A vibration-damping cutting tool device based on phononic crystals and its design method

Abstract

The present invention discloses a vibration damping tool device based on phononic crystals and its design method. Based on the transfer matrix theory, the mathematical relationships of the state parameters at both ends of a certain shaft section and the joint surface of two shaft sections are respectively determined to obtain the transfer matrix of the overall tool device system. Using the boundary conditions, the natural vibration analysis of the tool system is carried out to determine the natural frequency of the tool system. Based on the phononic crystal theory, with the natural frequency of the tool system determined by the transfer matrix method as the target value, the geometric parameters, material parameters and arrangement forms of the phononic crystals are designed. A phononic crystal is provided at the tool shank, and the phononic crystal includes a phononic crystal ring and a phononic crystal core. The phononic crystal ring wraps the phononic crystal core, and the phononic crystals are periodically distributed at a set distance in the sealed space. By adjusting the material properties of the annular elastic body and the cylindrical mass block in the cavity of the tool shank, the eccentricity problem during tool operation will not be caused, and it has a good vibration damping effect.

Description

Technical Field

[0001] The present invention relates to the field of tool design, and particularly to a vibration damping tool device based on phononic crystals and a design method thereof. Background Art

[0002] With the continuous development of the entire manufacturing industry, the machining accuracy requirements for parts are getting higher and higher. Tool vibration affects the machining quality of workpieces, and the emergence of vibration damping tools has greatly improved this problem. Currently, the methods for vibration suppression in vibration damping tool systems can be divided into cutting parameter adjustment, active vibration damping technology, and passive vibration damping technology.

[0003] Cutting parameter adjustment: Predict the machining stability in advance, and by adjusting the cutting angle, cutting depth, spindle speed, etc. of the tool, change the stiffness and damping of the machine tool system, so as to achieve vibration suppression; Active vibration damping technology: Rely on corresponding sensors or monitors to monitor and judge the tool vibration signal during the cutting process in real time, and rely on external actuators to make real-time adjustments, so as to achieve vibration suppression; Passive vibration damping technology: Mainly by changing the tool's own structure and materials or attached vibration absorption or damping devices, change the stiffness and damping of the tool, and achieve vibration suppression.

[0004] Although a variety of vibration damping tools have been developed according to different vibration damping technologies and machining requirements, most of the vibration damping tools in engineering applications adopt passive vibration damping technology. Because compared with other vibration damping technologies, passive vibration damping technology has a simple structure, low cost, and reliable vibration damping effect. Although passive vibration damping tools have been widely used in practice, some efficient passive vibration damping technologies are mostly applied to large-diameter vibration damping boring bars and vibration damping turning tools, and there is relatively little research on the vibration damping of long aspect ratio milling cutters or turning tools. Especially for some deep cavity thin-walled complex parts, when the tool's aspect ratio becomes larger, the chatter phenomenon is obvious during the milling process, greatly reducing the machining accuracy of the workpiece and seriously restricting the development of the industry. Summary of the Invention

[0005] The purpose of the present invention is to provide a vibration damping tool device based on phononic crystals and a design method thereof, to reduce the vibration of the tool device with a large aspect ratio during machining, and thus improve the machining accuracy.

[0006] To achieve the above purpose, the present invention provides the following technical solutions: A design method for a vibration damping tool device based on phononic crystals, comprising the following steps:

[0007] Based on the transfer matrix theory, respectively determine the mathematical relationship between the state parameters at both ends of a certain shaft section and the joint surface of two shaft sections, obtain the transfer matrix of the overall tool device system, and use the boundary conditions to perform the natural vibration analysis of the tool system to determine the natural frequency of the tool system;

[0008] Based on the phonon crystal theory, with the natural frequency of the tool system determined by the transfer matrix method as the target value, the geometric parameters, material parameters, and arrangement forms of the phonon crystal are designed.

[0009] The state parameters include displacement, rotation angle, bending moment, and shear force.

[0010] Based on the transfer matrix theory, the tool shank, tool bar, and end are modeled. Combining with the boundary conditions, the natural vibration analysis of the tool system is carried out to determine the natural frequency of the tool system. The specific steps are as follows: The transfer matrix at the left and right ends of a certain shaft segment is:

[0011]

[0012] Among them,

[0013]

[0014] And the transfer matrix at the joint surface between two shaft segments with different cross-sectional areas is:

[0015]

[0016] The transfer matrix relationship of the three-step stepped shaft model is:

[0017] T = T3P2T2P1T1

[0018] Among them, l is the length of the shaft segment, R is the radius of the shaft segment, the moment of inertia is I, ρ is the density, ω is the natural frequency, E is the elastic modulus, c l is the velocity of the longitudinal wave in the shaft, i represents the position of different shaft segments, T i represents the transfer matrix at the left and right ends of the shaft segment, T is the final transfer matrix model, k b is the derived expression;

[0019] Based on the total transfer matrix T of the tool system, using the boundary conditions, there are three boundary conditions at both ends of the model, namely fixed, simply supported, and free. According to different boundary conditions, the frequency equation is obtained using the total transfer matrix to determine the natural frequency and modal vibration mode of the tool system.

[0020] Based on the phonon crystal theory, with the natural frequency of the tool system as the target value, when designing the geometric parameters, material parameters, and arrangement forms of the phonon crystal, the phonon crystal is equivalent to a spring-mass system. The basic formula for equivalent of the phonon crystal to a spring-mass system is as follows:

[0021]

[0022] Where k is the stiffness of the phononic crystal ring, and m is the mass of the phononic crystal core. Taking the natural frequency of the tool system as the target value, based on the basic theory of phononic crystals, the natural frequency of the equivalent spring-mass system is made consistent with the natural frequency of the tool system, and the size, structure, and material parameters of the phononic crystal are designed accordingly.

[0023] A vibration-damping tool device based on phononic crystals, designed according to the above design method, includes a tool holder, a tool shank, and a tool tip connected in sequence; the inside of the tool shank is hollow, a sealed space is formed inside the tool shank, and phononic crystals are provided at the tool shank. The phononic crystals include a phononic crystal ring and a phononic crystal core; the phononic crystal ring wraps the phononic crystal core, and the phononic crystals are periodically distributed in the sealed space at a set distance, and a void area is provided between adjacent phononic crystal materials.

[0024] The phononic crystal ring is a circular elastic body, and the phononic crystal core is a cylindrical mass block. The phononic crystal ring and the phononic crystal core form an integral structure.

[0025] The phononic crystal ring and the phononic crystal core have different densities. The phononic crystal ring is made of rubber or resin material, and the phononic crystal core is made of copper or lead.

[0026] The void area is filled with damping oil.

[0027] The inner surface of the phononic crystal ring is tightly bonded to the outer surface of the phononic crystal core by strong glue.

[0028] Compared with the prior art, the beneficial effects of the present invention are as follows: Based on the transfer matrix theory, the transfer matrix of the overall tool system is determined, combined with the boundary conditions, and through the natural vibration analysis, the natural frequency of the tool system is determined. Taking the natural frequency of the tool system as the target value, based on the basic theory of phononic crystals, the geometric parameters, material parameters, and arrangement form of the phononic crystal are designed to construct a vibration-damping tool device using phononic crystals;

[0029] The present invention uses the tool shank as the design carrier of the phononic crystal. Utilizing the local resonance characteristics of the phononic crystal, without changing the overall structure of the tool, the vibration-damping effect of the tool on low-frequency vibration is effectively improved. A phononic crystal structure is designed in the inner cavity of the tool shank. The structure is simple and feasible, and has a relatively wide vibration suppression frequency band. By adjusting the installation quantity of the phononic crystals in the inner cavity of the tool shank, and adjusting the stiffness of the circular elastic body and the mass of the cylindrical mass block, the effect of adjusting the position of the vibration attenuation band gap and the width of the attenuation band gap frequency band can be achieved, effectively suppressing vibration, which is helpful to improve the machining accuracy. Description of the Drawings

[0030] Figure 1 It is a flow schematic diagram of a tool device using phononic crystals for vibration damping according to the present invention.

[0031] Figure 2Schematic diagram of a simplified model of a three - step shaft for a tool handle, tool shank, and tool tip.

[0032] Figure 3 Schematic diagram of the tool vibration - damping structure of the present invention.

[0033] Figure 4a Stereo structure diagram of a phononic crystal.

[0034] Figure 4b Side view of a phononic crystal.

[0035] Among them, 1 is the tool handle, 2 is the tool shank, 3 is the phononic crystal ring, 4 is the phononic crystal core, 5 is the void area, and 6 is the tool tip. Detailed implementation mode

[0036] The present invention will be further described below with reference to the accompanying drawings.

[0037] The present invention provides a tool device using a phononic crystal for vibration damping, as Figure 1 shown, and is specifically implemented according to the following steps: Establish a simplified model of a three - step shaft for a tool handle, tool shank, and tool tip, as Figure 2 the model shown. Based on the transfer - matrix theory, model the tool handle, tool shank, and tool tip, calculate the mathematical relationships of the state parameters on both sides of the three shaft segments respectively, then calculate the mathematical relationships of the state parameters at the joint surface where the cross - sectional area changes suddenly, determine the transfer matrix of the overall tool device system, and combine the boundary conditions to conduct the natural vibration analysis of the tool system to determine the natural frequency of the tool system; taking the natural frequency of the tool system as the target value, make the natural frequency of the equivalent spring - mass system basically the same as the natural frequency of the tool system, and thus design the size, structure, material parameters, and layout form of the phononic crystal.

[0038] Based on the transfer - matrix theory, model the tool handle, tool shank, and tool tip, and combine the boundary conditions to conduct the natural vibration analysis of the tool system to determine the natural frequency of the tool system. The specific steps are as follows: The transfer matrix between the left and right ends of a certain shaft segment is:

[0039]

[0040] Among them,

[0041]

[0042] And the transfer matrix at the joint surface between two shaft segments with different cross - sectional areas is:

[0043]

[0044] The transfer - matrix relationship of the three - step shaft model is:

[0045] T = T3P2T2P1T1

[0046] where \(l\) is the length of the shaft segment, \(R\) is the radius of the shaft segment, the moment of inertia is \(I\), \(\rho\) is the density, \(\omega\) is the natural frequency, \(E\) is the elastic modulus, \(c\) l is the velocity of the longitudinal wave in the shaft, \(i\) represents different shaft segment positions, \(T\) i represents the transfer matrix at both ends of the shaft segment, \(T\) is the final transfer matrix model, \(k\) b is the derived expression;

[0047] Based on the total transfer matrix \(T\) of the tool system, using the boundary conditions, there are three boundary conditions at both ends of the model, namely fixed, simply supported and free. According to different boundary conditions, the frequency equation is obtained using the total transfer matrix to determine the natural frequency and modal vibration mode of the tool system;

[0048] Based on the phonon crystal theory, with the natural frequency of the tool system as the target value, the geometric parameters, material parameters and layout form of the phonon crystal are designed. At this time, the phonon crystal is equivalent to a spring-mass system. The basic formula for the phonon crystal equivalent to a spring-mass system is as follows:

[0049]

[0050] In the formula, \(k\) is the stiffness of the phonon crystal ring, \(m\) is the mass of the phonon crystal core. With the natural frequency of the tool system as the target value, based on the basic theory of the phonon crystal, the natural frequency of the equivalent spring-mass system is made consistent with the natural frequency of the tool system, and thus the size, structure and material parameters of the phonon crystal are designed.

[0051] Figure 3 The schematic diagram of the vibration-damping tool structure of the present invention is shown as follows. As Figure 3 shown, a tool vibration-damping device based on a phonon crystal includes a tool holder 1, a tool shank 2, a phonon crystal ring 3, a phonon crystal core 4, a void region 5 and a tool tip 6. The phonon crystal includes a phonon crystal ring 3 and a phonon crystal core 4. The tool holder 1 and the tool tip 6 are respectively arranged at both ends of the tool shank 2, so that a strictly sealed space is formed inside the tool shank 2. The outer surface of the phonon crystal ring 3 is closely attached to the inner wall of the tool shank cavity, and the inner surface of the phonon crystal ring 3 is closely pasted to the outer surface of the phonon crystal core 4 by strong glue. The phonon crystal ring 3 wraps the phonon crystal core 4 to form an integral structure. The phonon crystal rods are periodically distributed in the tool shank cavity at a set distance, and the rest is the void region filled with damping oil; by adjusting the installation quantity of the phonon crystal in the tool shank 2 cavity and the material parameters of the phonon crystal ring 3 and the phonon crystal core 4, the effect of adjusting the position of the vibration attenuation band gap and the width of the attenuation band gap frequency band can be achieved, effectively suppressing vibration and improving machining accuracy.

[0052] Figure 4a and Figure 4bThe figure shows a schematic diagram of the phononic crystal structure. The phononic crystal structure can be described as a toroidal elastomer and a cylindrical mass block. The outer surface of the toroidal elastomer is in close contact with the inner wall of the tool shank cavity, and the inner surface of the toroidal elastomer is adhered to the outer surface of the cylindrical mass block with strong glue. The toroidal elastomer wraps the cylindrical mass block to form a complete cylindrical structure. The phononic crystals are periodically distributed in the tool shank cavity at a certain distance, and damping oil is added to the void area 5. The tool holder 1 and the tool tip 6 play a role in sealing the inner cavity of the tool shank 2.

[0053] Based on the local resonance principle of phononic crystals, the present invention can achieve vibration suppression of the tool device near its natural frequency. By utilizing the periodic characteristics of phononic crystals, a locally resonant phononic crystal structure is designed, which can be equivalent to a spring-mass system to effectively suppress the overall vibration of the tool. The phononic crystal ring 3 in the phononic crystal structure is made of elastic materials such as resin or rubber, such as epoxy resin or vulcanized rubber, which act as springs; the phononic crystal core 4 in the phononic crystal structure is made of metal materials such as copper, aluminum, and lead. In order to ensure the accuracy of the phononic crystal structure during the manufacturing process, a basic unit mold is designed to guarantee the forming quality of the phononic crystal structure.

[0054] In summary, according to the simplified tool model and the transfer matrix theory, combined with the boundary conditions, the natural frequency of the tool system is calculated using the basic transfer matrix theory. Taking the natural frequency as the target value, the geometric parameters, material parameters, and layout form of the phononic crystal are designed based on the basic theory of phononic crystals. A phononic crystal structure is added to the inner cavity of the tool shank, and a simple and feasible phononic crystal structure is used to achieve good vibration damping effects of "low bandgap" and "wide bandgap" for the tool device.

[0055] The above content is only to illustrate the technical idea of the present invention and cannot be used to limit the protection scope of the present invention. Any modification made on the basis of the technical solution according to the technical idea proposed by the present invention falls within the protection scope of the claims of the present invention.

Claims

1. A design method of a vibration damping tool device based on phononic crystals, characterized in that, Including the following steps: Based on the transfer matrix theory, respectively determine the mathematical relationship between the state parameters at both ends of a certain shaft section and the joint surface of two shaft sections, obtain the transfer matrix of the overall tool device system, and use the boundary conditions to conduct the natural vibration analysis of the tool system to determine the natural frequency of the tool system; Based on the transfer matrix theory, model the tool shank, tool rod and tool head, and combine the boundary conditions to conduct the natural vibration analysis of the tool system to determine the natural frequency of the tool system. The specific steps are as follows: Among them, the transfer matrix at the left and right ends of a certain shaft section is: Among them, And the transfer matrix at the joint surface between two shaft sections with different cross-sectional areas is: The transfer matrix relationship of the three-step stepped shaft model is: T = T3P2T2P1T1 where l is the length of the shaft segment, R is the radius of the shaft segment, the moment of inertia is I, ρ is the density, ω is the natural frequency, E is the elastic modulus, c l is the velocity of the longitudinal wave in the shaft, i represents the position of different shaft segments, T i represents the transfer matrix at both ends of the shaft segment, T is the final transfer matrix model, k b is the derived expression; Based on the total transfer matrix T of the tool system, using the boundary conditions, there are three boundary conditions at both ends of the model, namely fixed, simply supported and free. According to different boundary conditions, use the total transfer matrix to obtain the frequency equation to determine the natural frequency and modal vibration mode of the tool system; Based on the phononic crystal theory, with the natural frequency of the tool system determined by the transfer matrix method as the target value, design the geometric parameters, material parameters and arrangement form of the phononic crystal.

2. The design method of the vibration damping tool device based on phononic crystals according to claim 1, characterized in that, The state parameters include displacement, rotation angle, bending moment and shear force.

3. The design method of a vibration damping tool device based on phononic crystals according to claim 1, characterized in that, Based on the phononic crystal theory, with the natural frequency of the tool system as the target value, when designing the geometric parameters, material parameters and arrangement form of the phononic crystal, the phononic crystal is equivalent to a spring-mass system. The basic formula for the phononic crystal to be equivalent to a spring-mass system is as follows: In the formula, k is the stiffness of the phononic crystal ring (3), and is the mass of the phononic crystal core (4). With the natural frequency of the tool system as the target value, based on the basic theory of phononic crystals, make the natural frequency of the equivalent spring-mass system consistent with the natural frequency of the tool system, and thus design the size, structure and material parameters of the phononic crystal.

4. A vibration damping tool device based on phononic crystals, characterized in that, Designed according to the design method described in any one of claims 1 to 3, including a tool shank (1), a tool rod (2) and a tool head (6) connected in sequence; the inside of the tool rod (2) is hollow, a sealed space is formed inside the tool rod (2), and a phononic crystal is provided at the tool rod (2). The phononic crystal includes a phononic crystal ring (3) and a phononic crystal core (4); the phononic crystal ring (3) wraps the phononic crystal core (4), and the phononic crystals are periodically distributed at a set distance in the sealed space, and a gap area (5) is provided between adjacent phononic crystal materials; the phononic crystal ring (3) is a circular ring-shaped elastic body, the phononic crystal core (4) is a cylindrical mass block, and the phononic crystal ring (3) and the phononic crystal core (4) form an integral structure; the gap area (5) is filled with damping oil.

5. The vibration damping tool device based on phononic crystals according to claim 4, characterized in that, The density of the phononic crystal ring (3) and the phononic crystal core (4) is different. The phononic crystal ring (3) is made of rubber or resin material, and the phononic crystal core (4) is made of copper or lead.

6. The vibration damping tool device based on phononic crystals according to claim 4, characterized in that, The inner surface of the phononic crystal ring (3) is tightly bonded to the outer surface of the phononic crystal core (4) by strong glue.

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