An ultrasonic vibration horn suitable for high-speed broaching of small-module cylindrical gears

Abstract

The present invention discloses an ultrasonic vibration horn suitable for high-speed broaching of small-module cylindrical gears, relating to the field of ultrasonic machining technology. The horn comprises: a horizontal rod, a first vertical rod, and a second vertical rod. The horizontal rod is provided with a piezoelectric actuator to drive the vibration of the horizontal rod; the lower end of the first vertical rod is connected to the horizontal rod; the lower end of the second vertical rod is connected to the horizontal rod, the size of the second vertical rod is 0.9 times the size of the first vertical rod, and the distance from the connection point between the first vertical rod and the horizontal rod to the connection point between the second vertical rod and the horizontal rod is an odd multiple of half the wavelength of the resonant wave in the horizontal rod; the upper ends of the first vertical rod and the second vertical rod are respectively connected to the two ends of a fixture that fixes the gear. The piezoelectric actuator of the present invention causes the horizontal rod to vibrate axially in resonance. Due to the presence of the first and second vertical rods, axial and bending non-resonant vibrations are generated, achieving multi-directional coupled vibrations during the gear machining process, thereby improving machining efficiency, tool life, and workpiece surface quality.

Description

Technical Field

[0001] The invention relates to the technical field of ultrasonic machining, and in particular to an ultrasonic vibration horn suitable for high-speed broaching of small-module cylindrical gears. Background Art

[0002] Currently, broaching, as a specialized and effective machining method, offers advantages unmatched by other machining methods, such as high efficiency and precision, for machining parts with numerous specialized structures. High-performance gears are widely used in high-end equipment, including aerospace. The material used for these gears possesses remarkable strength and hardness, with tooth surface hardness reaching 68HRC after quenching. However, broaching involves high cutting forces, making it prone to tool deflection, resulting in reduced tool life, poor machining quality, and low efficiency. Summary of the Invention

[0003] The present invention aims to address at least one of the technical problems existing in the prior art. To this end, the present invention proposes an ultrasonic vibration horn suitable for high-speed broaching of small-module cylindrical gears. This horn can generate high-frequency, high-amplitude vibrations in the gears under high-load, high-frequency impact, thereby improving broaching efficiency and precision.

[0004] According to an embodiment of the first aspect of the present invention, an ultrasonic vibration amplitude transformer suitable for high-speed broaching of small-module cylindrical gears is used to drive the vibration of a fixture that fixes the gear, and a broach is passed through the gear, including: a horizontal rod, a first vertical rod, and a second vertical rod. Two mounting holes are symmetrically opened on the horizontal rod, and a connecting piece for fixing the horizontal rod on a horizontal support surface is passed through the mounting hole. A piezoelectric actuator is provided on the portion of the horizontal rod located between the two mounting holes to drive the horizontal rod to vibrate; the lower end of the first vertical rod is connected to the horizontal rod; the lower end of the second vertical rod is connected to the horizontal rod, the size of the second vertical rod is 0.9 times the size of the first vertical rod, and the distance from the connection point between the first vertical rod and the horizontal rod to the connection point between the second vertical rod and the horizontal rod is an odd multiple of half the wavelength of the resonant wave in the horizontal rod; the upper ends of the first vertical rod and the second vertical rod are respectively connected to the two ends of the fixture that fixes the gear.

[0005] According to some embodiments of the present invention, the horizontal rod includes two mating positioning sections, a first vibration fixing section, multiple vibration transmission sections, and a second vibration fixing section. The two mating positioning sections are respectively located on the side of the two mounting holes away from each other, the first vibration fixing section is located between the mounting hole and the piezoelectric actuator and the first vibration fixing section is connected to the first vertical rod, the second vibration fixing section is located between the mounting hole and the piezoelectric actuator and the second vibration fixing section is connected to the second vertical rod, and the multiple vibration transmission sections are located between each adjacent group of the piezoelectric actuators.

[0006] According to some embodiments of the present invention, the length of the mating positioning segment is defined as l1, l1=1000λψ1, and the excitation frequency f0 is calculated as: Wherein l2 is the spacing of the teeth on the broach, ψ1 is equal to when the broach cutting speed v is 1m / min, 5m / min, 10m / min, 20m / min, 25m / min, 30m / min, f0 is the excitation frequency that minimizes the vibration amplitude of the ultrasonic vibration transformer, λ is the wavelength of the vibration generated by the piezoelectric actuator propagating in the horizontal rod, and the vertical dimension of the horizontal rod is 10 to 14 mm.

[0007] According to some embodiments of the present invention, the diameter of the mounting hole is equal to 0.01l1.

[0008] According to some embodiments of the present invention, the piezoelectric actuator devices are arranged in multiple groups at intervals, and one group of the piezoelectric actuator devices includes two piezoelectric actuator devices symmetrically arranged up and down with a horizontal rod as the center, and the horizontal rod is provided with multiple installation grooves for embedding corresponding piezoelectric actuator devices, and the length of the installation groove is equal to 0.2l1.

[0009] According to some embodiments of the present invention, the lengths of the first vibration fixing section and the second vibration fixing section are equal to 20l1, and the length of the vibration transmission section is equal to l1.

[0010] According to some embodiments of the present invention, the piezoelectric actuator is located at the peak of the overall vibration mode of the ultrasonic vibration horn, and the mounting hole is located at a node where the vibration amplitude of the overall vibration mode of the ultrasonic vibration horn is zero.

[0011] According to some embodiments of the present invention, the first vertical rod includes a Gaussian curve transition section, a vertical transfer section, a cylindrical transition section, and a conical vibration expansion section connected in sequence from bottom to top, the length of the Gaussian curve transition section is equal to 3l1, the length of the vertical transfer section is equal to 2l1, the width of the vertical transfer section is equal to l1, the length of the cylindrical transition section is equal to 0.5l1, the minimum width of the cylindrical transition section is equal to 1.05l1, the length of the conical vibration expansion section is equal to 0.5l1, the minimum width of the conical vibration expansion section is equal to 1.2l1, and the taper of the conical vibration expansion section is equal to 1:10.

[0012] According to some embodiments of the present invention, there is a rounded corner with a radius of R1 between the Gaussian curve transition section and the vertical transfer section, there is a rounded corner with a radius of R2 between the vertical transfer section and the cylindrical transition section, and there is a rounded corner with a radius of R3 between the cylindrical transition section and the conical vibration expansion section.

[0013] According to some embodiments of the present invention, R1 is equal to one-sixth of the vertical dimension of the horizontal rod, R2 is equal to one-eighth of the vertical dimension of the horizontal rod, and R3 is determined by the equivalent diameter D1 and length l3 of the cross section of the cylindrical transition section, the equivalent diameter D2 and length l4 of the cross section at the middle position of the cylindrical transition section, and the vibration amplification coefficient N.

[0014] An ultrasonic vibration horn suitable for high-speed broaching of small-module cylindrical gears according to an embodiment of the present invention has at least the following beneficial effects:

[0015] (1) The piezoelectric actuator generates axial resonant vibration, which causes the first vertical rod and the second vertical rod to generate bending vibration. The existence of the first vertical rod and the second vertical rod generates axial and bending non-resonant vibration, which realizes the coupled vibration in the cutting speed direction and the cutting depth direction during the gear machining process, thereby improving the material removal efficiency, the tool life and the surface quality of the workpiece;

[0016] (2) Based on the ultrasonic vibration amplitude under multi-modal testing, the process parameters and ultrasonic vibration amplitude are optimized to improve the processing efficiency and processing accuracy.

[0017] Additional aspects and advantages of the present invention will be set forth in part in the description which follows and, in part, will be obvious from the description which follows, or may be learned by practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] The present invention will be further described below with reference to the accompanying drawings and embodiments, in which:

[0019] Figure 1 A schematic diagram of the structure of an embodiment of the present invention;

[0020] Figure 2 Schematic diagram of the horizontal rod vibration waveform of an embodiment of the present invention

[0021] Figure 3 This is a schematic diagram of the installation of an embodiment of the present invention.

[0022] Figure Number:

[0023] Gear 100, connecting member 101;

[0024] fixture 200;

[0025] Broach 300;

[0026] Horizontal rod 400, mounting hole 401, piezoelectric actuator 402, mounting slot 403, matching positioning section 410, first vibration fixing section 420, vibration transmission section 430, second vibration fixing section 440;

[0027] First vertical rod 500, Gaussian curve transition section 501, vertical transmission section 502, cylindrical transition section 503, conical vibration expansion section 504;

[0028] A second vertical rod 600 . DETAILED DESCRIPTION

[0029] The following describes embodiments of the present invention in detail. Examples of the embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are intended only to explain the present invention and are not to be construed as limiting the present invention.

[0030] In the description of the present invention, it should be understood that descriptions involving orientation, such as the orientation or positional relationship indicated by up, down, etc., are based on the orientation or positional relationship shown in the accompanying drawings, and are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as a limitation on the present invention.

[0031] In the description of the present invention, "a plurality" refers to more than two. The use of "first" or "second" is solely for the purpose of distinguishing technical features and should not be construed as indicating or implying relative importance, or implicitly indicating the number of the indicated technical features, or implicitly indicating the order of the indicated technical features.

[0032] In the description of the present invention, unless otherwise clearly defined, terms such as setting, installing, and connecting should be understood in a broad sense, and technicians in the relevant technical field can reasonably determine the specific meanings of the above terms in the present invention based on the specific content of the technical solution.

[0033] Reference Figures 1 to 3As shown, an embodiment of the present invention is an ultrasonic vibration amplitude transformer suitable for high-speed broaching of small-module cylindrical gears. It is used to drive the vibration of the fixture 200 that fixes the gear 100. A broach 300 is inserted into the gear 100. The broach 300 is driven by hydraulic equipment to perform broaching on the gear 100. The ultrasonic vibration amplitude transformer includes: a horizontal rod 400, a first vertical rod 500, and a second vertical rod 600. Two mounting holes 401 are symmetrically provided on the horizontal rod 400. The mounting holes 401 extend in the vertical direction. A connecting member 101 for fixing the horizontal rod 400 to a horizontal support surface is inserted into the mounting hole 401. The connecting member 101 can be a bolt. A piezoelectric actuator 402 is provided on the portion of the horizontal rod 400 located between the two mounting holes 401 to drive the horizontal rod 400 to vibrate. The piezoelectric actuator 402 converts electrical energy into mechanical energy that causes the horizontal rod 400 to vibrate. The structure of the piezoelectric actuator 402 is prior art and will not be described in detail. The lower end of the first vertical rod 500 is welded to the horizontal rod 400; the lower end of the second vertical rod 600 is welded to the horizontal rod 400. The size of the second vertical rod 600 is 0.9 times that of the first vertical rod 500. The distance from the connection point between the first vertical rod 500 and the horizontal rod 400 to the connection point between the second vertical rod 600 and the horizontal rod 400 is an odd-integer multiple of half the wavelength of the resonant wave in the horizontal rod 400. The upper ends of the first vertical rod 500 and the second vertical rod 600 are respectively connected to the ends of the clamp 200 of the fixed gear 100. Because the vertical height of the first vertical rod 500 is higher than that of the second vertical rod 600, after vibration transmission, the vibration amplitudes output by the first vertical rod 500 and the second vertical rod 600 at the same time will be significantly different, and the structural vibration peaks will occur at different times. A peak difference is formed between the first vertical rod 500 and the second vertical rod 600, thereby increasing the amplitude of the entire assembly consisting of the clamp 200, the ultrasonic vibration amplitude transformer, and the broach 300. It is foreseeable that by increasing the thickness of the gasket between the second vertical rod 600 and the clamp 200, the clamp 200 can be kept in a horizontal state during processing. The horizontal rod 400, the first vertical rod 500, and the second vertical rod 600 are all made of titanium alloy. Titanium alloy has high fatigue resistance and low acoustic impedance, which forms a large amplitude vibration. The material loss during operation is small, and it can withstand large vibration speeds and displacement amplitudes.

[0034] Reference Figures 1 to 3As shown, it can be understood that the horizontal rod 400 includes two mating positioning sections 410, a first vibration fixing section 420, a plurality of vibration transmission sections 430, and a second vibration fixing section 440. The two mating positioning sections 410 are respectively located on the side away from each other of the two mounting holes 401, the first vibration fixing section 420 is located between the mounting hole 401 and the piezoelectric actuator 402, and the first vibration fixing section 420 is connected to the first vertical rod 500, the second vibration fixing section 440 is located between the mounting hole 401 and the piezoelectric actuator 402, and the second vibration fixing section 440 is connected to the second vertical rod 600, and the plurality of vibration transmission sections 430 are located between each adjacent group of piezoelectric actuators 402.

[0035] Reference Figures 1 to 3 As shown, it can be understood that the length of the positioning section 410 is defined as l1, l1 = 1000λψ1, and the calculation formula of the excitation frequency f0 is: Where l2 is the spacing between the teeth on the broach, ψ1 is equal to the excitation frequency when the broach 300 cutting speed v is 1m / min, 5m / min, 10m / min, 20m / min, 25m / min, and 30m / min, f0 is the excitation frequency that minimizes the vibration amplitude of the ultrasonic vibration amplitude transformer composed of the horizontal rod 400, the first vertical rod 500, and the second vertical rod 600, and the vertical dimension of the horizontal rod 400 is 10 to 14 mm. Due to the periodic excitation of the broaching teeth cutting in and out, in order to reduce the vibration of the machine tool worktable caused by this excitation, a cutting processing test was conducted on the entire broaching device. The broaching speed v of the broach 300 was set to 1m / min, 5m / min, 10m / min, 20m / min, 25m / min, and 30m / min, respectively. The vibration amplitudes generated by the corresponding speeds were measured as ξ1, ξ2, L, ξ i ,L,ξ7, then calculate the excitation frequencies of the cutting teeth into and out as f1, f2, L, f i ,L,f7, comparative analysis to determine ξ1,ξ2,L,ξ i The excitation frequency calculated from the broaching speed corresponding to the minimum vibration amplitude is set to ψ1. Setting the length of the mating positioning segment 410 to a multiple of the wavelength prevents vibration from being transmitted simultaneously to the mating positioning segment 410 and the top of the first vertical rod 500, thereby reducing energy loss.

[0036] Reference Figures 1 to 3 As shown, it is understood that the diameter of the mounting hole 401 is equal to 0.01l1. The mounting hole 401 is used for connecting the connector 101 and plays a fixing role. Therefore, the size of the mounting hole 401 should be as small as possible under the premise of meeting the structural strength to reduce the impact on the vibration transmission in the horizontal rod 400.

[0037] Reference Figures 1 to 3As shown, it can be understood that there are three groups of piezoelectric actuators 402 spaced apart in the left-right direction. One group of piezoelectric actuators 402 includes two piezoelectric actuators 402 symmetrically arranged up and down with the horizontal rod 400 as the center. The horizontal rod 400 is provided with a plurality of mounting grooves 403 for corresponding piezoelectric actuators 402 to be inserted. The length of the mounting grooves 403 is equal to 0.2l1. The six piezoelectric actuators 402 are combined to generate vibration in both the left-right direction and the up-down direction. The vibration mode is as follows Figure 2 shown.

[0038] Reference Figures 1 to 3 As shown, it can be understood that the length of the first and second vibration fixing sections 420 and 440 is equal to 20l, and the length of the vibration transmission section 430 is equal to 1. The vibration transmission section 430 is used to transmit and superimpose the vibrations generated by the piezoelectric actuator 402, so its length does not need to be excessive. The first and second vibration fixing sections 420 and 440 are used to fix the first and second vertical rods 500 and 600, respectively.

[0039] Reference Figures 1 to 3 As shown, it can be understood that the six piezoelectric actuators 402 are all located at the peaks of the overall vibration mode of the ultrasonic vibration horn, so that the vibrations generated by the six piezoelectric actuators 402 can be superimposed to amplify the amplitude. The mounting hole 401 is located at a node where the vibration amplitude of the overall vibration mode of the ultrasonic vibration horn is zero. Because the connector 101 in the mounting hole 401 is fixed, locating the mounting hole 401 at the node where the vibration amplitude is zero can prevent the connector 101 from obstructing the vibration of the ultrasonic vibration horn, which is conducive to increasing the vibration amplitude.

[0040] Reference Figures 1 to 3As shown, it can be understood that the first vertical rod 500 includes, from bottom to top, a Gaussian curve transition section 501, a vertical transmission section 502, a cylindrical transition section 503, and a conical vibration amplification section 504. The Gaussian curve transition section 501 has a length of 3l1, the vertical transmission section 502 has a length of 2l1, a width of l1, the cylindrical transition section 503 has a length of 0.5l1, and a minimum width of 1.05l1. The conical vibration amplification section 504 has a length of 0.5l1, a minimum width of 1.2l1, and a taper of 1:10. The stepped shape of the first vertical rod 500 results in significant stress concentration at the cross-sectional transition, and fatigue fracture is prone to occur in details near the transition. The use of Gaussian curves, arcs, and tapered transitions can reduce stress concentration and simultaneously bring the actual resonant frequency of the ultrasonic vibration horn closer to the theoretical value. The second vertical rod 600 has the same structural shape as the first vertical rod 500, and its dimensions are 0.9 times that of the first vertical rod 500. Vibration is sequentially transmitted through the Gaussian curve transition section 501, the vertical transmission section 502, the cylindrical transition section 503, and the conical vibration amplification section 504, achieving vertical vibration transmission and amplification, achieving a high vibration velocity that meets the machining requirements of the high-hardness gear 100 workpiece. This results in a faster vibration velocity within a given vibration cycle, improving machining efficiency, precision, and surface quality.

[0041] Reference Figures 1 to 3 As shown, it can be understood that a fillet with a radius of R1 is provided between the Gaussian curve transition section 501 and the vertical transmission section 502, a fillet with a radius of R2 is provided between the vertical transmission section 502 and the cylindrical transition section 503, and a fillet with a radius of R3 is provided between the cylindrical transition section 503 and the conical vibration amplification section 504. The chamfers reduce the curvature of the surface of the first vertical rod 500, thereby reducing stress concentration and increasing service life.

[0042] Reference Figures 1 to 3 As shown, it can be understood that R1 is equal to one-sixth of the vertical dimension of the horizontal rod 400, R2 is equal to one-eighth of the vertical dimension of the horizontal rod 400, and R3 is determined by the equivalent diameter D1 and length l3 of the cross section of the cylindrical transition section 503. R3 is also determined by the equivalent diameter D2 and length l4 of the cross section at the middle position of the cylindrical transition section 503 and the vibration amplification coefficient N. The calculation formula for N is: Then based on Calculate the A value; A is the optimal transition arc radius of the stepped horn. Then, consult the relationship table between the optimal transition arc radius A and the vibration amplification factor N to obtain the β value. Finally, calculate the R3 value based on R3 = β·D1. This ensures that the vibration of the vibration horn is stable and controllable after being acted upon by the ultrasonic transducer.

[0043] The embodiments of the present invention are described in detail above with reference to the accompanying drawings. However, the present invention is not limited to the above embodiments. Various changes can be made within the knowledge of ordinary technicians in the relevant technical field without departing from the scope of the present invention.

Claims

1. An ultrasonic vibration horn suitable for high-speed broaching of small-module cylindrical gears, used to drive a fixture (200) for fixing a gear (100) to vibrate, wherein a broach (300) is provided in the gear (100), characterized in that: include: A horizontal rod (400), wherein two mounting holes (401) are symmetrically provided on the horizontal rod (400), a connecting piece (101) for fixing the horizontal rod (400) on a horizontal support surface is passed through the mounting holes (401), and a piezoelectric actuator (402) is provided on a portion of the horizontal rod (400) located between the two mounting holes (401) to drive the horizontal rod (400) to vibrate; a first vertical rod (500), wherein the lower end of the first vertical rod (500) is connected to the horizontal rod (400); A second vertical rod (600), the lower end of the second vertical rod (600) is connected to the horizontal rod (400), the size of the second vertical rod (600) is 0.9 times the size of the first vertical rod (500), and the distance from the connection point between the first vertical rod (500) and the horizontal rod (400) to the connection point between the second vertical rod (600) and the horizontal rod (400) is an odd multiple of half the wavelength of the resonant wave in the horizontal rod (400); the upper ends of the first vertical rod (500) and the second vertical rod (600) are respectively connected to the two ends of the clamp (200) of the fixed gear (100).

2. The ultrasonic vibration horn suitable for high-speed broaching of small-module cylindrical gears according to claim 1, characterized in that: The horizontal rod (400) comprises two matching positioning sections (410), a first vibration fixing section (420), a plurality of vibration transmission sections (430), and a second vibration fixing section (440). The two matching positioning sections (410) are respectively located on the sides of the two mounting holes (401) that are away from each other. The first vibration fixing section (420) is located between the mounting hole (401) and the piezoelectric actuator (402), and the first vibration fixing section (420) is connected to the first vertical rod (500). The second vibration fixing section (440) is located between the mounting hole (401) and the piezoelectric actuator (402), and the second vibration fixing section (440) is connected to the second vertical rod (600). The plurality of vibration transmission sections (430) are located between each adjacent group of the piezoelectric actuators (402).

3. The ultrasonic vibration horn suitable for high-speed broaching of small-module cylindrical gears according to claim 2, characterized in that: The length of the matching positioning section (410) is defined as l1, l1=1000λψ1, and the calculation formula of the excitation frequency f0 is: wherein l2 is the spacing between the teeth on the broach, ψ1 is equal to when the cutting speed v of the broach (300) is 1 m / min, 5 m / min, 10 m / min, 20 m / min, 25 m / min, 30 m / min, wherein f0 is the excitation frequency that minimizes the vibration amplitude of the ultrasonic vibration transformer, λ is the wavelength of the vibration generated by the piezoelectric actuator (402) propagating in the horizontal rod (400), and the vertical dimension of the horizontal rod (400) is 10 to 14 mm.

4. The ultrasonic vibration horn suitable for high-speed broaching of small-module cylindrical gears according to claim 3, characterized in that: The diameter of the mounting hole (401) is equal to 0.01l1.

5. The ultrasonic vibration horn suitable for high-speed broaching of small-module cylindrical gears according to claim 4, characterized in that: The piezoelectric actuator devices (402) are arranged in multiple groups at intervals, and a group of the piezoelectric actuator devices (402) includes two piezoelectric actuator devices (402) symmetrically arranged up and down with the horizontal rod (400) as the center. The horizontal rod (400) is provided with multiple installation grooves (403) for corresponding piezoelectric actuator devices (402) to be embedded, and the length of the installation grooves (403) is equal to 0.2l1.

6. The ultrasonic vibration horn suitable for high-speed broaching of small-module cylindrical gears according to claim 5, characterized in that: The lengths of the first vibration fixing section (420) and the second vibration fixing section (440) are equal to 20l1, and the length of the vibration transmission section (430) is equal to l1.

7. The ultrasonic vibration horn suitable for high-speed broaching of small-module cylindrical gears according to claim 6, characterized in that: The piezoelectric actuator (402) is located at the wave crest of the overall vibration mode of the ultrasonic vibration horn, and the mounting hole (401) is located at a node where the vibration amplitude of the overall vibration mode of the ultrasonic vibration horn is zero.

8. The ultrasonic vibration horn suitable for high-speed broaching of small-module cylindrical gears according to claim 7, characterized in that: The first vertical rod (500) comprises a Gaussian curve transition section (501), a vertical transmission section (502), a cylindrical transition section (503), and a conical vibration expansion section (504) which are sequentially connected from bottom to top. The Gaussian curve transition section (501) has a length of 3l1, the vertical transmission section (502) has a length of 2l1, the vertical transmission section (502) has a width of l1, the cylindrical transition section (503) has a length of 0.5l1, the minimum width of the cylindrical transition section (503) is 1.05l1, the length of the conical vibration expansion section (504) is 0.5l1, the minimum width of the conical vibration expansion section (504) is 1.2l1, and the taper of the conical vibration expansion section (504) is 1:

10.

9. The ultrasonic vibration horn suitable for high-speed broaching of small-module cylindrical gears according to claim 8, characterized in that: There is a rounded corner with a radius of R1 between the Gaussian curve transition section (501) and the vertical transfer section (502), there is a rounded corner with a radius of R2 between the vertical transfer section (502) and the cylindrical transition section (503), and there is a rounded corner with a radius of R3 between the cylindrical transition section (503) and the conical vibration expansion section (504).

10. The ultrasonic vibration horn suitable for high-speed broaching of small-module cylindrical gears according to claim 9, characterized in that: R1 is equal to one-sixth of the vertical dimension of the horizontal rod (400), R2 is equal to one-eighth of the vertical dimension of the horizontal rod (400), and R3 is determined by the equivalent diameter D1 and length l3 of the cross section of the cylindrical transition section (503), the equivalent diameter D2 and length l4 of the cross section at the middle position of the cylindrical transition section (503), and the vibration amplification coefficient N.

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