JP2002165906A - Golf club head - Google Patents

Abstract

PROBLEM TO BE SOLVED: To improve durability of a face part. SOLUTION: In this golf club head, the face part for hitting a ball has a face plate 7, and the face plate 7 comprises a rolled material 10 rolled from at least two mutually crossing rolling direction K1 orthogonal to the thickness direction.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

The present invention relates to a golf club head capable of improving the durability of a face portion.

[0002]

2. Description of the Related Art
For example, in a wood-type golf club head, a plate-shaped face plate made of a metal material having excellent resilience is arranged on a face portion for hitting a ball and fixed by welding or the like. The face plate is formed by various methods. For example, a rolled material obtained by rolling a massive metal material with a rotating roll may be used.

However, since such a rolled material is usually rolled repeatedly in a certain rolling direction, its crystal structure may have anisotropy. FIG. 9 (A),
(B) shows the relationship between the rolling direction K and the bending center line L of the bending moment m in order to explain such anisotropy of the rolled material against bending. When the rolling direction K of the rolled material is aligned parallel to the bending center line L along the rotation center line of the bending moment m as shown in FIG. 9B, the rolling of the rolled material is performed as shown in FIG. It was found that the bending strength was reduced by about 5 to 20% as compared with the case where the direction K was perpendicular to the bending center line of the bending moment m.

On the other hand, as shown in FIG. 10, in a general wood type golf club head a, a face portion f hitting a ball has a vertical portion between a crown portion b and a sole portion c. It is toe d than face height A which is length
Face width B, which is the horizontal length between heel e
Are formed in a horizontally elongated shape.

When the ball is hit at the center point of the face portion f, the face portion f is deformed to bend inward of the head a. 11 (a) and 11 (b) show an XX end view and a YY end view of FIG. 10 at the time of impact, respectively. Here, when FIGS. 11A and 11B are considered as both end supporting beams, the bending amount Z inward of the head at the time of impact is the same for both beams, but the bending stress (σ = E Y / ρ, E: Young's modulus, y: distance from the neutral axis of the beam, ρ: radius of curvature), FIG. 1 in which the span of the beam is small.
1 (b) is larger than the beam shown in FIG.

That is, in the beams shown in FIGS. 11A and 11B, if the value is gradually increased while maintaining the same amount of bending, the beams shown in FIG. 11B are broken first. In particular, when the face portion f has a concave face line groove extending in the toe-heel direction, a notch (notch) is formed in the beam in FIG. Cheap. Such dynamics can be applied to the face portion f having a plate shape in substantially the same manner.
In order to prevent the durability of the face portion f due to the bending stress generated at the time of hitting the ball, it is necessary to improve the bending resistance in the crown portion-sole portion direction as compared with the toe heel direction.

However, if the rolling direction K of the rolled material 10 is used in parallel with the toe-heel direction of the face plate, the rolled material 10 is moved in the crown-sole direction (vertical direction) where bending stress acts greatly. The directions in which the bending resistance is low coincide with each other, and the durability of the face portion f is reduced. To prevent such a problem, it is conceivable to increase the thickness of the rolled material. However, in this method, there is a problem that the rigidity of the face plate becomes excessive and the resilience performance of the face portion is reduced.

[0008] As a result of intensive studies in view of the above situation, the inventors have found that the face plate is formed from a rolled material rolled from at least two rolling directions perpendicular to the thickness direction and intersecting with each other. Basically, by reducing the anisotropy of a rolled material to bending as much as possible, it is possible to provide a golf club head that can improve the durability in a well-balanced manner without causing a problem such as a decrease in the resilience performance of the face portion, and can solve the above problems. It is intended to be.

[0009]

According to a first aspect of the present invention, a face plate for hitting a ball is provided with a face plate, and the face plates are perpendicular to the thickness direction and intersect each other. A golf club head comprising a rolled material rolled from at least two rolling directions.

The invention according to claim 2 is the golf club head according to claim 1 or 2, wherein the intersection angle between the two rolling directions is 10 to 90 degrees.

The invention according to claim 3 is the golf club head according to claim 1 or 2, wherein the rolled material is rolled from two to five rolling directions intersecting each other.

According to a fourth aspect of the present invention, the face plate is made of a titanium alloy, and the rolling is cold rolling with a draft of 10% or more. A golf club head according to any one of the above.

The invention according to claim 5 is the golf club head according to any one of claims 1 to 4, wherein the face plate is made of a titanium alloy represented by the following composition formula. . Ti100-xy M1x M2y (all numerical values are atomic%) where M1 is one or more elements selected from Zr and Hf, and M2 is V, Nb, Ta, Mo, Cr, W
One or more elements selected from the group consisting of: and x + y ≦ 5
0 (0 <x <50, 0 <y <50).

[0014]

An embodiment of the present invention will be described below with reference to the drawings. FIG. 1 shows a golf club head (hereinafter, may be simply referred to as “head”) 1 of the present embodiment.
2 is a cross-sectional view of the head 1, and each shows a reference state in which the head 1 is placed on the horizontal plane HP at a prescribed lie angle α and loft angle β.

In FIG. 1, a head 1 according to the present embodiment has a face portion 2 for hitting a ball, a crown portion 3 connected to an upper edge 2a of the face portion 2 and forming an upper surface of the head, and a lower edge 2b of the face portion 2. A sole 4 extending from the toe 2t of the face 2 to the heel 2h through the back face, between the crown 3 and the sole 4, and a shaft (not shown). And a shaft mounting portion 6. The head 1 of the present embodiment is exemplified by a wood type head made of a metal material and having a hollow inside.

The head 1 is formed by integrally fixing a plate-like face plate 7 constituting a main part of the face portion 2 and a main body 9 having an opening for disposing the face plate 7 on the front surface. The boundary of the face plate 7 is illustrated by a dotted line in FIG.

The main body 9 is formed by appropriately welding one member or two or more members, and preferably a titanium alloy can be used. Further, the shaft mounting portion 6 includes:
In this example, the shaft is formed to protrude upward, and a shaft mounting hole 6a into which a shaft (not shown) can be inserted and fixed with an adhesive or the like is formed therein. Since the hole center line CL of the shaft mounting hole 6a substantially coincides with the axial center line of the shaft to be mounted later, the lie angle α is determined based on the hole center line CL in this specification.

If the thickness t of the face plate 7 is too small, the practical strength is reduced. Conversely, if the thickness t is too large, the rigidity of the face portion 2 is excessively increased, and the resilience performance is reduced, so that the ball is not hit. This is not preferable because the distance tends to decrease and the head weight increases. From such a viewpoint, the thickness t of the face plate 7 is, for example, 1.0 to 4.0 mm, more preferably 1.5 to 3.0 mm, and further preferably 1.5 to 2.5 mm.
The thickness t is desirably set to about mm, and in this example, it is formed with a substantially constant thickness.

As shown in FIG. 1, the face plate 7 has a plurality of face line grooves 11 extending substantially parallel to the surface thereof. The face line groove 11 has a face surface 2f which is a surface of the face portion 2.
And has a role of increasing friction with a ball, particularly when hit from a rough or when it rains, and is formed, for example, with a groove section having a rectangular or substantially triangular cross section. The face line groove 11 is defined in the Golf Rules of the Japan Golf Association as having a groove width of 0.9 mm or less, a groove depth of 0.5 mm or less, and a groove interval of three times or more the groove width.

The face line groove 11 of this embodiment has a groove width of 0.5 to 0.9 mm, a groove depth of 0.3 to 0.5 mm, and a groove interval of 3 to 5 times the groove width. You. The face line groove 9 is recessed in a direction extending substantially parallel to the horizontal plane HP in a reference state so that the ball can be firmly held at the time of hitting and an appropriate back spin can be given to the ball.

The face plate 7 is made of a rolled material 10 formed through a rolling process. That is, the face plate 7 is subjected to a rolling process during the manufacturing process, that is, a process in which the metal material M is bitten by friction between the pair of rolls R rotating as shown in FIG. Before the rolling step, for example, a casting, forging, grinding step, etc. for preparing the metal material M may be performed, or a pressing,
A punching or cutting step and, if necessary, a heat treatment step may be included.

When plastic deformation is applied to a metal material by a rolling process, there is an advantage that mechanical properties of the material can be improved, for example, strength can be increased by work hardening. Rolling is broadly divided into cold rolling, in which rolling is performed at room temperature, and hot rolling, in which the material is heated and rolled. Preferably, work hardening is reduced and production costs are low. It is desirable to employ cold rolling. In the present embodiment, in order to perform such cold rolling, a material having excellent workability at room temperature is used, and specifically, a β-type titanium alloy (described later) is desirable. The face plate 7 is integrated with the main body 9 by an appropriate fixing means such as bonding, caulking, welding or the like in this example.

The face plate 7 of the present invention is similar to that of FIG.
As shown in (A) to (C), at least two rolling directions K1, K2,.
One of the features is that it is made of a rolled material 10 that is rolled from. Thus, the rolled material 1 rolled from at least two rolling directions K1, K2,.
A value of 0 can reduce as much as possible anisotropy in mechanical properties, particularly in bending and fatigue properties, as compared to a rolled material having only one rolling direction. For example, in a conventional rolled material in which the rolling direction is only one direction, especially when the rolling direction is along the toe-heel direction of the face plate 7, the durability tends to decrease due to anisotropy. Since the anisotropy of the mechanical properties of such a rolled material can be reduced, it is possible to effectively prevent a decrease in the durability of the face plate 7 due to the anisotropy. In addition, since the durability can be improved without increasing the thickness t of the face portion 2, for example, deterioration of the resilience performance of the face portion 2 can be suppressed. In FIG. 3, the rolled material 10
Is rolled and discharged in the direction of the symbol Q in the figure, and the symbol K in the figure is discharged.
Is the rolling direction.

FIG. 4A shows two rolling directions K1 and K1.
2 shows the face plate formed in 2. Two rolling directions K1,
In the case of K2, if the intersection angle θ is too small, the rolled material 1
There is a tendency that the effect of alleviating the anisotropy with respect to the mechanical properties and fatigue properties of No. 0 tends to decrease. From this viewpoint, although not particularly limited, the angle θ is preferably 5 degrees or more, more preferably 10 to 90 degrees, further preferably 30 to 90 degrees, more preferably 60 to 90 degrees, More preferably, it is desirably substantially 90 degrees.

FIGS. 4B to 4D show a face plate 7 made of a rolled material 10 formed in three or more rolling directions K1, K2, K3. In addition, the crossing angle θ of each rolling direction
It is particularly desirable to roll uniformly at substantially 180 ° / N (where N is the number of rolling directions). That is, the angle θ is approximately 60 when the rolling direction is three directions.
It is preferable that the angle is approximately 45 degrees in the case of the four directions, and approximately 36 degrees in the case of the five directions. When the number of rolling directions is increased, the effect of reducing the anisotropy of the mechanical properties of the rolled material 10 is improved, but even if the number of rolling directions is increased unnecessarily, the above-mentioned effect peaks out, and conversely, the working efficiency is poor. As a result, the production cost is likely to increase. From such a viewpoint, it is desirable that the number of rolling directions is 2 to 5, more preferably 2 to 4, and still more preferably 3 to 4.

In addition, since such a rolled material 10 has a reduced anisotropy, the relationship between the rolling direction and the face plate 7, for example, the toe-heel direction, is particularly taken into consideration when used as the face plate 7. It can be used without doing. Therefore, the face plate 7 can be punched out of the rolled material with good yield, pressed, and the like, and parts can be taken out.
It also helps improve productivity.

The face plate 7 of this embodiment is preferably subjected to cold rolling at a rolling reduction of 10% or more, more preferably 30% or more, further preferably 50% or more, and particularly preferably 70% or more. It is desirable to increase the dislocation density and work harden. By performing cold rolling at such a high reduction ratio, a high-strength rolled material 10 having a fine and dense crystal structure can be obtained. The rolling reduction is determined by the following formula: rolling reduction [%] = {(h1−h2) / h1} × 100, where h1 is the thickness before rolling and h2 is the thickness after rolling.

The face plate 7 of the present embodiment is manufactured through rolling a plurality of times in different rolling directions. At this time, it is desirable that the rolling reduction in each step is substantially the same. This is preferable in that the distortion that does not occur due to rolling can be reduced and a rolled material 10 having a uniform structure can be obtained.

In the head 1 of this embodiment, the ratio (A / B) between the face height A (measured in the vertical direction) and the face width B shown in FIG. 1 is set to about 0.4 to 0.7. It is formed in a horizontally long shape. Generally, among the variations of the hit ball, the variation in the left-right direction is O.D. B. Because of the dangers, the golf score is affected more closely than the variation in the vertical direction. For this reason, the head 1 of the present embodiment has a laterally elongated shape by regulating the ratio (A / B) as described above, so that the moment of inertia of the head 1 in the left-right direction (around the vertical axis passing through the center of gravity of the head 1). The moment of inertia of the ball is increased, and the variation in the lateral direction of the hit ball is reduced. The face height A is preferably 3 from the viewpoint of the height of the center of gravity of the head 1.
The face width B is desirably set in the range of 70 to 100 mm from the viewpoint of the moment of inertia of the right and left sides.

The metal material used for the face plate 7 of the present embodiment is not particularly limited as long as it can be formed through rolling, but is preferably a titanium alloy having a low specific gravity and a high strength. A β-type titanium alloy which is relatively easy to cold-roll is desirable. Since β-type titanium alloy has a body-centered cubic structure (bcc) with many slips, the resistance required for deformation is smaller than that of α-type titanium alloy, which has a close-closed cubic structure with less slip, resulting in better workability at room temperature. Excellent. As such a β-type titanium alloy, for example,
Ti-15V-3Cr-3Al-3Sn, Ti-15M
o-5Zr-3Al, Ti-10V-2Fe-3Al,
Ti-13V-11Cr-3Al, Ti-8Mo-8V
-2Fe-3Al, Ti-22V-4Al, Ti-15
Mo-5Zr and the like.

The inventors have found a novel titanium alloy represented by the following composition formula (1). Ti100-xy M1x M2y (all numerical values are atomic%) (1) where M1 is one or more elements selected from Zr and Hf, and M2 is V, Nb, Ta, Mo, Cr, W
One or more elements selected from the group consisting of: and x + y ≦ 5
0 (0 <x <50, 0 <y <50).

As a result of experiments by the present inventors, the titanium alloy represented by the above formula (1) has a significantly low Young's modulus and a large elastic elongation and plastic elongation while increasing the tensile strength and hardness. I found something to show. The high strength and hardness of such a titanium alloy are mainly attributable to solid solution strengthening by dissolving elements having a large atomic radius difference, for example, an element having an atomic radius difference of 10% or more as in the above combination, and a low Young's strength. The rate is mainly that atoms can move reversibly with low stress because the constituent elements do not have attractive interaction with each other, and the large elastic elongation limit etc. It is considered that reversible atom transfer can occur up to a high strain region due to diversity, and deformation stress does not easily rise.

Particularly, since the constituent elements containing at least two elements having a large difference in atomic radius are dissolved,
Since the rearrangement of atoms is unlikely to occur and the diffusivity is reduced, even when the molten metal is gradually cooled without being quenched, for example, β is excellent in cold workability mainly containing a bcc solid solution single phase or a bcc solid solution. A type titanium alloy can be easily obtained. Further, such a solid solution can be easily imparted with higher strength by performing cold rolling and causing work hardening.

As an example, a titanium alloy represented by a particularly preferred composition of “Tia Zrb Nbc Tad” satisfying the above formula (1) (atomic radius difference is about 11.7% at minimum-maximum) is cold-rolled. Was applied, yield strength of 980 MPa, tensile strength of 1070 MPa, Young's modulus of 40 GPa, elastic elongation of 1.7%, plastic elongation of 15% and 350%
An alloy having a Vickers hardness of Hv and a volume fraction of bcc solid solution of 90% or more could be obtained. Table 1 shows such a new titanium alloy, pure titanium, and α + β which is currently the mainstream material for wood type golf club heads.
Physical properties of a titanium alloy (Ti-6Al-4V). FIG. 5 shows the tensile stress of these materials.
FIG. 6 shows the relationship between the tensile strength and the Young's modulus including other metal materials, respectively.

[0035]

[Table 1]

As is clear from Table 1, FIG. 5 and FIG. 6, despite having a higher tensile strength σf than the titanium alloy represented by the above formula (1), pure titanium or titanium alloy, It can be seen that the Young's modulus E is as low as 40 MPa, which is less than half of those, and that the elasticity or plastic elongation is large and the hardness is also large. In other words, by using a titanium alloy having such characteristics of high strength and low Young's modulus as the face plate 7 of the head 1, the durability and the trauma resistance of the face portion 2 are sufficiently secured, and the coefficient of restitution of the head is reduced. This is particularly preferable in that it can improve the initial velocity of the ball, and thereby increase the flight distance. In addition, such a novel titanium alloy has low deformation resistance and large plastic elongation, so it has excellent cold-rolling workability,
For example, it is preferable in that a rolled material having a rolling reduction of 10% or more can be easily formed.

In the above formula (1), the content of each element is limited based on the following reason. First, when the content of titanium is less than 50 atomic%, the above-described alloy can exhibit excellent mechanical properties, but tends to have a large specific gravity, so that when it is applied to a head, the weight increases and the cost increases. In addition, the melting point tends to be increased.
If the element of Zr or Hf is not contained, it tends to be difficult to form a solid solution of a metal element having a large difference in atomic radius in a large amount, and solid solution strengthening tends to be impossible. Conversely, Zr, Hf
When the total content of the elements exceeds 50 atomic%, there are disadvantages such as an increase in specific gravity and an increase in melting point.

When one or two elements selected from V, Nb, Ta, Mo, Cr and W are not contained, the strength and the corrosion resistance are liable to be reduced. Further, when the total content of these elements exceeds 50 atomic%, the specific gravity of the alloy is increased, the melting point is increased, and the cost is easily increased.

Such a titanium alloy is rolled from at least two rolling directions perpendicular to the thickness direction and intersecting with each other as described above, and has a rolling reduction of 10% or more, more preferably 30% or more, and still more preferably. It is preferable to increase the dislocation density by performing cold rolling of 50% or more, particularly preferably 70% or more, and to perform work hardening. This makes it possible to further improve the tensile strength by work hardening while maintaining a low Young's modulus, and to alleviate the anisotropy of the mechanical properties and fatigue properties of the material.

The titanium alloy represented by the above formula (1) is dissolved in a vacuum arc melting furnace, for example, in an atmosphere that is evacuated and replaced with argon, and the alloy having the above composition is formed into a block (for example, having a diameter of 100mm x 10mm in thickness) or rod (20mm in diameter x 100mm in length), then cold-rolled at a reduction rate of 50-70% to form a 3mm thick plate-shaped rolled material. This is pressed and punched according to the shape of the face plate 7. In the cold rolling, it is desirable to repeat rolling a plurality of times, for example, using a plurality of rolling rollers, to gradually reduce the cross section, and to approach a desired thickness. The surface area S1 of the face portion 2 and the surface area S1 of the face plate 7 made of the rolled material 10
The ratio (S2 / S1) to 2 is set to 0.9 or more.

Although the embodiment of the present invention has been described taking a wood type golf club head as an example, the present invention
The present invention is not limited to the wood type golf club head, and can be suitably applied to iron type, putter type, and utility type heads in which the inside of the face portion 2 is substantially empty.

[0042]

EXAMPLE A wood-type golf club head shown in FIGS. 1 and 2 was prototyped using a face plate having the specifications shown in Table 2, and the same shaft was attached to each head to form a golf club. A durability test was conducted in which the golf ball was attached to a swing robot manufactured by True Temper Co., Ltd., and a 10,000 hits of a golf ball were hit at a head speed of 54 m / s and a center position of the face portion. Each face plate is Ti50Zr30T
An alloy raw material of a10Nb10 (the number is atomic%) is melted in a vacuum arc melting furnace to form an ingot, which is formed by a cold rolling machine at a predetermined rolling reduction, a predetermined rolling direction and a predetermined crossing angle (Table 2). ) Was cold-rolled to obtain a sheet material, which was stamped and manufactured to a thickness of 3 mm. The roll and bulge of each face plate were set to a radius of curvature of 10 inches, and the face height was 40 mm and the face width was 95 mm.

Further, the rolled material used for each face plate was obtained from JI
When a No. 3 test piece was prototyped in accordance with the specifications of FIGS. 7A to 7F based on SZ2204 “Metallic material bending test piece”, and the bending test shown in FIG. Was measured for bending stress. (Average value of n = 3) And FIG.
The ratio of (A) to the bending stress was determined, and the state of relaxation of the anisotropy was examined. The closer the ratio is to 100%, the better. Table 2 shows the test results.

[0044]

[Table 2]

As a result of the test, it was confirmed that in the rolled material rolled from at least two rolling directions crossing each other, the bending strength was improved and the anisotropy with respect to bending was reduced. In particular, it was confirmed that the effect was particularly great in the case where the crossing angle of the rolling direction was 60 degrees or more (Examples 4 and 5) and in the case where rolling was performed in three or more directions (Examples 6, 7, and 8). Was.

As described above, according to the first aspect of the present invention, the face plate is made of a rolled material rolled from at least two rolling directions perpendicular to the thickness direction and intersecting with each other. Can reduce the anisotropy of mechanical properties, especially bending and fatigue properties, as compared with a rolled material in only one direction, and effectively prevent a decrease in the durability of the face plate due to such anisotropy. sell. In addition, this makes it possible to improve the durability without increasing the thickness of the face portion, for example, so that the resilience performance of the face portion can be prevented from deteriorating.

As described in the second and third aspects of the present invention,
By limiting the crossing angle of the two rolling directions to a certain range, or by limiting the number of rolling directions, the anisotropy of the rolled material can be more reliably alleviated, and the durability of the face portion is advantageously reduced. Can be prevented.

In the invention according to claim 4, the face plate is made of a titanium alloy, and the rolling process is a cold rolling process with a rolling reduction of 10% or more, so that the rolled material can be effectively processed. Hardening is caused, and the bending strength and tensile strength of the rolled material can be further improved.

Further, since the composition of the titanium alloy is limited to a certain range as in the invention according to claim 5, excellent cold workability, high strength and low Young's modulus can be obtained. In addition, it is possible to improve durability while improving resilience by making the face portion thinner.

[Brief description of the drawings]

FIG. 1 is a front view of a golf club head according to an embodiment in a reference state.

FIG. 2 is an end view in a vertical plane perpendicular to the face surface.

FIG. 3 is a schematic view showing a rolling process.

FIGS. 4A to 4D are front views showing a rolling direction of a face plate.

FIG. 5 is a graph showing a relationship between tensile stress and elongation of the titanium alloy of the present embodiment.

FIG. 6 is a graph showing the relationship between tensile strength and Young's modulus of the titanium alloy of the present embodiment.

FIGS. 7A to 7F are plan views illustrating a bending test piece of a rolled material.

FIG. 8 is a schematic diagram illustrating a bending test.

FIGS. 9A and 9B are perspective views showing anisotropy of a rolled material.

FIG. 10 is a front view showing a conventional golf club head.

11 (a) is an end face taken along line XX of FIG. 7, and FIG.

[Explanation of symbols]

 DESCRIPTION OF SYMBOLS 1 Golf club head 2 Face part 3 Crown part 4 Sole part 5 Side part 6 Shaft attachment part 7 Face plate 10 Rolled material K1, K2, K3 ... Rolling direction θ Crossing angle in rolling direction

 ──────────────────────────────────────────────────続 き Continuing on the front page (72) Inventor Yoshie Takano 3-6-9, Wakihama-cho, Chuo-ku, Kobe City, Hyogo Prefecture Inside Sumitomo Rubber Industries, Ltd. (72) Inventor Akihisa Inoue Kawauchi, Aoba-ku, Sendai City, Miyagi Prefecture Former 35 Hasekura Kawauchi House 11-806 F term (reference) 2C002 AA02 CH01 CH06 PP02

Claims (5)

[Claims] 1. A face plate for hitting a ball, comprising a face plate, wherein the face plate is made of a rolled material rolled from at least two rolling directions perpendicular to the thickness direction and intersecting with each other. And golf club head. 2. An intersection angle between the two rolling directions is 10 to 10.
3. The golf club head according to claim 1, wherein the angle is 90 degrees. 3. The golf club head according to claim 1, wherein said rolled material is rolled from two to five rolling directions crossing each other. 4. The golf according to claim 1, wherein said face plate is made of a titanium alloy and said rolling is cold rolling with a rolling reduction of 10% or more. Club head. 5. The golf club head according to claim 1, wherein said face plate is made of a titanium alloy represented by the following composition formula. Ti100-xy M1x M2y (all numerical values are atomic%) where M1 is one or more elements selected from Zr and Hf, and M2 is V, Nb, Ta, Mo, Cr, W
One or more elements selected from the group consisting of: and x + y ≦ 5
0 (0 <x <50, 0 <y <50).