an X table 2 that slides in the X direction (left and right direction in the drawing) on a bed (not shown) and its rotation axis (work axis) l.
It is composed of a work spindle device 11 fixed on the X table 2 with ₁ directed in the X direction, and a work holder 3 attached to the tip of the work spindle device 11 so as to rotate around a work axis l _1. ing. Then, a workpiece (a cemented carbide blank, a glass blank, etc.) W is mounted on the work holder 3.

On the other hand, the grindstone portion B is Y on a bed (not shown).
Y table 5 that slides in the direction (vertical direction in the figure)
On the Y table 5 in the Z direction (X direction and Y
Rotating around the θ axis (direction orthogonal to the direction)
The table 6, a grindstone spindle device 12 fixed on the θ table 6 with its rotation axis (grinding wheel axis) l ₂ orthogonal to the θ axis, and the tip of the grindstone spindle apparatus 12 centered on the grindstone axis l _2. And a tapered grindstone holder 7 attached to the. And this grindstone holder 7
A bottomed cylindrical cup grindstone C is fixed to the tip of the. The grindstone holder 7 and the cup grindstone C have a grindstone axis l.
_It is coaxial with ₂ . The inner edge of the tip of the cup grindstone C functions as a point of action when grinding the convex surface,
The outer edge of the tip functions as a point of action when grinding the concave surface. Below, the inner diameter of this cup grindstone C (the inner diameter of the grindstone)
_Is denoted as r _i, and the outer diameter (grinding stone outer diameter) is denoted as r _o . Further, an angle formed by the work axis l ₁ and the grindstone axis l ₂ is represented by θ _n, and an angle formed by the line connecting the intersection point of the work axis l ₁ and the grindstone axis l ₂ and the working point with respect to the work axis l ₁ is represented. θ _sn (However, 0 degree <θ _sn <90
Degree). Further, a surface including both the work axis l ₁ and the grindstone axis l ₂ is hereinafter referred to as “XY plane”.

The above X table 2, Y table 5, and θ table 6 are NC via a cable 10, respectively.
(Numerical control) Connected to the controller 8. This NC controller 8 is the N stored in the memory.
The tables 2, 5 and 6 are individually controlled based on the C data. <Principle of Rotationally Symmetrical Aspherical Surface Machining Method> Next, the principle of machining a rotationally symmetric aspherical surface by using the above-described grinding apparatus will be described.

Due to its structure, the above-described grinding machine can machine only a spherical surface (or a part thereof) having the center of curvature on the work axis l ₁ . On the other hand, the rotationally symmetric aspherical surface can be considered as a set of a large number of annular zones that are concentric with the optical axis, as shown in FIG.
Then, if the radial width of the annular zone is narrowed to a certain extent or less, the surface of each annular zone can be approximated to a spherical surface having its center of curvature on the work axis l ₁ . Therefore, the surface of the workpiece W is divided into a plurality of fine ring zones centering on the work axis l ₁ , and the position of the action point of the cup grindstone C in the XY plane and the grindstone axis l ₂ are determined. By appropriately setting the angle formed with respect to the work axis l ₁ for each ring zone, the surface of each ring zone can be machined as a spherical surface having its own radius of curvature. A surface shape that can be treated as a spherical surface can be obtained.
The respective ring zones whose surfaces are processed as spherical surfaces in this way are hereinafter referred to as "spherical ring zones S _n ".

FIG. 3 is a vertical sectional view conceptually showing a state in which the workpiece W is cut by a radial surface including the work axis 11, and a desired rotationally symmetric aspheric surface is shown by a broken line and a spherical ring. A rotationally symmetric aspherical surface processed as a set of bands S _n is shown by a solid line. Δd in FIG. 3 indicates an error in the X direction with respect to the desired rotationally symmetric aspherical surface in each spherical zone S _n . The width of each spherical annular zone S _n is appropriately adjusted within a range in which the error Δd does not exceed the design specification (range satisfying the design performance). For example, the desired change in curvature is large portion of the rotationally symmetric aspherical surface, the width of the spherical annular S _n is set narrow, the portion of curvature change is small, the width of the spherical annular S _n is set widely.

In FIG. 3, P _n is the inner edge of each spherical orbicular zone S _n in the XY plane, that is, the point where the point of action of the cup grindstone C is applied (hereinafter referred to as the "orbital zone boundary").
And R _n represents the radius of curvature of the surface of each spherical annular zone S _n . <Process of rotationally symmetric aspherical surface processing> In order to process the rotationally symmetric aspherical surface, in the present embodiment, the radius of curvature R _n of each spherical ring zone S _n , the width in the radial direction, and each spherical ring body S. _n
The amount of axial deviation of the boundary of is calculated as a set value by an NC data calculation computer (not shown), and the calculated NC data is stored in the memory in the NC controller.

Then, first, a circular portion (so-called paraxial portion) S _{0 at} the center of the surface of the workpiece W is ground. In this case, based on the set radius of curvature R ₀ , the angle θ ₀ (θ ₀ = s) between the work axis l ₁ and the grindstone axis l ₂ is set.
in ⁻¹ (r _{i or o} / R ₀ )) is calculated, and the work axis l ₁
On the other hand, the θ table 6 is rotationally driven so that the grindstone axis l ₂ intersects at this angle θ ₀ . Along with that, the workpiece W
Cup grindstone C at the surface center (intersection with the work axis l ₁ ) P ₀ of
The X-table 2 and the Y-table 5 are slid so that the action points of (1) and (2) hit. Both spindles 1 in this state
When 1 and 12 rotate, the circular portion S ₀ and its vicinity are processed into a spherical surface having a radius of curvature R ₀ .

Next, the spherical annular zone S ₁ immediately outside the circular portion S ₀ is ground. In this case, based on the set radius of curvature R ₁ , the work axis l ₁ and the grindstone axis l ₂
Angle θ ₁ (θ ₁ = sin ⁻¹ (r _{i or o} / R ₁ ) +
θ _s1 ) is calculated, and the θ table 6 is rotationally driven so that the grindstone axis l ₂ intersects the work axis l _{1 at} this angle θ ₁ . At the same time, the X table 2 and the Y table 5 are slid so that the working point of the cup grindstone C hits the ring zone boundary P ₁ which is displaced from P _{0 in the} radial direction by the set width. When both spindles 11 and 12 rotate in this state,
The surface of the spherical ring S ₁ has a radius of curvature R ₁ (R ₁ = r _{i or o} /
It is processed into a spherical surface of sin (θ ₁ −θ _s1 ).

Thereafter, such grinding is repeated until the outermost spherical ring zone is reached. At this time, when grinding the spherical ring Sn of the nth surface from the center side, the work axis l ₁ and the grindstone axis l ₂ are based on the set radius of curvature R _n.
Angle θ _n (θ _n = sin ⁻¹ (r _{i or o} / R _n ) +)
θ _sn ) is calculated, and the θ table 6 is rotationally driven so that the grindstone axis l ₂ intersects the work axis l _{1 at} this angle θ _n . At the same time, the (n-1) th spherical ring S
_The X table 2 and the Y table 5 are slidably driven so that the working point of the cup grindstone C hits the ring zone boundary P _n which is deviated from the position P _n-1 during the _n-1 grinding process by the set width. When both spindles 11 and 12 rotate in this state,
The surface of the spherical ring S _n of the _nth surface has a radius of curvature R _n (R _n = r
It is processed into a spherical surface of _{i or o} / sin (θ _n −θ _sn ).

By repeating such a grinding process, finally, a rotationally symmetric aspherical surface as a set of spherical annular zones as shown by a solid line in FIG. 3 is created. According to the rotationally symmetric aspherical surface processing method of this embodiment, the workpiece W
Since each spherical ring zone (circular portion) S _n is ground by the cup grindstone C on a line-by-line basis, the machining efficiency is significantly improved as compared with the conventional method of point-by-point machining. The surface roughness is also improved.

[0027]

Second Embodiment Next, a second embodiment of the present invention will be described.
It The second embodiment is different from the first embodiment described above.
And each spherical ring S_nInstead of the width data of each ring zone boundary P_n
The coordinate position data of is set to the NC controller 8
It is characterized by being input. In the second embodiment
The principle of grinding machine and aspherical surface processing method used as
Since it is exactly the same as that of the first embodiment, its explanation is omitted.
To do. <Process of rotationally symmetric aspherical surface machining> Below, concave rotationally symmetric aspherical surface
Example (Example 1) in the case of processing a surface and convex rotational symmetry
Divided into an example (Example 2) for processing an aspherical surface
Then, the steps of the rotationally symmetric aspherical surface processing according to the second embodiment will be described.
explain. In addition, in FIGS. 4 to 9 referred to below.
The coordinates shown represent the XY plane, the x-axis of which is the work axis.
l₁Is consistent with the direction of. The y-axis is the bottom of each figure.
The direction is the + direction. Also, the work axis l ₁And grindstone axis l₂
Angle θ formed by_n, That is, the work axis l₁The direction parallel to
Grindstone axis l₂Rotation angle of_nIs counterclockwise + direction
I am trying. The position of the θ axis, that is, the grindstone axis l₂The times
The center of rotation is θ_axisnIs shown.

Further, in FIGS. 4 to 9, the cup grindstone C is drawn to be quite small for the sake of clarity, but during actual processing, the cup grindstone C is shown.
Is in a state in which a part of its line of action always protrudes from the workpiece W, that is, the outermost periphery of the workpiece is always machined.

[0029]

[First Embodiment] First, a case of forming a concave rotationally symmetric aspherical surface will be described. [Grinding of circular portion S ₀ ] FIG. 4 shows a state in which the circular portion S ₀ forming the center of the aspherical surface is processed. At this time, the coordinate point at the center of the circular portion S ₀ as the machining target is the origin P.
Defined as ₀ (0,0). In addition to the grinding wheel outer diameter r _o of the cup grindstone C is a constant value, the radius of curvature R ₀ of the sphere concave in the circular portion S _0, not shown as a set value N
It is calculated by the C data calculation computer. The radius of curvature R ₀ has almost the same value as the paraxial R coefficient of the designed aspherical surface to be processed. Since the paraxial R coefficient is often given, it may be a known value in this way.

Now, if the tip outer edge (point of action) of the cup grindstone C is made to coincide with this origin P ₀ (0,0), the center of curvature of the spherical concave surface that is ground by the tip outer edge of the cup grindstone C becomes It coincides with the intersection of the axis l ₁ and the grindstone axis l ₂ . Therefore, in order to set the radius of curvature of the spherical concave surface to R ₀ , the intersection of the work axis l ₁ and the grindstone axis l ₂ must be located at the coordinate point O ₀ (R ₀ , 0). The relationship between R ₀ and r _o at this time and the rotation angle θ ₀ of the grindstone shaft l ₂ is represented by the following formula (1).

[0031]

[Equation 1]

Then, if this equation (1) is modified, the rotation angle θ ₀ is expressed by the following equation (2).

[0033]

[Equation 2]

[0034] Therefore, calculated grinding outer diameter r _o of the cup grinding wheel C, and by substituting the radius of curvature R ₀ set in the circular portion S ₀ in Equation (2), the rotation angle theta ₀ of wheel spindle l ₂ can do. The NC controller 8 gives a rotation instruction to the θ table 6 so as to rotate the grindstone shaft l ₂ according to the NC data set to the rotation angle θ ₀ thus calculated. Next, the NC controller 8 gives a slide instruction to the X table 2 and the Y table 5, respectively, and sets the outer edge of the tip of the cup grindstone C after the rotation of the grindstone shaft l ₂ to the coordinate point P ₀ (0, 0). Match. Θ at this point
Hereinafter, the position of the axis will be referred to as θ _axis0 .

The work spindle 11 is controlled by the above control.
And since the grindstone spindle 12 is rotated, after the operation is completed
Is the coordinate point P₀Radius of curvature R centered at (0,0)₀Sphere
A concave surface is formed. [Spherical ring S₁Grinding process] FIG. 5 shows a circular portion S₀Immediately
Spherical ring S located outside₁Shows the state when processing
You At this time, the central portion S₀Outer edge (spherical ring S₁Of
Ring boundary P indicating the edge ₁Coordinates of (x₁, Y₁) And a sphere
Face ring S₁Zone boundary P showing the outer edge of₂Coordinates of (x₂, Y₂)
Only given as setpoint.

First, the coordinate values are set so that the outer edge of the tip of the cup grindstone C coincides with P ₁ . Now, assuming that the curvature center coordinate of the spherical concave surface to be formed is O ₁ (a, 0), the relationship between a point P (x, y) on the spherical concave surface and the radius of curvature R of the spherical concave surface is expressed by the following equation (3). Represented by

[0037]

[Equation 3]

Therefore, in the equation (3), the ring zone boundary P ₁
Coordinates (x ₁ , y ₁ ) and coordinates of the ring boundary P ₂ (x ₂ ,
Substituting each of y ₂ ) yields the following simultaneous equations (4).

[0039]

[Equation 4]

By solving this simultaneous equation for a, the following equation (5) is obtained.

[0041]

[Equation 5]

On the other hand, from the above equation (3), the following equation (6)
Is obtained.

[0043]

[Equation 6]

By substituting the equation (5) into the equation (6), the following equation (7) is obtained.

[0045]

[Equation 7]

[0046] As is apparent from the equation (7), in the premise under that the center of curvature of the sphere concave is present on the x-axis (the workpiece axis l _1), the curvature radius R _n of the spherical annular S _n is It is uniquely determined only by the coordinate positions of two points on the spherical concave surface.

By the way, in FIG. 5, the spherical ring S ₁
The radius of curvature R _{1 of the above} and the whetstone outer diameter r _o of the cup whetstone C have a relationship represented by the following equation (8).

[0048]

[Equation 8]

Here, θ _s represents an angle formed by a line connecting the center of curvature O ₁ (a, 0) of the spherical ring S _{1 and} the outer edge of the tip of the cup grindstone C with respect to the work axis l ₁ . Further, the y-coordinate and radius of curvature R ₁ and zonal boundary P ₁ of the spherical annular S _1, a relationship represented by the following formula (9).

[0050]

[Equation 9]

When θ _S is deleted by using these two equations (8) and (9) as simultaneous equations, the following equation (10) showing the rotation angle θ ₁ of the grindstone shaft l ₂ when forming the ring-shaped curved surface S ₁ is obtained. Is obtained

R

[Equation 10]

By substituting the above equation (7) into this equation (10), the following equation (11) is obtained.

[0054]

[Equation 11]

As is clear from the equation (11), under the assumption that the center of curvature of the spherical concave surface exists on the x axis (workpiece axis l ₁ ), the rotation angle θ _n of the grindstone axis l ₂ also becomes spherical. It is uniquely determined only by the coordinate positions of two points on the concave surface.

However, from the state shown in FIG.
Grindstone axis l₂The tip of the cup grindstone C is simply rotated.
The outer edge is the ring boundary P₁Does not match with the grindstone axis l₂Is the coordinate
Point O ₁Work axis l at (a, 0)₁Don't intersect
Then, both ring zone boundary P₁, P₂By forming a curved surface containing
I can't come. Therefore, the outer edge of the tip of the cup grindstone C is set as the ring boundary.
P₁Match with and grindstone axis l₂Coordinate point O₁At (a, 0)
Work axis l₁The position of the θ-axis to θ
_axis0To θ in FIG._axis1Need to move to
is there. X table 2 and Y table 5 for this movement
The calculation of the correction movement amount that should be instructed to
It

Now, as shown in FIG. 6, the grindstone shaft l ₂ is
It is assumed that the rotation angle θ _{0 is} further rotated by an angle dθ. In this case, the cup grindstone C moves from the position of α to the position of β, and the coordinate position of its tip edge is from P (x, y) to P ′.
It changes to (x + Δx, y + Δy). At this time, in order to change only the rotation angle of the grindstone axis l ₂ without moving the coordinate position of the outer edge of the tip of the cup grindstone C, the position θ of the θ axis is set.
_It is sufficient to move the _axis by -Δx in the x direction and -Δy in the y direction.

By the way, in FIG. 6, the position θ of the θ axis
_If the distance from the _axis to the center of the tip of the cup grindstone C is R ′, the diagonal distance R ″ between the coordinate position θ _axis of the θ _axis and the coordinate points P and P ′ of the outer edge of the tip of the cup grindstone C is (1
Given by 2).

[0059]

[Equation 12]

Therefore, if the angle formed by the line connecting θ _axis and the outer edge of the tip of the cup grindstone C with respect to the grindstone axis l ₂ is θ _r ,
The distance α _x in the X direction between the coordinate position θ _axis of the θ _axis and the coordinate position P of the tip outer edge of the cup grindstone C at the position α.
Is represented by the following formula (13).

[0061]

[Equation 13]

Similarly, the distance β _x in the X direction between the coordinate position θ _axis of the θ _axis and the coordinate position P ′ of the tip outer edge of the cup grindstone C at the position β is represented by the following formula (14). It

[0063]

[Equation 14]

Therefore, the distance Δx in the x direction between the coordinate position P and the coordinate position P ′ is calculated by the following equation (15).

[0065]

[Equation 15]

Here, θ _r is represented by the following equation (16).

[0067]

[Equation 16]

The rotation angle θ ₁ in FIG.
This corresponds to (θ ₀ + dθ) in 5). Therefore, the movement amount of the position θ _axis of the θ _{axis in} the x direction, that is, the correction movement amount −Δx to be instructed to the x table 2 is calculated by the following formula (17).

[0069]

[Equation 17]

On the other hand, the distance α _y in the Y direction between the coordinate position θ _axis of the θ _axis and the coordinate position P of the tip outer edge of the cup grindstone C at the position of α is represented by the following equation (18).

[0071]

[Equation 18]

Similarly, the distance β _y in the Y direction between the coordinate position θ _axis of the θ _axis and the coordinate position P ′ of the tip outer edge of the cup grindstone C at the position β is represented by the following equation (19). It

[0073]

[Formula 19]

Therefore, the distance Δx in the y direction between the coordinate position P and the coordinate position P ′ is calculated by the following equation (20).

[0075]

[Equation 20]

Therefore, the movement amount of the position θ _axis of the θ _{axis in} the y direction, that is, the correction movement amount −Δy to be instructed to the y table 5 is calculated by the following equation (21).

[0077]

[Equation 21]

From the above, the wheel outer diameter r _o of the cup grindstone C, the coordinate data (x ₁ , y ₁ ) of the ring zone boundary P ₁ , and the coordinate data (x ₂ , y ₂ ) of the ring zone boundary P ₂ can be calculated. By substituting into (11), the rotation angle θ ₁ of the grindstone shaft l ₂ can be calculated. The NC controller 8 gives a rotation instruction to the θ table 6 so as to rotate the grindstone shaft l ₂ according to the rotation angle θ ₁ thus calculated.

Further, the grindstone outer diameter r _{o of} the cup grindstone C, the distance R ′ from the θ _axis position θ _axis to the tip center of the cup grindstone C, and the rotation angle θ of the grindstone axis l ₂ calculated by the above equation (2). ₀ and the rotation angle θ ₁ calculated by the above equation (11)
By substituting into the above equations (17) and (21) respectively, the corrected movement amount −Δx in the x direction and the corrected movement amount −Δy in the y direction of the θ axis can be calculated.
The corrected movement amounts −Δx, −Δy thus calculated.
Is a moving amount for keeping the position of the outer edge of the tip of the cup grindstone C irrespective of the rotation of the grindstone axis l _2, the NC data calculation computer (not shown) calculates the position of the outer edge of the tip of the cup grindstone C as a circle. Zone boundary P ₁ (x ₁ , y ₁ ) to zone boundary P ₂
Amount of movement in the x direction (x ₂ − for moving to (x ₂ , y ₂ ).
x ₁ ) and the amount of movement in the y direction (y ₂ −y ₁ ) are also calculated. The NC data calculation computer (not shown) adds up the respective movement amounts calculated in this way, and calculates the x-direction movement amount (−Δx + x ₂
−x ₁ ) and the amount of movement in the y direction (−Δy + y ₂ −y ₁ ) are calculated and stored in the memory. The NC controller 8 reads the amount of movement in the x direction and the amount of movement in the y direction from the memory respectively, gives a slide instruction to the x table 2 so as to slide by the amount of movement in the x direction (−Δx + x ₂ −x ₁ ), and y A slide instruction is given to the y table 5 so as to slide by the amount of directional movement (−Δy + y ₂ −y ₁ ).

By performing the above control, the work spindle 11
And so rotate the grindstone spindle 12, after the operation is completed, outside, the annular boundary _{P 1 (x 1, y 1} ) and zones boundary of the outer annular boundary _{P 1 (x 1, y 1} ) P ₂ (x ₂ , y ₂ )
And is formed as a spherical concave surface having the center of curvature on the work axis l ₂ . When processing any spherical annular S _n positioned outside the n-th circular portion S ₀ [grinding of the spherical annular S _n] is annular boundary indicating the inner edge of the spherical annular S _n P _n Coordinates (x _n ,
y _n ), and an annular zone boundary P indicating the outer edge of the spherical annular zone S _{n.
n + 1} of coordinate (x n _{+ 1,} y n _{+ 1)} only, NC as a set value
It is given to the controller 8.

Equations (7), (10), (11) and (1
When 7) and (21) are generalized by n, the following equations (7 ′), (10 ′), (11 ′), (17 ′), and
It becomes as (21 ').

[0082]

[Equation 22]

[0083]

[Equation 23]

[0084]

[Equation 24]

[0085]

[Equation 25]

[0086]

[Equation 26]

[0087] Thus, grindstone outer diameter r _o of the cup grindstone C, the coordinate data (x _n, y _n) of the annular boundary P _n, and zonal boundary P _{n + 1} of coordinate data (x _{n +} 1, y _{n + 1} ) into the formula (1
By substituting it into 1 ′), the rotation angle θ _n of the grindstone shaft l ₂ can be calculated. The NC controller 8 gives a rotation instruction to the θ table 6 so as to rotate the grindstone shaft l ₂ according to the rotation angle θ _n thus calculated.

Further, the grindstone outer diameter r _{o of} the cup grindstone C, the distance R ′ from the position θ _{axis of the} θ _axis to the tip center of the cup grindstone C, and the rotation angle θ calculated this time by the above equation (11 ′).
_n, and, n-1 th above formula when grinding the spherical annular S _n-1 (11 ') above formula was the rotation angle theta _n-1 of the wheel spindle l ₂ calculated by (17') and By substituting each into equation (21 ′), the corrected movement amount in the x direction of the θ axis −
The corrected movement amount −Δy in the Δx and y directions can be calculated. The NC data calculation computer (not shown) determines the position of the tip outer edge of the cup grindstone C as the ring boundary Pn.
The amount of movement in the x direction (x _{n + 1} −x _n ) and the amount of movement in the y direction (x _{n + 1} −x _n ) to move from (x _n , y _n ) to the ring boundary P _{n + 1} (x _{n + 1} , y _{n + 1} ). y _{n + 1} −y _n ) is also calculated. The NC data calculation computer (not shown) adds the respective movement amounts calculated in this way to obtain the x-direction movement amount (−Δx + x _{n + 1} −x _n ) and y.
The directional movement amount (−Δy + y _{n + 1} −y _n ) is calculated and stored in the memory. The NC controller 8 reads the x-direction movement amount and the y-direction movement amount from the memory, respectively, and gives a slide instruction to the x-table 2 so as to slide by the x-direction movement amount (−Δx + x _{n + 1} −x _n ). , Slide in the y direction by the amount of movement (−Δy + y _{n + 1} −y _n ), y
A slide instruction is given to the table 5.

By performing the above control, the work spindle 11
And so rotate the grindstone spindle 12, after the operation is completed, outside, the annular boundary _{P n (x n, y n} ) and zones boundary of the outer annular boundary _{P n (x n, y n} ) P _{n + 1} (x _{n + 1} ,
y _{n + 1} ), and is formed as a spherical concave surface having its center of curvature on the work axis l ₂ .

In the above description of [grinding of the circular portion S ₀ ], the radius of curvature R ₀ of the spherical concave surface is set in advance, but if the above equation (11 ') is used, , Even if the radius of curvature R ₀ is unknown, the origin P
If only the coordinate position of the ring zone boundary P _{1 with} respect to ₀ (0, 0) is set, the rotation angle θ ₀ of the grindstone axis l ₂ at that time can be calculated.

As described above, the outermost ring zone boundary P _n
By grinding up to, the aspherical surface is formed as a compound spherical concave surface in which all the preset annular zone boundaries P are connected by spherical concave surfaces (spherical concave surfaces each having a center of curvature on the work axis l ₁ ).

However, not all aspherical surfaces can be processed as described above, and in the case of a concave surface, the radius of curvature, that is, the above R _n, must increase from the center to the outside. Processing is impossible.

[0093]

[Embodiment 2] Next, a description will be given of a case of forming a convex rotationally symmetric aspherical surface. [Grinding of circular portion S ₀ ] FIG. 7 shows a state in which the circular portion S ₀ forming the center of the aspherical surface is processed. At this time, the coordinate point at the center of the circular portion S ₀ as the machining target is the origin P.
Defined as ₀ (0,0). Further, in addition to the grindstone inner diameter r _i of the cup grindstone C which is a constant value, the radius of curvature R ₀ of the spherical convex surface in the circular portion S ₀ is not shown as a set value N.
It is calculated by the C data calculation computer. The radius of curvature R ₀ has almost the same value as the paraxial R coefficient of the designed aspherical surface to be processed. Since the paraxial R coefficient is often given, it may be a known value in this way.

Now, if the tip inner edge (point of action) of the cup grindstone C is made to coincide with this origin P ₀ (0,0), the center of curvature of the spherical convex surface that is ground by the tip inner edge of the cup grindstone C becomes It coincides with the intersection of the axis l ₁ and the grindstone axis l ₂ . Therefore, in order to set the radius of curvature of the spherical convex surface to R ₀ , the intersection of the work axis l ₁ and the grindstone axis l ₂ must be located at the coordinate point O ₀ (−R ₀ , 0). The relationship between R ₀ and r _i at this time and the rotation angle θ ₀ of the grindstone shaft l ₂ is represented by the following formula (22).

[0095]

[Equation 27]

Then, if this expression (22) is modified, the rotation angle θ ₀ is expressed by the following expression (23).

[0097]

[Equation 28]

[0098] Thus, grindstone internal diameter r _i of the cup grinding wheel C, and a radius of curvature R ₀ set in the circular portion S ₀ By substituting the equation (23), to calculate the rotation angle theta ₀ of wheel spindle l ₂ be able to. The NC controller 8 gives a rotation instruction to the θ table 6 so as to rotate the grindstone shaft l ₂ according to the NC data set to the rotation angle θ ₀ thus calculated. Next, the NC controller 8 uses the X table 2
And slide instructions to the Y table 5, respectively,
The inner edge of the tip of the cup grindstone C after the rotation of the grindstone axis l ₂ is aligned with the coordinate point P ₀ (0, 0). The position of the θ axis at this point is hereinafter referred to as θ _axis0 .

The work spindle 11 is controlled by the above control.
And since the grindstone spindle 12 is rotated, after the operation is completed
Is the coordinate point P₀Radius of curvature R centered at (0,0)₀Sphere convex
A surface is formed. [Spherical ring S₁Grinding process] FIG. 8 shows a circular portion S₀Immediately
Spherical ring S located outside₁Shows the state when processing
You At this time, the central portion S₀Outer edge (spherical ring S₁Of
Ring boundary P indicating the edge ₁Coordinates of (x₁, Y₁) And a sphere
Face ring S₁Zone boundary P showing the outer edge of₂Coordinates of (x₂, Y₂)
Only given as setpoint.

Similarly to the case of the above-mentioned concave rotationally symmetric aspherical surface, the radius of curvature R ₁ of the spherical orbicular zone S ₁ is calculated by the above equation (7) by the coordinates (x ₁ , y ₁ ) of the orbicular zone boundary P _1. And ring boundary P ₂
(7) is uniquely determined by the coordinates (x ₂ , y ₂ ) of (1) (the derivation of formula (7) is exactly the same as in the case of the above-described first embodiment, and therefore the description thereof is omitted).

By the way, in FIG. 8, the spherical ring S ₁
The radius of curvature R ₁ and the inner diameter r _i of the grindstone of the cup grindstone C have a relationship represented by the following equation (24).

[0102]

[Equation 29]

Here, θ _s represents the angle formed by the line connecting the center of curvature O ₁ (-b, 0) of the spherical ring S _{1 and} the inner edge of the tip of the cup grindstone C with the work axis l ₁ . . Further, the y-coordinate and radius of curvature R ₁ and zonal boundary P ₁ of the spherical annular S _1, a relationship represented by the following formula (25).

[0104]

[Equation 30]

When θ _S is eliminated by using these two equations (24) and (25) as simultaneous equations, the following equation (26) showing the rotation angle θ ₁ of the grindstone shaft l ₂ when forming the ring-shaped curved surface S ₁ is obtained.
Is obtained.

[0106]

[Equation 31]

By substituting the above equation (7) into this equation (26), the following equation (27) is obtained.

[0108]

[Equation 32]

As is clear from this equation (27), on the assumption that the center of curvature of the spherical convex surface exists on the x-axis (workpiece axis l ₁ ), the rotation angle θ _n of the grindstone axis l ₂ also becomes It is uniquely determined only by the coordinate positions of two points on the convex surface.

[0110] Next, the calculation of the correction movement amount to be instructed to the X table 2 and Y table 5 in order to correct the movement position of the theta axis from theta _axis0 to theta _axis1 in FIG. 8 will be described below .

Now, as shown in FIG. 9, the grindstone shaft l ₂ is
It is assumed that the rotation angle θ _{0 is} further rotated by an angle dθ. In this case, the coordinate position of the inner edge of the tip of the cup grindstone C is P
It changes from (x, y) to P '(x + Δx, y + Δy). At this time, in order to change only the rotation angle of the grindstone axis l ₂ without moving the coordinate position of the inner edge of the tip of the cup grindstone C, the position θ _axis of the θ _axis is −x in the x direction, −Δx, in the y direction.
It may be moved by Δy.

By the way, in FIG. 9, the position θ of the θ axis
_If the distance from the _axis to the center of the tip of the cup grindstone C is R ′, the diagonal distance R ″ between the coordinate position θ _axis of the θ _axis and the coordinate points P, P ′ of the inner edge of the tip of the cup grindstone C is (2
Given by 8).

[0113]

[Expression 33]

Therefore, if the angle formed by the line connecting the θ _axis and the inner edge of the tip of the cup grindstone C with respect to the grindstone axis l ₂ is θ _r ,
The distance α _x in the X direction between the coordinate position θ _axis and the coordinate position P is represented by the following equation (29).

[0115]

[Equation 34]

Similarly, the distance β _x in the X direction between the coordinate position θ _axis and the coordinate position P ′ is represented by the following equation (30).

[0117]

[Equation 35]

Therefore, the distance Δx in the x direction between the coordinate position P and the coordinate position P ′ is calculated by the following equation (31).

[0119]

[Equation 36]

Here, θ _r is represented by the following equation (32).

[0121]

[Equation 37]

Further, the rotation angle θ ₁ in FIG.
This corresponds to (θ ₀ + dθ) in 1). Therefore, the movement amount of the position θ _axis of the θ _{axis in} the x direction, that is, the corrected movement amount −Δx to be instructed to the x table 2 is calculated by the following formula (33).

[0123]

[Equation 38]

On the other hand, the distance α _y in the Y direction between the coordinate position θ _axis and the coordinate position P is expressed by the following equation (34).

[0125]

[Formula 39]

Similarly, the distance β _y in the Y direction between the coordinate position θ _axis and the coordinate position P ′ is represented by the following equation (35).

[0127]

[Formula 40]

Therefore, y between the coordinate point P and the coordinate point P '
The distance Δy in the direction is calculated by the following equation (36).

[0129]

[Formula 41]

Therefore, the movement amount of the position θ _axis of the θ _{axis in} the y direction, that is, the correction movement amount −Δy to be instructed to the y table 5 is calculated by the following equation (37).

[0131]

[Equation 42]

The [0132] above, grinding the inner diameter r _i of the cup grindstone C, the coordinate data (x _1, y ₁₎ of the annular boundary P _1, and annular coordinate data (x _2, y ₂₎ of the boundary P ₂ of formula ( 27), the rotation angle θ ₁ of the grindstone shaft l ₂ can be calculated. The NC controller 8 gives a rotation instruction to the θ table 6 so as to rotate the grindstone shaft l ₂ according to the rotation angle θ ₁ thus calculated.

Further, the grindstone inner diameter r _{i of} the cup grindstone C, the distance R ′ from the θ _axis position θ _axis to the tip center of the cup grindstone C, and the rotation angle θ ₀ of the grindstone axis l ₂ calculated by the above equation (23). , And the rotation angle θ ₁ calculated by the above equation (27) are respectively substituted into the above equations (33) and (37), the corrected movement amount in the x direction of the θ axis−Δx and the corrected movement amount in the y direction. -Δy can be calculated. The corrected movement amount −Δx, − calculated in this way
Since Δy is a movement amount for keeping the position of the tip outer edge of the cup grindstone C constant regardless of the rotation of the grindstone axis l _2, the NC data calculation computer (not shown) determines the position of the tip outer edge of the cup grindstone C. The amount of movement in the x direction (x ₂ −x ₁ ) and the amount of movement in the y direction (y ₂ −) for moving from the ring zone boundary P ₁ (x ₁ , y ₁ ) to the ring zone boundary P ₂ (x ₂ , y ₂ ). y ₁ ) is also calculated. The NC data calculation computer (not shown) adds up the respective movement amounts calculated in this way, and calculates the x-direction movement amount (−Δ
x + x ₂ −x ₁ ) and the amount of movement in the y direction (−Δy + y ₂ −y ₁ ).
Are calculated and stored in the memory respectively. NC controller 8
, Respectively reads the x-direction movement amount and the y-direction movement amount from the memory, the x-direction movement amount (-Δx + x ₂ -x ₁₎ only as to slide, together with providing a slide instruction to x Table 2, y-direction movement amount A slide instruction is given to the y table 5 so as to slide by (−Δy + y ₂ −y ₁ ).

After performing the above control, the work spindle
11 and the grindstone spindle 12 are rotated,
After completion, ring boundary P₁(X₁, Y₁) Is the outer ring
Boundary P₁(X₁, Y₁) And the outer ring zone boundary P₂(X₂，
y₂) And and the work axis l ₂Has its center of curvature on
It is formed as a spherical convex surface. [Spherical ring S_nGrinding process] Circular part S₀Outside the nth
Arbitrary spherical ring S located_nWhen processing the sphere
Face ring S_nZone boundary P indicating the inner edge of_nCoordinates of (x_n，
y_n), And the spherical zone S_nZone boundary P showing the outer edge of
_{n + 1}Coordinates of (x_{n + 1}, Y_{n + 1}) Only has NC as set value
It is given to the controller 8.

Equations (26), (27), (33),
When (37) is generalized by n, the following equations (26 '), (27'), (33 '), and (37') are obtained (the above equation (7) is changed by n). When generalized, the above formula (7) 'is obtained).

[0136]

[Equation 43]

[0137]

[Equation 44]

[0138]

[Equation 45]

[0139]

[Equation 46]

As described above, the grindstone inner diameter r _i of the cup grindstone C, the coordinate data (x _n , y _n ) of the ring boundary P _n , and the coordinate data (x _{n + 1} , y _n ) of the ring boundary P _{n + 1. +1} ) into the formula (2
The rotation angle θ _n of the grindstone shaft l ₂ can be calculated by substituting it into 7 ′). The NC controller 8 gives a rotation instruction to the θ table 6 so as to rotate the grindstone shaft l ₂ according to the rotation angle θ _n thus calculated.

Further, the grindstone inner diameter r _{i of} the cup grindstone C, the distance R ′ from the position θ _{axis of the} θ _axis to the center of the tip of the cup grindstone C, the rotation angle θ calculated this time by the above equation (27 ′).
_n, and, n-1 th above formula when grinding the spherical annular S _n-1 (27 ') calculated wheel spindle l ₂ of the rotation angle theta _n-1 the above equation by (33') and By substituting each into the equation (37 ′), the corrected movement amount in the x direction of the θ axis −
The corrected movement amount −Δy in the Δx and y directions can be calculated. The NC data calculation computer (not shown) determines the position of the tip outer edge of the cup grindstone C as the ring boundary Pn.
The amount of movement in the x direction (x _{n + 1} −x _n ) and the amount of movement in the y direction (x _{n + 1} −x _n ) to move from (x _n , y _n ) to the ring boundary P _{n + 1} (x _{n + 1} , y _{n + 1} ). y _{n + 1} −y _n ) is also calculated. The NC data calculation computer (not shown) adds the respective movement amounts calculated in this way to obtain the x-direction movement amount (−Δx + x _{n + 1} −x _n ) and y.
The directional movement amount (−Δy + y _{n + 1} −y _n ) is calculated and stored in the memory. The NC controller 8 reads the x-direction movement amount and the y-direction movement amount from the memory, respectively, and gives a slide instruction to the x-table 2 so as to slide by the x-direction movement amount (−Δx + x _{n + 1} −x _n ). , Slide in the y direction by the amount of movement (−Δy + y _{n + 1} −y _n ), y
A slide instruction is given to the table 5.

By performing the above control, the work spindle 11
And so rotate the grindstone spindle 12, after the operation is completed, outside, the annular boundary _{P n (x n, y n} ) and zones boundary of the outer annular boundary _{P n (x n, y n} ) P _{n + 1} (x _{n + 1} ,
y _{n + 1} ), and is formed as a spherical convex surface having its center of curvature on the work axis l ₂ .

In the description of [grinding of circular portion S ₀ ] above, the radius of curvature R ₀ of the spherical concave surface is set in advance, but if the above equation (27 ′) is used, , Even if the radius of curvature R ₀ is unknown, the origin P
If only the coordinate position of the ring zone boundary P _{1 with} respect to ₀ (0, 0) is set, the rotation angle θ ₀ of the grindstone axis l ₂ at that time can be calculated.

As described above, the outermost ring zone boundary P _n
By grinding up to, the aspherical surface is formed as a compound spherical convex surface in which all preset annular zone boundaries P are connected by spherical convex surfaces (spherical convex surfaces each having a curvature center on the work axis l ₁ ).

However, not all aspherical surfaces can be processed as described above, and in the case of a convex surface, the radius of curvature, that is, the above R _n, must be reduced from the center toward the outside, and the opposite is true in this method. Processing is impossible.

According to the rotationally symmetric aspherical surface processing method of the present embodiment, the workpiece W is ground by the cup grindstone C for each spherical ring zone (circular portion) S _n , so The machining efficiency is significantly improved and the surface roughness is also improved as compared with the conventional method of machining by hitting.

Up to now, the method of intermittently machining each ring S has been described, but the machining with high machining efficiency is also possible by performing the movement continuously. Rather,
The continuous movement has the effect of reducing the time required for processing itself. However, in this case, the surface roughness tends to be lower than in the intermittent processing.

Further, as shown in FIG. 11, in the case of a grindstone in which the tip cross-sectional shape of the cup grindstone C is arcuate, the radius of the arc is e and the distance from the central axis to the arc center is r. In this case, when the angle with the workpiece is θ and the curvature to be machined is R, the relationship between them is expressed by the following equation (3
8).

[0149]

[Equation 47]

Further, if this equation (38) is modified, it becomes the following equation (39).

[0151]

[Equation 48]

Therefore, when using the grindstone C'as shown in FIG. 11, the above formulas (1), (2), (8), (9),
(27), (28), (29), etc. may be replaced according to the above equation (38) or (39), and the following equation may be modified. By doing so, exactly the same effect can be expected.

[0153]

According to the rotationally symmetric aspherical surface processing method of the present invention configured as described above, the NC controllable grinding processing device, which is used for normal spherical surface processing, that is, the work spindle It becomes possible to grind a rotationally symmetric aspherical surface by using a grinding device capable of obliquely intersecting the axial direction and the axial direction of the grindstone spindle. In addition, in that case, the surface of the workpiece W and the grindstone come into contact with each other in line contact, so that the processing efficiency and the surface roughness of the rotationally symmetric aspherical surface to be processed can be improved.

[Brief description of drawings]

FIG. 1 is a grinding machine used in a first embodiment of the present invention.

FIG. 2 is a front view of a rotationally symmetric aspherical surface that is ground according to the first embodiment.

FIG. 3 is a longitudinal sectional view of a rotationally symmetric aspherical surface that is ground according to the first embodiment.

FIG. 4 is a coordinate diagram showing a grinding state of a circular portion in the center of a concave rotationally symmetric aspherical surface according to a second embodiment of the present invention.

5 is a coordinate diagram showing a grinding state of a spherical zone immediately outside the circular portion of FIG.

FIG. 6 is a coordinate diagram showing the relationship between the rotation of the grindstone shaft and the movement of the action point.

FIG. 7 is a coordinate diagram showing a grinding state of a circular portion in the center of a convex rotationally symmetric aspherical surface according to the second embodiment of the present invention.

8 is a coordinate diagram showing a grinding state of a spherical ring zone immediately outside the circular portion of FIG. 7. FIG.

FIG. 9 is a coordinate diagram showing the relationship between the rotation of the grindstone shaft and the movement of the action point.

FIG. 10 is a diagram showing conventional grinding of a rotationally symmetric aspherical surface.

FIG. 11 is a view showing another configuration of the cup grindstone used in the second embodiment.

[Explanation of symbols]

2 X table 5 Y table 6 θ table 8 NC controller 11 Work spindle 12 Grindstone spindle C Cup grindstone P _n Ring zone boundary S _n Spherical ring zone W Workpiece 1 ₁ Work axis l ₂ Grindstone axis

Claims (9)

(57) [Claims] 1. A method for processing a rotationally symmetric aspherical surface by using a grinding apparatus capable of obliquely intersecting an axial direction of a work spindle to which a workpiece is attached and an axial direction of a grindstone spindle to which a grindstone is attached, The surface of the workpiece is divided into a plurality of concentric circular zones, and the surface of each circular zone is processed as a spherical surface having a radius of curvature that minimizes the error from the corresponding portion of the rotationally symmetric aspherical surface to be processed. A rotationally symmetric aspherical surface processing method comprising: 2. The rotationally symmetric aspherical surface processing method according to claim 1, wherein the grindstone has an annular action point about the axis of the grindstone spindle. 3. The rotationally symmetric aspherical surface processing method according to claim 2, wherein the grindstone is a cup grindstone. 4. The surface of the workpiece is divided into a plurality of concentric circular zones based on preset data for specifying the boundary position of each circular zone. Rotationally symmetric aspherical surface processing method. 5. When machining the surface of each ring zone, based on the data for specifying the boundary position of each ring zone, the boundary positions inside and outside the ring zone are respectively included and the work spindle of The rotationally symmetric aspherical surface processing method according to claim 4, wherein one point on the axis is processed as a spherical surface having its center of curvature as a spherical surface. 6. The surface of the workpiece is divided into a plurality of concentric annular zones based on preset data specifying the width of each annular zone. A rotationally symmetric aspherical surface processing method. 7. The surface of each ring zone is processed as a spherical surface having a preset radius of curvature and having a point on the axis of the work spindle as its center of curvature. Item 7. A rotationally symmetric aspherical surface processing method according to Item 6. 8. When processing the surface of each ring, the working point of the grindstone is set at the boundary position inside the ring in a plane including the axis of the work spindle and the axis of the grindstone spindle. The rotationally symmetric aspherical surface processing method according to claim 2, which is applied. 9. When machining the surface of each ring zone, the distance between the intersection of the axis of the work spindle and the axis of the grindstone spindle and the point of action of the grindstone should match the radius of curvature of the spherical surface. 9. The rotationally symmetric aspherical surface processing method according to claim 8, wherein the axial direction of the work spindle and the axial direction of the grindstone spindle are inclined with respect to each other.