KR910009207B1 - Tennis racket - Google Patents

Abstract

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Description

Tennis racket

1 is a plan view of a tennis racket according to the present invention.

2 is a side view of the racket of FIG.

3 is a plan view of the racket of FIG. 1 without a string and handle coating.

4 is a side view of the racket frame of FIG.

5 is a sectional view taken along line 5-5 of FIG.

6 is a sectional view taken along line 6-6 of FIG.

7 is a cross sectional view taken against the line 7-7 of FIG.

8 is a sectional view taken along line 8-8 of FIG.

9 is a partial perspective view of a portion of a racket frame, showing a multilayer of graphite fibers.

10 shows the first and second bending modes of a tennis racket under free-free constraints.

11 shows the first, second and third bending modes of a tennis racket under fixed-free constraints.

12 is a view showing a deformation of the racket according to the prior art, when the conventional tennis ball is returned from the racket after the collision.

13 is a view showing a modification of the tennis racket according to the present invention when the conventional tennis ball is returned from the racket after the collision.

* Explanation of symbols for the main parts of the drawings

15: tennis racket 17: frame

18: handle portion 19: draw portion

20: head portion 21, 22: frame portion (draw pieces)

23: yoke piece 24: longitudinal strip

25: lateral line 26: plastic buffer

27: plastic insert 28: handle coating

29: end cap

31,32,33,34,35,36,37,38,39,40,41,42: floor

45 Groove 46 Hole in the Row

The present invention relates to a racket for playing a game using a ball having a limited elasticity, such as a tennis racket.

In a conventional tennis racket, the rigidity of the frame portion and the shaft portion is such that the head frame portion is forced out of the racket's length axis when the ball strikes the strand face of the racket. This deflection adversely affects the flight path of the bouncing ball.

For any object subjected to an input load, some complex vibrational response will occur. This complex deformed shape of an object is decomposed into the sum of a myriad of single oscillation mode shapes of varying amplitude and frequency. The specific frequency, mode shape and amplitude associated with the vibrating object depends on a number of factors. Among these factors are not only the level of constraint of the object, but also the stiffness and weight distribution in the object.

Stiffness and weight distribution are controlled in two ways. One method is to use a specific reinforcement having a higher ratio of weight to stiffness and weight to stiffness on some of the objects. Another method of controlling stiffness and weight distribution is to change the cross-sectional area of the object, changing the geometrical shape of the cross-sectional area of the object so that the ratio of stiffness to weight changes, more specifically Is to use a positive material. The increase in stiffness increases the frequency and the dynamic strain amplitude and the increase in weight reduces the frequency and the dynamic strain amplitude.

Two specific constraints are important in this description. One extreme, the condition of a ″ free-free ″ constraint, represents an object that vibrates unbound in space. It is approximated in the laboratory by hanging the object with an elastic band and allowing the object to vibrate freely. When flexed under the ″ free-free ″ constraints, two first vibration mode shapes for a simple beam are shown in FIG. 10.

At the other extreme, there is a ″ clamped-free ″ constraint, in which one end of the object is forcibly fixed to the supporting fixture, while the other end can vibrate freely. Three simple complementary first vibration mode shapes are shown in Figure 11 when they are bent under the fixed-free constraints. It should be noted that the modes 1 and 2 of FIG. 10 have roughly the same shape as the modes 2 and 3 of FIG. 11, respectively. When bent under the ″ free-free ″ limits, an additional low frequency vibration mode (mode 1 in FIG. 11) is produced by adding a rigid clamp to the object.

Under ″ free-free ″ constraints, the frequencies of modes 1 and 2 are not the same as the frequencies for the associated mode shapes (modes 2 and 3, respectively) under ″ fixed-free ″ conditions. The frequency of the mode shape under any one of the constraints can be approximated from the frequency of the mode shape under other conditions using the following relationship.

[Formula 1]

In the above formula

Freq _cf = frequency of morphology under fixed-free conditions

Freq _ff = frequency of morphology under free-free conditions

L _ff = length of beam under ″ free-free ″ conditions

L _cc = length of beam held in clamping fixture

L _cf = equivalent length of beam under ″ fixed-free ″ conditions

L _cf = L _ff -L _cc

Tennis rackets exhibit characteristics similar to those of the simple beam described above due to the ball / racquet collision during play. Laboratory tests were conducted on a variety of rackets. For conventional tennis rackets under ″ free-free ″ constraints, the test results show that the first mode of bending is in the range of 100 Hz to 170 Hz. Under ″ fixed-free ″ constraints, conventional rackets exhibit frequencies of 25 Hz to 50 Hz and 125 Hz to 210 Hz for the first and second flexural modes, respectively. In US Pat. No. 4,664,360 (DE-OS 3434898), the resonant frequency of the racket described herein under the ″ fixed-free ″ limit was 70-200 Hz.

Studies have shown that a tennis racket that vibrates under ″ free-free ″ conditions is closer to the tennis racket's behavior during play than a racquet under ″ free-free ″ conditions. If a ″ fixed-free ″ constraint exists during the test, Equation 1 sets the frequency value so that the second mode of bending under ″ fixed-free ″ conditions approximates the first mode frequency value under ″ free-free ″ conditions. Should be used to modify

For a conventional tennis ball, it was observed that the ball / racquet collision time is in the range of 2 × 10 ⁻³ to 7 × 10 ⁻³ seconds and the average value is 2 × 10 ⁻³ to 3 × 10 ⁻³ seconds. During this time, the head of the racket is bent back by the force input from the ball. In a conventional racket, the ball leaves the line at some time between the ball / racquet collision point at which the racket begins to deform and immediately after reaching the maximum point of the racket's deflection. Thus, the flight path of the shot is affected (see Figure 12) and loses energy because it has not returned to the undeformed position, with a bounce angle of zero and a maximum racket head speed.

은 테니스공이 줄에 머무는 시간과 동일해야만 한다 ″자유-자유″ 제한조건하에서, 휨의 제1모우드는 이 모우드가 플레이동안에 발생된 주 진동모우드이기 때문에, 선택된다.If the ball stays on the line while the racket is bent and does not leave the line until the racket returns to its undeformed position, the ball's flight path is unaffected and the accuracy of the shot is increased (see Figure 13). In addition, since the racket head speed is at its maximum, more energy is delivered to the ball, resulting in more powerful shorts. Changing the deformation time of the tennis ball is not considered a desirable solution to this problem. Therefore, for optimal performance, the tennis racket must be designed so that the frequency of the main vibration mode generated in the racket during play is balanced while the ball / racquet contact continues. More specifically, the time of the first bending mode for the tennis racket under the ″ free-free ″ constraints.

Must be equal to the time the tennis ball stays on the line. Under the ″ free-free ″ constraint, the first mode of bending is chosen since this mode is the main oscillating mode generated during play.

Since ball / racquet collision times of 2 × 10 ⁻³ seconds to 3 × 10 ⁻³ seconds are common, an optimal tennis racket will have a first mode of bending under a ″ free-free ″ constraint between 170 Hz and 250 Hz. Using Equation 1, assuming a 27-inch racket is suspended by a rigid support 3 inches above the handle, under ″ fixed-free ″ conditions the frequency range would be 215 Hz to 315 Hz for the second mode of bending. One particular embodiment of the racket has a frequency of 200 Hz to 210 Hz for the first bending mode under ″ free-free ″ constraints and a frequency of 230 Hz to 265 Hz for the second bending mode under ″ fixed-free ″ conditions. .

The invention will be described in connection with the exemplary embodiment shown in the accompanying drawings.

As described above, it is desirable to adjust the stiffness of the tennis racket so that the racket returns to its initial undeformed position after the conventional tennis ball hits the racket and before the ball leaves the racket string. Under those conditions, the flight path of the ball before and after colliding with the racket will not be affected, and the accuracy of the shot will be increased, as illustrated in FIG. In addition, more energy will be transferred to the bounce ball, resulting in a more powerful short.

It is desirable to adjust the stiffness of the tennis racket such that the racket has the first bending mode under free-free constraints between 170 Hz and 250 Hz. Such a racket will have a second bending mode under fixed-free constraints between 215 Hz and 315 Hz. 1-9 illustrate one particular embodiment of a tennis racket 15 having such a frequency.

Referring first to FIGS. 1 and 2, the racket 15 comprises a frame 17 having a handle portion 18, a draw portion 19 and a head portion 20. The draw portion 19 includes a pair of frame portions 21 and 22 which are separated from the handle portion 18 and are integrated with the head portion 20. A yoke piece 23 extends between the draw pieces 21 and 22 and forms the bottom of the head portion, which is usually looped or elliptical.

The tennis racket also includes a plurality of longitudinal strings 24 and transverse strings 25 extending into a conventional opening between the head portion 20 and the yoke piece 23. The plastic buffer 26 extends above the head portion so that the head does not wear out or wear out. The buffer is held in place by the string, and the buffer also prevents the string from touching the holes in the racket frame to wear out. The plastic insert 27 extends between the end of the buffer 26 and the draw portion 19 to protect the strings under the head.

The racket also includes a conventional handle coating 28 and an end cap 29 on the handle portion 18. Handle cloth is made of spirally wound leather strips.

3 and 4 illustrate a racket frame 17 without a string and handle covering.

Referring to FIGS. 5-8, each of the frame portions 18-23 is made of a tubular frame member having a wall thickness of about 0.045 to about 0.050 inches. The tubular frame member is made of a layer of resin-impregnated graphite fibers, wound around an inflatable bladder. As is well known in the art, when the racket frame is placed in a mold, the breather contacts the layer of graphite fibers with the mold until it swells and the resin cures.

9 shows layers 31-42 of resin fibers infused with resin used to make the tubular frame member of the preferred embodiment. Each of the layers 31-42 includes unidirectional graphite fibers oriented in the direction indicated by the hatched. Layers 31, 32 and 35-42 comprise graphite fibers having an elastic modulus of about 33,000,000. Layers 33 and 34 comprise graphite fibers having about 45,000,000 modulus. About 10 to 20% of the graphite fibers used in the racket frame have a higher modulus, and about 80 to 90% of the graphite fibers have a lower modulus. By using graphite fibers of higher elastic modulus, the stiffness of the racket is increased without increasing the weight of the racket. The outer layer 43 of the racket frame illustrated in FIG. 9 is a paint layer.

Referring to Figures 3-6, the outer surface of the head has a groove 45 with a hole 46 in the string. Groove 45 is also used to position the buffer 26 and insert 27 (FIG. 2).

The height of the racket frame is determined by FIG. 4, which is perpendicular to the central plane MP and measured by the dimensions of the racket passing through the longitudinal center line CL of the handle portion 18. The longitudinal center line CL also forms the longitudinal axis of the racket of FIG. The row of rackets lies on the center plane MP, and the warping of the racket illustrated in FIGS. 10 and 11 occurs on a plane extending perpendicular to the center plane.

The height of the racket frame of FIG. 4 continuously increases from dimension A of the top of the head portion of the frame to dimension B of the draw portion of the frame. The height of the racket continuously decreases from dimension B to dimension C at the top of the handle portion 18. The height of the handle portion increases from dimension C to dimension D and then continues to the bottom of the handle portion.

The maximum height B of the frame of the racket occurs where the draw members 21 and 22 meet the head portion 20. Comparing the third and fourth degrees, the maximum dimension B corresponds to the center of the yoke piece in which the yoke piece 23 intersects the longitudinal center line CL. 6 and 7 degrees, the height of the yoke piece 23 is substantially lower than the height of the yoke members 21 and 22 and the head portion 20 in the maximum height B zone.

In one particular embodiment of a large head rack, the inner length dimension E of the head portion is 13.7647 inches, the inner lateral dimension of the head portion is 10.1563 inches, and the total length L is 26.960 inches. The height A of the top of the head portion is 1.090 inches, the maximum height B is 1.500 inches, the height C is l.000 inches, and the height D is varied depending on the handle size according to the conventional handle dimensions. Referring to FIG. 5, the overall width G of the head portion at the top of the head portion was 0.380 inches. Referring to FIG. 7, the height H of the yoke piece 23 was 1.080 inches, and the width I was 0.400 inches. The ratio of the maximum height B to the minimum height A of the head was 1.5 / 1.09 or 1.376.

The area moment of inertia of the racket was 0.33 inch ⁴ at the point of maximum cross-sectional height on the frame. The frequency of the first bending mode was 204 Hz under free-free constraints, and the frequency of the second bending mode was 230 Hz under fixed-free conditions.

In one particular embodiment of a medium racket, the inner length directional dimension E of the head portion was 12.520 inches, the inner transverse dimension F was 9.330 inches, and the length L was 26.938 inches. The height of the headtop was 0.920 inches, the maximum height B was 1.250 inches, the height C was 1.000 inches, and the height D varied according to the handle size. The width G of the head at the top of the head was 0.405 inches. The height H of the yoke piece 23 was 0.905 inches and the width I was 0.4497 inches.

The ratio of the maximum height B to the minimum height A of the head was 1.25 / 0.92 or 1.3589.

Under free-free conditions, the frequency of the first bending mode was 208 Hz, and under fixed-free conditions, the frequency of the second bending mode was 230 Hz. The shape and dimensions of the racket frame illustrated in FIGS. 3-9 are such that the racket is more rigid than conventional rackets and has a fixed or fixed frequency of 170 to 250 Hz for the first bending mode under free-limiting restrictions. The moment of inertia for the midplane MP is provided to have a desired frequency of 215 to 315 Hz for the second flexural mode under free constraint. The ratio of the maximum height B to the minimum height A is preferably about 1.35 to about 1.38.

By using relatively high modulus graphite fibers in the layers 33 and 34, the weight of the frame can be reduced to accommodate the buffer 26 while keeping the total weight of the racket within the normal range. The frame uses about 270 g of resin and graphite fibers, which are conventional resins.

Large head rackets and medium size rackets with specific shapes and dimensions are described herein to achieve the desired stiffness and frequency.

However, it will be appreciated that other stiffnesses and dimensions may be used as long as the resulting stiffness provides the desired frequency. An important purpose is to obtain the frequency of the first bending mode between 170 Hz and 250 Hz under free-free limits, or the frequency of the second bending mode between 215 Hz and 315 Hz under fixed-free limits.

While the foregoing detailed description of specific embodiments of the invention has been presented for purposes of illustration, it will be appreciated that many of the details given herein vary significantly by those skilled in the art without departing from the scope and concept of the invention.

Claims (12)

A tennis racket having a handle portion, a looped head portion, and a draw portion for joining the handle portion and the head portion, the longitudinal axis being arranged in line with the center line of the handle, and along the longitudinal axis parallel to the plane of the loop-shaped head portion. A tennis racket having an extended center section and having a frequency of a first bending mode in the range of 170 Hz to 250 Hz under free-free constraints on a plane obtained perpendicular to the center plane. The tennis racket according to claim 1, wherein the frequency is in the range of 200 Hz to 210 Hz. 2. The racket of claim 1, wherein the racket is made of a multilayered tube of resin-infused graphite fibers, wherein the fibers of some layers have an elastic modulus of about 33,000,000, and the fibers of the other layers have an elastic modulus of 45,000,000. Tennis racket. The tennis racket of claim 3, wherein about 10-20% of the fibers have an elastic modulus of about 45,000,000 and about 80-90% of the fibers have an elastic modulus of about 33,000,000. The racket of claim 1, wherein the racket is made from a tube of twelve layers of resin-infused graphite fibers, wherein two of the layers have an elastic modulus of about 45,000,000, and the fibers of the other layers have an elastic modulus of about 33,000,000. The tennis racket characterized by. The yoke according to claim 1, wherein the draw portion includes a pair of frame members which are separated from the handle portion, and are integrated with the head portion, and the racket extends between the split frame members to form the bottom of the loop-shaped head portion. And a racket, the height of the racket perpendicular to the center surface of the tennis racket characterized in that the maximum in the split frame member of the area where the yoke portion is combined with the split frame member. 7. A tennis racket according to claim 6, wherein the ratio of the maximum height of the racket to the height at the top of the head portion is about 1.35 to 1.38. 7. A tennis racket according to claim 6, wherein the height of the racket continuously decreases from the maximum height to the top of the head portion and continuously decreases from the maximum height to the top of the handle portion. A tennis racket having a handle portion, a looped head portion, and a draw portion for engaging the handle portion and the head portion, the tennis racket having a center line extending beyond a longitudinal axis parallel to the plane of the looped head portion and the center line of the hand And a frequency of the first bending mode in the range of 215 Hz to 315 Hz under fixed-free constraints on a plane extending perpendicular to the central plane. 10. A tennis racket according to claim 9, wherein under fixed-free constraints the frequency of the second bending mode is in the range of 230 Hz to 265 Hz. The tennis racket of claim 1, wherein the overall length L is about 27 inches. 12. The tennis racket according to claim 11, wherein the frequency is in the range of 200 Hz to 210 Hz.

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