Design method of longitudinal bending ultrasonic vibration assisted deep hole drilling device

Abstract

The application discloses a design method of a longitudinal-bending ultrasonic vibration assisted deep hole drilling device, which comprises the following steps: selecting a working frequency of the longitudinal-bending ultrasonic vibration assisted deep hole drilling device and materials of each part of the device; sequentially performing transducer design to determine the length and diameter of a front cover plate, a middle cover plate and a rear cover plate and the position of a piezoelectric sheet; performing amplitude rod design to determine the length and diameter of each section of the amplitude rod; constructing a geometric model according to the size of the transducer and the amplitude rod, a bolt pre-tightening structure and a connecting structure of a tool and the device, the device and a machine tool; outputting trajectory modeling; and performing structure optimization and frequency degeneration of the longitudinal-bending ultrasonic vibration assisted deep hole drilling device based on finite element simulation. Thus, the general structure design of the double-excitation longitudinal-bending ultrasonic vibration assisted deep hole drilling device is realized, the frequency degeneration of the longitudinal vibration and the bending vibration is achieved and the amplification coefficient reaches the maximum, so that the design problem of the double-excitation longitudinal-bending same-frequency vibration device is solved.

Description

Technical Field

[0001] This invention relates to the field of CNC machining, and in particular to a design method for a longitudinal bending ultrasonic vibration-assisted deep hole drilling device. Background Technology

[0002] Deep hole machining plays a crucial role in aerospace, defense, and other fields. However, traditional deep hole machining techniques suffer from reduced machining accuracy and poor surface quality due to excessive cutting forces and heat. Longitudinal bending ultrasonic vibration-assisted drilling technology can effectively solve these problems. The longitudinal bending composite generates an elliptical trajectory output. The design of the ultrasonic elliptical vibration longitudinal bending composite device is key and fundamental in generating this elliptical vibration trajectory. Currently, the design of longitudinal bending ultrasonic vibration-assisted deep hole drilling devices is primarily based on specific design requirements, leading to some degree of randomness in the design process. A universal design methodology has not been developed to effectively guide the design of such devices, and current research rarely addresses the optimization of structural parameters for dual-excitation devices. For dual-excitation longitudinal bending ultrasonic vibration-assisted deep hole drilling devices, the design challenge lies in minimizing the frequencies of longitudinal and bending vibrations and maximizing their amplification factor, considering factors such as tool installation, flange fixation, and piezoelectric element insertion. Summary of the Invention

[0003] Purpose of the invention: In order to overcome the shortcomings of the prior art, the purpose of this invention is to provide a design method for a longitudinal bending ultrasonic vibration-assisted deep hole drilling device.

[0004] Technical solution: The design method of the longitudinal bending ultrasonic vibration assisted deep hole drilling device provided by the present invention includes the following steps: S1. Select the working frequency and materials of each component of the longitudinal bending ultrasonic vibration-assisted deep hole drilling device; S2. Transducer design of longitudinal bending ultrasonic vibration assisted deep hole drilling device, determining the length and diameter of the front cover plate, middle cover plate, and rear cover plate, as well as the position of the piezoelectric sheet; S3. Design of the amplitude transformer of the longitudinal bending ultrasonic vibration-assisted deep hole drilling device, determining the length and diameter of each section of the amplitude transformer; S4. Geometric model construction of longitudinal bending ultrasonic vibration assisted deep hole drilling device: Three-dimensional modeling is carried out based on the dimensions of transducer and amplitude rod, bolt pre-tightening structure, and connection structure between tool and device, and device and machine tool. S5. Modeling of the output trajectory of the longitudinal bending ultrasonic vibration-assisted deep hole drilling device; S6. Structural optimization and frequency degeneracy of longitudinal bending ultrasonic vibration-assisted deep hole drilling device based on finite element simulation.

[0005] Furthermore, the longitudinal bending ultrasonic vibration-assisted deep hole drilling device includes a transducer and a stepped amplitude transformer. The transducer consists of a front cover plate, a middle cover plate, a rear cover plate, electrode plates, longitudinally vibrating piezoelectric ceramic plates, and bending vibrating piezoelectric ceramic plates. The ultrasonic vibration operating frequency, as well as the materials of the amplitude transformer, transducer, electrode plates, piezoelectric ceramic plates, ER clamp, and nut, are determined according to the requirements, and the material parameters, including density, elastic modulus, Poisson's ratio, and sound velocity, are obtained.

[0006] Furthermore, S2 specifically refers to the transducer adopting a single-stage design; During longitudinal vibration, the waveforms at both ends of the transducer are at antinodes. In bending vibration, according to Timoshenko rod theory, one end of the transducer is in a free state and the other end is fixed. The transducer adopts the free-fixed bending vibration frequency equation. Based on the frequency equations of the transducer's longitudinal and bending vibrations, the resonance curves of the longitudinal and bending vibrations are obtained. Following the principle that both the longitudinal and bending vibration orders are controlled to be at least order 2 and require at least two nodes, the longitudinal and bending vibration orders of the transducer, i.e., m and n, are determined. To achieve longitudinal and bending vibrations of the transducer at the same vibration frequency, the intersection point of the curves containing the m-order longitudinal vibration and the n-order bending vibration is found, and the length and diameter of the transducer are determined accordingly. The longitudinally vibrating piezoelectric ceramic sheet is placed at one node, and the other node is used to fix the device. The bending vibrating piezoelectric ceramic sheet is placed at the antinode of the bending vibration waveform, and the connection position between the transducer end and the amplitude transformer is at the antinode of the bending vibration. The piezoelectric ceramic sheet is in the form of a ring, and the outer diameter of the piezoelectric sheet is the same as the outer diameter of the rear end cover. The piezoelectric ceramic sheet for longitudinal vibration is in the form of a whole sheet, while the piezoelectric ceramic sheet for bending vibration is in the form of 1 / 2 or 1 / 4. The lengths and diameters of the front cover plate, middle cover plate, and rear cover plate, as well as the positions of the piezoelectric sheets, are determined based on the intersection of the longitudinal vibration m-order and bending vibration n-order curves and the principle of piezoelectric ceramic sheet placement, thereby completing the transducer design.

[0007] Furthermore, the stepped amplitude transformer can be configured with different numbers of segments depending on the requirements; The section change occurs at the antinode of the bending vibration waveform and at the node of the longitudinal vibration waveform. In the last section of the amplitude transformer, one end of the amplitude transformer must be connected to the tool. In order to maximize the displacement of the tool, the end of the amplitude transformer connected to the tool must be at the antinode. In longitudinal vibration, the waveforms at both ends of each segment of the amplitude transformer are at antinodes. In bending vibration, there are two types of boundary conditions: free-fixed and fixed at both ends. In the last segment of the amplitude transformer, since the boundary conditions are the same as those of the transducer, the free-fixed frequency equation should be used. In other segments of the amplitude transformer, according to the boundary conditions of the amplitude transformer, the bending vibration in this segment should use the fixed-at-both-ends frequency equation. Based on the frequency equations of the longitudinal and bending vibrations of each segment of the amplitude transformer, the resonance curves of the longitudinal and bending vibrations of each segment are plotted, and the order m of the longitudinal vibration and the order n of the bending vibration of each segment are determined. Based on this, the length and diameter of each segment of the amplitude transformer are determined, thus completing the design of the amplitude transformer.

[0008] Furthermore, in terms of connection method, the longitudinal vibration piezoelectric ceramic ring is pre-tightened to the transducer by bolts, and the bending vibration piezoelectric ceramic ring is glued in 1 / 2 or 1 / 4 form and also pre-tightened to the transducer by bolts, thus completing the design of the bolt pre-tightening structure of the transducer piezoelectric sheet; The cutting tool is connected to the amplitude transformer via an ER collet and nut. The transducer and amplitude transformer are integrated and connected to the machine tool via a flange, thus completing the design of the cutting tool clamping and connection structure with the machine tool. Based on the obtained dimensions of the transducer and amplitude rod, as well as the bolt pre-tightening structure and the connection structure between the tool and the device, and between the device and the machine tool, a three-dimensional initial model is obtained.

[0009] Furthermore, the longitudinal and bending vibration resonant frequencies are the same. It is assumed that the amplitudes applied to the longitudinally vibrating piezoelectric ceramic sheet and the bending vibrating piezoelectric ceramic sheet are the same. α and β are the initial phases of the vibration in the radial and axial directions, respectively. d is the outer diameter of the piezoelectric ceramic sheet, and L is the distance from the piezoelectric sheet to the tip of the tool. The displacement excited by the longitudinally vibrating piezoelectric ceramic sheet is: D L =Asin(ωt+β; The displacement excited by the bending vibration of the piezoelectric ceramic sheet is: D B =Asin(ωt+α; Transforming the above equation using trigonometric methods, we obtain its general form: (D B / A) 2 +(D L / A) 2 -2cos(β-α)((D B D L ) / A 2 )=sin 2 (β-α); The output trajectory equation is: .

[0010] Furthermore, S6 specifically includes the following steps: S601. Use Ansys Workbench software to perform modal analysis on the device, select the mode closest to the design frequency, and use the post-processing function to set the starting point of the device's axis to complete the path creation. Analyze and obtain the displacement diagram of the path at each point along the axial direction of the device. The displacement of 0 points is the position of the amplitude transformer of the fixed device and the node where the longitudinal vibration piezoelectric sheet is placed. The position of the maximum displacement is the position of the transducer antinode where the bending vibration piezoelectric sheet is placed. Select the node and antinode positions that are closest to the calculation to complete the adjustment of the fixed device position, the longitudinal vibration piezoelectric sheet position, and the bending vibration piezoelectric sheet position. S602. The equal mass method is used to reduce the length of the end section of the luffing rod so that the reduced mass of the luffing rod is equal to the increased mass of the ER nut clamp. S603. Simplify the tool into a cylindrical rod model, and use the same method to design a new amplitude transformer by using the boundary conditions of each rod segment, so that the tool and the original amplitude transformer form a new amplitude transformer. S604. Use finite element simulation to analyze the influence of the length and diameter of the front cover plate, middle cover plate and rear cover plate on the longitudinal vibration and bending vibration frequencies. Use the method of controlling variables to find the influence law. Finally, optimize the size of each part by APDL parametric modeling to make the frequency degeneracy. S605. Through the above analysis and optimization, a suitable device size was selected, and the model of the longitudinal bending ultrasonic vibration assisted deep hole drilling device was determined. The device was then manufactured and tested based on the determined device model.

[0011] Furthermore, static and modal analyses were performed on the longitudinal bending ultrasonic vibration-assisted deep hole drilling device. Modal analysis reduced the influence of the front, middle, and rear cover plates, ER nut chuck, and cutting tools on the longitudinal and bending resonance frequencies. Since the longitudinal bending resonance frequency was not degenerate, the device needed to be optimized and modified. The device optimization and modification required parametric modeling in ANSYS. By defining design variables, state variables, setting objective functions, and specifying optimization design methods, the longitudinal bending ultrasonic vibration-assisted deep hole drilling device was optimized and modified to achieve degeneracy of the longitudinal bending resonance frequency and increase the amplification factor.

[0012] Beneficial effects: Compared with the prior art, the significant advantages of this invention are as follows: By considering the resonant frequency and the combined longitudinal and bending vibration modes of the longitudinal and bending ultrasonic vibration-assisted drilling device, the longitudinal vibration frequency equation and the bending vibration frequency equation are established to obtain the resonance curve. Based on the principle that the longitudinal and bending vibrations are at least of the second order and the cross-sectional area of ​​the amplitude transformer decreases with the segment, the order of the longitudinal and bending vibrations is determined. The length and diameter of each segment of the longitudinal and bending ultrasonic vibration-assisted drilling device are determined by the intersection of the longitudinal vibration resonance curve and the bending vibration resonance curve, and a model of the longitudinal and bending ultrasonic vibration-assisted deep hole drilling device is constructed. The finite element method is used, and the model is optimized and frequency degenerate by the equal mass method and the APDL parametric modeling method. The output trajectory model of the longitudinal and bending ultrasonic vibration-assisted drilling device is constructed through theoretical analysis, verifying the feasibility of the designed longitudinal and bending ultrasonic vibration-assisted drilling device design method. This realizes the general structural design of the dual-excitation longitudinal and bending ultrasonic vibration-assisted deep hole drilling device, simplifies the frequencies of longitudinal vibration and bending vibration, and maximizes the amplification factor, thereby solving the design problem of the dual-excitation longitudinal and bending synchronous vibration device. Attached Figure Description

[0013] Figure 1 These are the longitudinal and bending vibration waveforms of the longitudinal and bending ultrasonic vibration-assisted deep hole drilling device of the present invention. Figure 2 This is a diagram showing the resonance curves of longitudinal and bending vibrations in this invention; Figure 3 This is a finite element simulation diagram of the three-dimensional elliptical trajectory output by the longitudinal bending ultrasonic vibration assisted deep hole drilling device in this invention at 62000HZ; Figure 4 The elliptical trajectory diagram is generated by substituting the parameter examples of the longitudinal bending ultrasonic vibration assisted deep hole drilling device in this invention into the elliptical trajectory expression when the phase difference is 90°. Detailed Implementation

[0014] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0015] A design method for a longitudinal bending ultrasonic vibration-assisted deep hole drilling device, characterized by the following steps: S1. Select the working frequency and materials of each component of the longitudinal bending ultrasonic vibration-assisted deep hole drilling device; The longitudinal bending ultrasonic vibration assisted deep hole drilling device includes a transducer and a stepped amplitude transformer. The transducer consists of a front cover plate, a middle cover plate, a rear cover plate, electrode plates, longitudinal vibration piezoelectric ceramic plates, and bending vibration piezoelectric ceramic plates. The ultrasonic vibration operating frequency and the materials of the amplitude transformer, transducer, electrode plates, piezoelectric ceramic plates, ER chuck, and nut are determined according to the requirements, and the material parameters, including density, elastic modulus, Poisson's ratio, and sound velocity, are obtained.

[0016] S2. Transducer design of longitudinal bending ultrasonic vibration assisted deep hole drilling device, determining the length and diameter of the front cover plate, middle cover plate, and rear cover plate, as well as the position of the piezoelectric sheet; like Figure 1 The longitudinal and bending vibration waveforms of the ultrasonic vibration-assisted deep hole drilling device shown are as follows: Figure 2 The diagram shows the resonance curves for longitudinal and bending vibrations.

[0017] In longitudinal vibration, the wave equation for longitudinal vibration is: ; Where ξ represents the longitudinal displacement, ξ represents the cross-sectional area at any coordinate x, and k l It is the P-wave number; In bending vibration, the wave equation is: ; ; Where v b v represents the lateral displacement caused by bending. s denoted by , I represents the lateral displacement caused by shearing, A0 represents the cross-sectional moment of inertia, and k' represents the area coefficient related to the cross-sectional shape.

[0018] In longitudinal vibration, for ultrasonic transducers and ultrasonic amplitude transformers with uniform cross-sections, the longitudinal vibration waveforms at both ends should be at antinodes. Therefore, the longitudinal vibration frequency equation can be derived from the longitudinal vibration wave equation and boundary conditions as follows: fl=mc / 2 ; It is denoted as formula (1); where f is the vibration frequency, Hz; l is the designed length of the segment, mm; m is the vibration order; and c is the propagation speed of the longitudinal wave in the rod, mm / s.

[0019] In bending vibration, for ultrasonic transducers and ultrasonic amplitude transformers with uniform cross-sections, there are two types of boundary conditions: free-cyclic and cyclic-cyclic. Under the free-cyclic boundary condition, the frequency equation can be obtained from the wave equation and boundary conditions of bending vibration as follows: ; Let it be denoted as formula (2), where, ; In the formula: ω is the angular frequency, and A is the cross-sectional area of ​​the rod (m²). 2 ), where ρ is the density (kg / m³) 3 E is Young's modulus (N / m) 2 I is the moment of inertia (m) 4 ), k' G: effective shear modulus, μ is Poisson's ratio.

[0020] In the cyclic-cyclic boundary condition, this condition is equivalent to the node-node condition. From the wave equation and boundary conditions of bending vibration, the frequency equation can be obtained as follows: ; It is denoted as formula (3), where m is the vibration order.

[0021] The transducer adopts a single-stage design; In longitudinal vibration, the waveforms at both ends of the transducer are at the antinodes, so the longitudinal vibration frequency equation is adopted as formula (1). In bending vibration, according to Timoshenko rod theory, one end of the transducer is in a free state and the other end is fixed. The transducer adopts the free-fixed bending vibration frequency equation, which is formula (2). Based on the frequency equations of the transducer's longitudinal and bending vibrations, the resonance curves of the longitudinal and bending vibrations are obtained. Following the principle that both the longitudinal and bending vibration orders are controlled to be at least order 2 and require at least two nodes, the longitudinal and bending vibration orders of the transducer, i.e., m and n, are determined. To achieve longitudinal and bending vibrations of the transducer at the same vibration frequency, the intersection point of the curves containing the m-order longitudinal vibration and the n-order bending vibration is found, and the length and diameter of the transducer are determined accordingly. The longitudinally vibrating piezoelectric ceramic sheet is placed at one node, and the other node is used to fix the device. The bending vibrating piezoelectric ceramic sheet is placed at the antinode of the bending vibration waveform, and the connection position between the transducer end and the amplitude transformer is at the antinode of the bending vibration. The piezoelectric ceramic sheet is in the form of a ring, and the outer diameter of the piezoelectric sheet is the same as the outer diameter of the rear end cover. The piezoelectric ceramic sheet for longitudinal vibration is in the form of a whole sheet, while the piezoelectric ceramic sheet for bending vibration is in the form of 1 / 2 or 1 / 4. The lengths and diameters of the front cover plate, middle cover plate, and rear cover plate, as well as the positions of the piezoelectric sheets, are determined based on the intersection of the longitudinal vibration m-order and bending vibration n-order curves and the principle of piezoelectric ceramic sheet placement, thereby completing the transducer design.

[0022] S3. Design of the amplitude transformer of the longitudinal bending ultrasonic vibration-assisted deep hole drilling device, determining the length and diameter of each section of the amplitude transformer; The stepped amplitude transformer can use different numbers of segments depending on the requirements; The section change occurs at the antinode of the bending vibration waveform and at the node of the longitudinal vibration waveform. In the last section of the amplitude transformer, one end of the amplitude transformer must be connected to the tool. In order to maximize the displacement of the tool, the end of the amplitude transformer connected to the tool must be at the antinode. In longitudinal vibration, the waveforms at both ends of each segment of the amplitude transformer are at the antinodes, so the longitudinal vibration frequency equation is formula (1). In bending vibration, there are two types of boundary conditions: free-fixed and fixed at both ends. In the last section of the amplitude transformer, since the boundary conditions are the same as those of the transducer, the free-fixed frequency equation should be used, formula (2). In other sections of the amplitude transformer, according to the boundary conditions of the amplitude transformer, the bending vibration in this section should use the fixed-at-both-ends frequency equation, formula (3). Based on the frequency equations of the longitudinal and bending vibrations of each segment of the amplitude transformer, the resonance curves of the longitudinal and bending vibrations of each segment are plotted, and the order m of the longitudinal vibration and the order n of the bending vibration of each segment are determined. Based on this, the length and diameter of each segment of the amplitude transformer are determined, thus completing the design of the amplitude transformer.

[0023] S4. Geometric model construction of longitudinal bending ultrasonic vibration assisted deep hole drilling device: Three-dimensional modeling is carried out based on the dimensions of transducer and amplitude rod, bolt pre-tightening structure, and connection structure between tool and device, and device and machine tool. In terms of connection method, the longitudinal vibration piezoelectric ceramic ring is pre-tightened to the transducer by bolts, and the bending vibration piezoelectric ceramic ring is glued in 1 / 2 or 1 / 4 form and also pre-tightened to the transducer by bolts, thus completing the design of the bolt pre-tightening structure of the transducer piezoelectric sheet; The cutting tool is connected to the amplitude transformer via an ER collet and nut. The transducer and amplitude transformer are integrated and connected to the machine tool via a flange, thus completing the design of the cutting tool clamping and connection structure with the machine tool. Based on the obtained dimensions of the transducer and amplitude rod, as well as the bolt pre-tightening structure and the connection structure between the tool and the device, and between the device and the machine tool, a three-dimensional initial model is obtained.

[0024] S5. Modeling of the output trajectory of the longitudinal bending ultrasonic vibration-assisted deep hole drilling device; The longitudinal and bending vibration resonant frequencies are the same. It is assumed that the amplitude applied to the longitudinally vibrating piezoelectric ceramic sheet and the bending vibrating piezoelectric ceramic sheet is the same. α and β are the initial phases of the vibration in the radial and axial directions, respectively. d is the outer diameter of the piezoelectric ceramic sheet, and L is the distance from the piezoelectric sheet to the tip of the tool. The displacement excited by the longitudinally vibrating piezoelectric ceramic sheet is: D L =Asin(ωt+β; The displacement excited by the bending vibration of the piezoelectric ceramic sheet is: D B =Asin(ωt+α; Transforming the above equation using trigonometric methods, we obtain its general form: (D B / A) 2 +(D L / A) 2 -2cos(β-α)((D B D L ) / A2 )=sin 2 (β-α); The output trajectory equation is: .

[0025] Figure 3 To generate a three-dimensional elliptical trajectory finite element simulation diagram of a longitudinal bending ultrasonic vibration-assisted deep hole drilling device at 62000HZ, the parameter examples are substituted to generate the elliptical trajectory diagram in the elliptical trajectory expression when the phase difference is 90°.

[0026] S6. Structural optimization and frequency degeneracy of longitudinal bending ultrasonic vibration-assisted deep hole drilling device based on finite element simulation.

[0027] For the designed three-dimensional initial model, errors exist in the calculations of nodal positions, transducer nodal positions for longitudinal vibration piezoelectric elements, transducer antinode positions for bending vibration piezoelectric elements, and maximum output displacement positions at the end of the amplitude transformer due to simplification. Furthermore, the insertion of tools, ER nut chucks, and bolts causes frequency changes, resulting in different frequencies in the longitudinal bending device and suboptimal output amplitude. Therefore, the finite element method is used to analyze the vibration modes of the designed initial model. The equal mass method and APDL parametric modeling method are used to optimize the structure and reduce the frequency of the established initial model. Specifically, the following steps are included: S601. For the adjustment of the node positions of the amplitude transformer of the fixed device, the transducer node positions for the longitudinal vibration piezoelectric element, and the transducer antinode positions for the bending vibration piezoelectric element, the node positions and antinode positions calculated by theoretical analysis are obtained without considering the connection method. The device is modally analyzed using Ansys Workbench software. The mode closest to the design frequency is selected, and the starting point of the device axis is set using the post-processing function to complete the path creation. The displacement diagram of the path at each point along the axial direction of the device is analyzed and obtained. The displacement of 0 points is the node position of the amplitude transformer of the fixed device and the node position for the longitudinal vibration piezoelectric element. The displacement of the maximum point is the transducer antinode position for the bending vibration piezoelectric element. The node and antinode positions closest to the calculation are selected to complete the adjustment of the fixed device position, the longitudinal vibration piezoelectric element position, and the bending vibration piezoelectric element position. S602. Regarding the influence of the ER nut chuck on the frequency, after inserting the ER nut chuck, the overall mass of the device will increase and the frequency will decrease. In order to reduce the influence of the ER nut chuck on the frequency of the device, the equal mass method is adopted by reducing the length of the end section of the amplitude rod so that the reduced amplitude rod mass is equal to the mass increase of the ER nut chuck. S603. Regarding the influence of the cutting tool on the frequency, increasing the diameter and length of the cutting tool will reduce the frequency of the device. In order to reduce the influence of the cutting tool on the frequency of the device, the cutting tool is simplified into a cylindrical rod model. The same method is used to design a new amplitude transformer rod through the boundary conditions of each rod segment, so that the cutting tool and the original amplitude transformer rod form a new amplitude transformer rod. S604. Regarding the frequency degeneracy problem, the influence of the insertion of the tool, ER nut chuck, and bolt on the frequency has been reduced, but it is still necessary for the longitudinal and bending vibration frequencies to be the same. Finite element simulation is used to analyze the influence of the length and diameter of the front cover plate, middle cover plate, and rear cover plate on the longitudinal and bending vibration frequencies. The influence law is found by using the method of controlling variables. Finally, the dimensions of each part are optimized through APDL parametric modeling to achieve frequency degeneracy. S605. Through the above analysis and optimization, a suitable device size was selected, and the model of the longitudinal bending ultrasonic vibration assisted deep hole drilling device was determined. The device was then manufactured and tested based on the determined device model.

[0028] In the model analysis and optimization of the longitudinal bending ultrasonic vibration-assisted deep hole drilling device, the device operates under high-frequency vibration, requiring sufficient strength and rigidity. Static and modal analyses are performed on the device. Modal analysis reduces the influence of the front, middle, and rear cover plates, ER nut chuck, and cutting tools on the longitudinal and bending resonant frequencies. Since the longitudinal bending resonant frequency is not degenerate, the device needs optimization. This optimization requires parametric modeling in ANSYS, defining design variables, state variables, setting objective functions, and specifying optimization design methods to achieve degeneracy of the longitudinal bending resonant frequency and increase the amplification factor.

Claims

1. A design method for a longitudinal bending ultrasonic vibration-assisted deep hole drilling device, characterized in that, Includes the following steps: S1. Select the working frequency and materials of each component of the longitudinal bending ultrasonic vibration-assisted deep hole drilling device; S2. Transducer design of longitudinal bending ultrasonic vibration assisted deep hole drilling device, determining the length and diameter of the front cover plate, middle cover plate, and rear cover plate, as well as the position of the piezoelectric sheet; S3. Design of the amplitude transformer of the longitudinal bending ultrasonic vibration-assisted deep hole drilling device, determining the length and diameter of each section of the amplitude transformer; S4. Geometric model construction of longitudinal bending ultrasonic vibration assisted deep hole drilling device: Three-dimensional modeling is carried out based on the dimensions of transducer and amplitude rod, bolt pre-tightening structure, and connection structure between tool and device, and device and machine tool. S5. Modeling of the output trajectory of the longitudinal bending ultrasonic vibration-assisted deep hole drilling device; S6. Structural optimization and frequency degeneracy of longitudinal bending ultrasonic vibration-assisted deep hole drilling device based on finite element simulation.

2. The design method of the ultrasonic longitudinal bending vibration-assisted deep hole drilling device according to claim 1, characterized in that, The longitudinal bending ultrasonic vibration-assisted deep hole drilling device includes a transducer and a stepped amplitude transformer. The transducer consists of a front cover plate, a middle cover plate, a rear cover plate, electrode plates, longitudinally vibrating piezoelectric ceramic plates, and bending vibrating piezoelectric ceramic plates. The ultrasonic vibration operating frequency, as well as the materials of the amplitude transformer, transducer, electrode plates, piezoelectric ceramic plates, ER clamp, and nut, are determined according to the requirements, and the material parameters, including density, elastic modulus, Poisson's ratio, and sound velocity, are obtained.

3. The design method of the ultrasonic longitudinal bending vibration-assisted deep hole drilling device according to claim 2, characterized in that, S2 specifically refers to the transducer adopting a single-stage design; During longitudinal vibration, the waveforms at both ends of the transducer are at antinodes. In bending vibration, according to Timoshenko rod theory, one end of the transducer is in a free state and the other end is fixed. The transducer adopts the free-fixed bending vibration frequency equation. Based on the frequency equations of the transducer's longitudinal and bending vibrations, the resonance curves of the longitudinal and bending vibrations are obtained. Following the principle that both the longitudinal and bending vibration orders are controlled to be at least order 2 and require at least two nodes, the longitudinal and bending vibration orders of the transducer, i.e., m and n, are determined. To achieve longitudinal and bending vibrations of the transducer at the same vibration frequency, the intersection point of the curves containing the m-order longitudinal vibration and the n-order bending vibration is found, and the length and diameter of the transducer are determined accordingly. The longitudinally vibrating piezoelectric ceramic sheet is placed at one node, and the other node is used to fix the device. The bending vibrating piezoelectric ceramic sheet is placed at the antinode of the bending vibration waveform, and the connection position between the transducer end and the amplitude transformer is at the antinode of the bending vibration. The piezoelectric ceramic sheet is in the form of a ring, and the outer diameter of the piezoelectric sheet is the same as the outer diameter of the rear end cover. The piezoelectric ceramic sheet for longitudinal vibration is in the form of a whole sheet, while the piezoelectric ceramic sheet for bending vibration is in the form of 1 / 2 or 1 / 4. The lengths and diameters of the front cover plate, middle cover plate, and rear cover plate, as well as the positions of the piezoelectric sheets, are determined based on the intersection of the longitudinal vibration m-order and bending vibration n-order curves and the principle of piezoelectric ceramic sheet placement, thereby completing the transducer design.

4. The design method of the ultrasonic longitudinal bending vibration-assisted deep hole drilling device according to claim 3, characterized in that, The stepped amplitude transformer can use different numbers of segments depending on the requirements; The section change occurs at the antinode of the bending vibration waveform and at the node of the longitudinal vibration waveform. In the last section of the amplitude transformer, one end of the amplitude transformer must be connected to the tool. In order to maximize the displacement of the tool, the end of the amplitude transformer connected to the tool must be at the antinode. In longitudinal vibration, the waveforms at both ends of each segment of the amplitude transformer are at antinodes. In bending vibration, there are two types of boundary conditions: free-fixed and fixed at both ends. In the last segment of the amplitude transformer, since the boundary conditions are the same as those of the transducer, the free-fixed frequency equation should be used. In other segments of the amplitude transformer, according to the boundary conditions of the amplitude transformer, the bending vibration in this segment should use the fixed-at-both-ends frequency equation. Based on the frequency equations of the longitudinal and bending vibrations of each segment of the amplitude transformer, the resonance curves of the longitudinal and bending vibrations of each segment are plotted, and the order m of the longitudinal vibration and the order n of the bending vibration of each segment are determined. Based on this, the length and diameter of each segment of the amplitude transformer are determined, thus completing the design of the amplitude transformer.

5. The design method of the ultrasonic longitudinal bending vibration-assisted deep hole drilling device according to claim 4, characterized in that, In terms of connection method, the longitudinal vibration piezoelectric ceramic ring is pre-tightened to the transducer by bolts, and the bending vibration piezoelectric ceramic ring is glued in 1 / 2 or 1 / 4 form and also pre-tightened to the transducer by bolts, thus completing the design of the bolt pre-tightening structure of the transducer piezoelectric sheet; The cutting tool is connected to the amplitude transformer via an ER collet and nut. The transducer and amplitude transformer are integrated and connected to the machine tool via a flange, thus completing the design of the cutting tool clamping and connection structure with the machine tool. Based on the obtained dimensions of the transducer and amplitude rod, as well as the bolt pre-tightening structure and the connection structure between the tool and the device, and between the device and the machine tool, a three-dimensional initial model is obtained.

6. The design method of the ultrasonic longitudinal bending vibration-assisted deep hole drilling device according to claim 5, characterized in that, The longitudinal and bending vibration resonant frequencies are the same. It is assumed that the amplitude applied to the longitudinally vibrating piezoelectric ceramic sheet and the bending vibrating piezoelectric ceramic sheet is the same. α and β are the initial phases of the vibration in the radial and axial directions, respectively. d is the outer diameter of the piezoelectric ceramic sheet, and L is the distance from the piezoelectric sheet to the tip of the tool. The displacement excited by the longitudinally vibrating piezoelectric ceramic sheet is: D L =Asin(ωt+β); The displacement excited by the bending vibration of the piezoelectric ceramic sheet is: D B =Asin(ωt+α); Transforming the above equation using trigonometric methods, we obtain its general form: (D B / A) 2 +(D L / A) 2 -2cos(β-α)((D B D L ) / A 2 )=sin 2 (b-a); The output trajectory equation is: 。 7. The design method of the ultrasonic longitudinal bending vibration-assisted deep hole drilling device according to claim 6, characterized in that, S6 specifically includes the following steps: S601. Use Ansys Workbench software to perform modal analysis on the device, select the mode closest to the design frequency, and use the post-processing function to set the starting point of the device's axis to complete the path creation. Analyze and obtain the displacement diagram of the path at each point along the axial direction of the device. The displacement of 0 points is the position of the amplitude transformer of the fixed device and the node where the longitudinal vibration piezoelectric sheet is placed. The position of the maximum displacement is the position of the transducer antinode where the bending vibration piezoelectric sheet is placed. Select the node and antinode positions that are closest to the calculation to complete the adjustment of the fixed device position, the longitudinal vibration piezoelectric sheet position, and the bending vibration piezoelectric sheet position. S602. The equal mass method is used to reduce the length of the end section of the luffing rod so that the reduced mass of the luffing rod is equal to the increased mass of the ER nut clamp. S603. Simplify the tool into a cylindrical rod model, and use the same method to design a new amplitude transformer by using the boundary conditions of each rod segment, so that the tool and the original amplitude transformer form a new amplitude transformer. S604. Use finite element simulation to analyze the influence of the length and diameter of the front cover plate, middle cover plate and rear cover plate on the longitudinal vibration and bending vibration frequencies. Use the method of controlling variables to find the influence law. Finally, optimize the size of each part by APDL parametric modeling to make the frequency degeneracy. S605. Through the above analysis and optimization, a suitable device size was selected, and the model of the longitudinal bending ultrasonic vibration assisted deep hole drilling device was determined. The device was then manufactured and tested based on the determined device model.

8. The design method of the ultrasonic longitudinal bending vibration-assisted deep hole drilling device according to claim 7, characterized in that, Static and modal analyses were performed on the longitudinal bending ultrasonic vibration-assisted deep hole drilling device. Modal analysis was used to reduce the influence of the front, middle, and rear cover plates, ER nut chuck, and cutting tools on the longitudinal and bending resonance frequencies. Since the longitudinal bending resonance frequency was not degenerate, the device needed to be optimized and modified. The device optimization and modification required parametric modeling in ANSYS. By defining design variables, state variables, setting objective functions, and specifying optimization design methods, the longitudinal bending ultrasonic vibration-assisted deep hole drilling device was optimized and modified to achieve degeneracy of the longitudinal bending resonance frequency and increase the amplification factor.

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