Reversible blade tenon tooth ultrasonic vibration machining device and design and operation method thereof

Abstract

The invention relates to a reversible blade tenon tooth ultrasonic vibration machining device and a design and operation method thereof. And the size weight of the tenon teeth is in a range of 20-300g. The device is obtained by establishing a tenon tooth ultrasonic vibration model based on an ultrasonic vibration principle and combining finite element modal analysis and optimization, and comprises an ultrasonic assembly, a porous ultrasonic tool, a reversible ultrasonic clamp and a tenon tooth to be machined; wherein the porous ultrasonic tool is mounted on the machine tool bottom plate through supporting legs at the bottom; the ultrasonic assembly is installed on the back face of the multi-hole ultrasonic tool, and after blade tenon teeth to be machined are clamped in the turnover ultrasonic clamp, the whole is fixed to the center area of the ultrasonic vibration platform. Ultrasonic vibration generated by the ultrasonic assembly is transmitted to the multi-hole ultrasonic tool, and expanded and uniform single longitudinal ultrasonic vibration is achieved on the workpiece; by means of tenon tooth feeding rotation motion and grinding wheel rotation feeding motion, turnover ultrasonic vibration auxiliary grinding of tenon teeth is achieved. Uniform single longitudinal vibration with the maximum amplitude is formed in the center of the multi-hole ultrasonic tool, and nearly-amplitude-free areas appear at the four corners of a rectangle of a longitudinal vibration area. Compared with a common ultrasonic platform, the mass is reduced, and the inherent frequency of a corresponding mode is reduced.

Description

Technical Field

[0001] The present invention belongs to the technical field of ultrasonic vibration assisted machining, and in particular relates to a reversible blade tenon ultrasonic vibration machining device and a design and operation method thereof. Background Art

[0002] The processing technology for single-crystal alloy blade tenons represents one of the key capabilities of various countries in aero-engine manufacturing. However, due to the unique and sensitive nature of single-crystal alloy blade tenons, current research on single-crystal alloy blade tenon grinding is primarily limited to the material level, with very few studies examining analog component-level or part-level grinding techniques. Consequently, the focus has been on analyzing high-efficiency grinding techniques for single-crystal alloys. Limited research data indicates that chatter marks, burns, cracks, white layers, and residual tensile stresses caused by high grinding temperatures and grinding wheel wear remain the primary difficulties and bottlenecks in the efficient grinding of single-crystal alloy materials. Therefore, addressing the issue of sudden burns during single-crystal alloy grinding is crucial for improving the efficiency of single-crystal alloy blade tenon machining. Multi-energy field composite grinding methods offer new insights into the efficient processing of single-crystal alloys.

[0003] For example, the patent application document with application number CN202322396435.X discloses an ultrasonic horn-assisted grinding device, which includes a base plate, a fixed plate fixedly connected to the surface of the base plate, and a fixed seat fixedly connected to the back of the base plate. A workpiece is placed on the top surface of a support mechanism, a clamping assembly is activated to clamp and fix the workpiece, the support mechanism is recovered and separated from the workpiece, and a rotating mechanism is activated to drive the clamping assembly to rotate inside the fixed plate. The rotation of the clamping assembly drives the workpiece to rotate and adjust to a specified processing surface. The ultrasonic assembly is activated to apply ultrasonic frequency vibration to the workpiece to change the formation mechanism of the grinding surface. The grinding tool is fixed by a grinding fixture. The first electric push rod and the grinding motor are activated to drive the grinding fixture and the grinding tool to grind the workpiece. This achieves the goal of automatically adjusting the grinding surface of the workpiece during ultrasonic grinding, avoiding the problem that the grinding process is cumbersome, time-consuming and labor-intensive due to the difficulty of automatically adjusting the processing surface of the workpiece in existing ultrasonic-assisted grinding devices during use. However, its processing efficiency and processing quality can still be improved.

[0004] The patent application document with the application number CN202110962257.5 discloses a new integrated machining fixture for aeroengine turbine blades and its machining process, including a base, a support arranged on the base, and a chuck assembly and an end face positioning assembly respectively arranged on the support; the chuck assembly includes a tenon tooth positioning block arranged on the support, a tenon tooth clamping block cooperatively connected with the tenon tooth positioning block, and a locking member arranged on the tenon tooth clamping block. A tenon tooth groove for clamping the blade is formed between the tenon tooth positioning block and the tenon tooth clamping block, and tooth teeth are arranged on the end face of the tenon tooth positioning block close to the tenon tooth clamping block and the end face of the tenon tooth clamping block close to the tenon tooth positioning block. This machining fixture has a reliable structure, good use performance, improves the machining positioning accuracy, and is convenient for grinding machining. This machining process adopts the design principle of process concentration, concentrates the machining surfaces with the same positioning method into one process for machining, and ensures the machining accuracy through the accuracy of the CNC powerful grinding equipment. It reduces the repeated clamping error and the tooling manufacturing cost. However, ultrasonic vibration-assisted grinding is still not introduced, and there is still room for improvement in the machining efficiency.

[0005] The invention patent with the publication number CN113182946.A applied by the inventor before discloses a unidirectional ultrasonic vibration platform with an adjustable fixture and its operation method. A set of adjustable fixtures are respectively fixed on the upper and lower surfaces of the two-dimensional porous vibration platform, and the ultrasonic transducer is connected to the center position of one side of the two-dimensional porous ultrasonic vibration platform. The adjustable fixture restricts 5 degrees of freedom of the part, and the clamping force is parallel to the ultrasonic vibration direction; there are symmetrically distributed threaded holes and through holes on the two-dimensional porous ultrasonic vibration platform for isolating transverse vibration and increasing the longitudinal vibration amplitude, and there are uniformly distributed through holes on the side for controlling the vibration mode and reducing the device volume; the ultrasonic transducer drives the two-dimensional porous ultrasonic vibration platform to form a coupled vibration mode of longitudinal full wave and transverse half wave, and the coupled vibration forms a single longitudinal vibration at the center of the platform, and the central longitudinal vibration area is enlarged through the coupled vibration. Although this device introduces ultrasonic vibration-assisted grinding, it is not applicable to the positioning of complex-shaped parts such as tenon teeth on the fixture. Summary of the Invention

[0006] In order to solve the problems of low machining efficiency or low machining quality in the existing tenon tooth grinding, the present invention proposes a rotatable blade tenon tooth ultrasonic vibration machining device and its design and operation method. After clamping the tenon tooth to be machined with a rotatable fixture and installing it at the center position of the porous ultrasonic tooling, tangential ultrasonic vibration is realized, and a unidirectional uniform vibration area is formed in the tenon tooth area of the blade. The integrated design of ultrasonic vibration can realize the 360° rotation of the turntable without interference and avoid repeated clamping. Compared with the ordinary ultrasonic platform, the quality is reduced, and the natural frequency of the corresponding mode is reduced.

[0007] In order to achieve the above invention purpose, the technical solution adopted by the present invention is:

[0008] A flip - type blade tenon ultrasonic vibration machining device, which consists of a porous ultrasonic vibration platform, an ultrasonic transducer, a porous ultrasonic tooling, a flip - type ultrasonic fixture, the tenon to be machined, etc. The porous ultrasonic vibration platform is installed on the machine tool base plate through the feet at the bottom. The feet are located at the vibration nodes of the ultrasonic platform, which can effectively reduce its influence on resonance. The horn and the porous ultrasonic tooling are connected by fine - thread bolts, which can effectively transmit vibration. The tenon to be machined is fixed in the central area of the ultrasonic vibration platform through the flip - type ultrasonic fixture and realizes unidirectional ultrasonic vibration.

[0009] The blade tenon together with the flip - type ultrasonic fixture is fixed at the central position of the porous ultrasonic tooling. The ultrasonic transducer is installed on the back of the porous ultrasonic tooling through bolts. In the working state, the ultrasonic transducer generates longitudinal vibration, driving the ultrasonic tooling to drive the flip - type ultrasonic fixture to resonate, and horizontal ultrasonic vibration is generated on the surface of the blade tenon. On this basis, through the tenon feed motion, tenon rotation motion, grinding wheel rotation motion and grinding wheel feed motion, the flip - type ultrasonic vibration - assisted grinding of the tenon is realized.

[0010] A design method for a flip - type blade tenon ultrasonic vibration machining device. First, based on the ultrasonic vibration principle, a tenon ultrasonic vibration model is established. Combining with the finite - element modal analysis, the relationship between the tenon expansion - contraction vibration modal frequency and geometric parameters is obtained. Then, based on the design method of a one - dimensional longitudinal vibration ultrasonic device, the structural parameters of the ultrasonic transducer are initially determined according to the tenon resonance frequency. On this basis, finite - element modal analysis and harmonic response analysis are carried out, and the structural parameters of the ultrasonic transducer are optimized according to the results. The size and weight of the tenon are in the range of 20 - 300 grams.

[0011] The size selection method of the ultrasonic transducer is as follows:

[0012] Since the diameters of the ultrasonic transducer and the horn are less than 1 / 4 wavelength, the internal radial vibration of the transducer can be ignored, and the ultrasonic transducer and the horn can be simplified as the vibration of a slender rod. According to the one - dimensional vibration theory, the ultrasonic transducer can be regarded as a variable - cross - section circular rod model, and the ultrasonic transducer can be regarded as an equal - cross - section circular rod.

[0013] 1. Under the one - dimensional vibration condition, Newton's second law (F = ma) of the variable - cross - section rod model can be expressed as:

[0014]

[0015] In the formula, S(x) represents the rod cross - section area function, and m, a, and V x respectively represent mass, acceleration, and volume. According to formula (1) and formula (2), a mechanical equation is established:

[0016]

[0017] Substituting formula (4) into formula (3) gives:

[0018]

[0019] After simplification, the one-dimensional wave equation can be obtained:

[0020]

[0021] Under the condition of simple harmonic vibration, there is:

[0022]

[0023] Combining formula (6) and formula (7) to obtain the one-dimensional wave equation of simple harmonic vibration:

[0024]

[0025] where ω is the circular frequency of vibration, ω = 2πf, and c represents the one-dimensional longitudinal wave velocity.

[0026] 2. For a rod with a constant cross-sectional area and unchanged diameter, since the wave equation can be further simplified to obtain the one-dimensional wave equation of simple harmonic vibration for a rod with a constant cross-sectional area:

[0027]

[0028] where The solution of this wave equation can be expressed as:

[0029] ε = Acos(kx) + Bsin(kx) (10)

[0030]

[0031] where A and B are coefficients, and under the condition of free vibration, they can be determined by the boundary conditions. In this study, a half-wavelength ultrasonic transducer and a horn are used. According to the continuity requirement, under the condition of free vibration of the ultrasonic transducer, the boundary conditions are satisfied:

[0032]

[0033] where the subscripts R and L represent the boundary conditions on the right and left sides of the interface respectively. According to the wave equation (11) and the boundary condition equation (12), the frequency equation of the transducer can be obtained:

[0034]

[0035] where l 12 and l 23 represent the thickness of the rear cover plate and the total thickness of the piezoelectric ceramics respectively, and Z represents the impedance of each part of the transducer, Z = ρcS. According to the ultrasonic horn model ( Figure 4), the boundary conditions for free vibration can be constructed:

[0036]

[0037] Based on Equation (14) and the boundary conditions (14), the frequency equation of the conical horn can be constructed:

[0038]

[0039] 3. The rear cover plate is made of C45 steel. Due to its large impedance, it can effectively improve the radiation ratio of ultrasonic energy forward and can also adjust the ultrasonic bandwidth. Piezoelectric ceramic PZT-8 has a large electromechanical coupling coefficient, permittivity, piezoelectric constant, tensile strength and stability, and is often used to make emission-type ultrasonic transducers at high mechanical amplitudes. Considering the power requirements, the diameter of the piezoelectric ceramic is 50 mm, the thickness is 5 mm, and the number is 6 pieces. The ultrasonic horn is made of TC4 titanium alloy. The sound attenuation coefficient of the titanium alloy is very small, which helps to increase the amplitude. According to the frequency equations (13) and (15), the parameters of the ultrasonic transducer are calculated as follows:

[0040] Length of the rear cover plate l 12 = 19.3 mm; length of the piezoelectric ceramic l 23 = 6×5 mm; length of the front cover plate l 34 = 61.7 mm; length of the horn l 45 = 125.2 mm

[0041] In order to adjust the ultrasonic frequency, amplify the ultrasonic amplitude and improve the performance of the tenon tooth ultrasonic vibration device, it is necessary to optimize the size of the ultrasonic tooling by adopting a uniformly distributed porous structure. For this purpose, a certain number of uniformly distributed circular through holes are to be evenly and equidistantly opened on the surface of the ultrasonic tooling along a certain direction to reduce the weight of the ultrasonic device and increase the amplitude under the condition of unchanged resonant frequency. It is intended to establish the relationship between the parameters (pore diameter, pore distance, number of pores) of the uniformly distributed porous structure and the resonant frequency based on the apparent elasticity method. Among them, according to the previous research results of the inventor, the equivalent apparent elastic modulus E eff of the porous structure can be expressed as:

[0042]

[0043] where r s is the pore radius, l m and l n represent the pore distances in the x and y directions, and E is the elastic modulus of the material. Substituting this formula into the vibration model, the parameter optimization model of the ultrasonic transducer is constructed. Based on this, the modal analysis of the finite element is carried out to further optimize the structural parameters of the tenon tooth ultrasonic vibration device.

[0044] Circular through-holes are evenly distributed on the upper surface and the side surface of the ultrasonic vibration platform. Reasonable aperture, hole pitch, and number of holes have an obvious improvement effect on the vibration characteristics of the resonator. However, the traditional apparent elasticity method is not applicable to the design of perforated plates. Therefore, the frequency equation of the porous ultrasonic vibration platform needs to consider the influence of holes on vibration based on the traditional apparent elasticity method. The frequency equation of the porous ultrasonic vibration platform is expressed as:

[0045]

[0046] where E ax and E ay represent the apparent elastic modulus of the platform after opening holes, and η represents the frequency correction coefficient, whose values are determined in previous work. The material of the ultrasonic vibration platform is 316L stainless steel.

[0047] The blade tenon tooth, together with the flip - type ultrasonic fixture, is fixed at the central position of the porous ultrasonic tooling. The ultrasonic transducer is installed on the back of the porous ultrasonic tooling through bolts. Four feet connect the machine tool and the porous ultrasonic vibration platform at the vibration nodes. Fine slots are opened on the feet to increase impedance and reduce the efficiency of ultrasonic vibration transmitted to the machine tool. In the working state, the ultrasonic transducer generates longitudinal vibration, driving the ultrasonic tooling to drive the flip - type ultrasonic fixture to resonate, and horizontal ultrasonic vibration is generated on the surface of the blade tenon tooth. On this basis, through the tenon tooth feeding motion, tenon tooth rotating motion, grinding wheel rotating motion, and grinding wheel feeding motion, the flip - type ultrasonic vibration - assisted grinding of the tenon tooth is realized.

[0048] The flip - type fixture includes a locking bolt, a fixture pressing plate, a positioning bolt, a pair of top blocks (below the tenon tooth), a top - block base, two positioning pins (located above and on the side respectively), a positioning block (behind the tenon tooth), a tip (on the right side of the tenon tooth), and a fixture housing; the fixture housing cooperates with the external ultrasonic tooling. By rotating the locking bolt, the fixture pressing plate drives the positioning bolt and the upper positioning pin to restrict the vertical displacement of the tenon tooth. The positioning block restricts the axial displacement of the tenon tooth. The top block is fixed to the base by bolts to support the grinding process of the tenon tooth, and different - sized tenon teeth can be positioned by replacing the top block. The tip restricts the horizontal displacement of the tenon tooth, and the side positioning pin restricts the disturbance of the tail of the tenon tooth during processing. The above - mentioned positioning parts also play the role of transmitting ultrasonic vibration to the tenon tooth, and jointly act to completely position the tenon tooth, achieving reliable positioning and clamping of dimensions.

[0049] After the fixture is fixed, grind one side of the tenon tooth. After the processing is completed, only by rotating the compression bolt 21, loosening the tooling pressing plate 20, horizontally removing the flip - type ultrasonic fixture and the semi - processed tenon tooth from the ultrasonic tooling and flipping them, and then assembling and clamping them with the ultrasonic tooling, the grinding of the upper and lower surfaces can be efficiently completed without re - positioning the tenon tooth.

[0050] The ultrasonic vibration assisted grinding system consists of a porous ultrasonic vibration platform, an ultrasonic generator, an ultrasonic transducer, a horn, a grinding wheel and feet. The ultrasonic generator includes a signal generator and a matching circuit for the vibration system. The ultrasonic power supply outputs high-frequency pulsed electrical signals. The ultrasonic transducer converts the signals into mechanical vibrations of corresponding frequencies. The amplitude is amplified through the ultrasonic horn, driving the porous ultrasonic vibration platform to generate mechanical vibrations, and two-dimensional coupled vibrations are generated on the platform to form a single longitudinal vibration region in the central area.

[0051] Beneficial effects:

[0052] (1) The flip - type blade tenon ultrasonic vibration device provided by the present invention can form a unidirectional and uniform vibration region in the tenon region of the workpiece blade.

[0053] (2) The present invention uses a flip - type fixture to clamp the blade tenon and then performs creep feed plunge grinding, which can achieve non - interference during 360° rotation of the workpiece.

[0054] (3) The combination of the porous ultrasonic tooling and the flip - type fixture in the present invention enables rapid positioning and reliable clamping of the workpiece, thereby realizing ultrasonic vibration of batch workpieces and improving work efficiency.

[0055] (4) The improved apparent elasticity method adopted in the present invention can accurately calculate the resonance frequency of the porous ultrasonic vibration platform and the processing parameters of the ultrasonic components.

[0056] (5) There are symmetrically and uniformly distributed threaded holes and through - holes on the two - dimensional porous ultrasonic tooling for isolating transverse vibrations and increasing the longitudinal vibration amplitude. There are uniformly distributed through - holes on the side for controlling the vibration mode and reducing the device volume; compared with the ordinary ultrasonic platform, the overall mass is reduced by 0.454 kg, the natural frequency is reduced, and the vibration mode is improved; the ultrasonic transducer drives the two - dimensional porous ultrasonic vibration platform to form a coupled vibration mode of longitudinal full - wave and transverse half - wave, and the coupled vibration forms a single longitudinal vibration at the center of the platform. The area of the central longitudinal vibration region is enlarged through the coupled vibration ( Figure 6 the central black rectangular part). The amplitude of the central longitudinal vibration region is the largest and uniform. At this time, near - zero - amplitude regions appear at the four corners of the rectangle in the longitudinal vibration region. Using these weak - amplitude nodes for fixing the vibration platform can minimize ultrasonic vibration dissipation to the greatest extent, improve the ultrasonic - assisted processing effect, and realize reliable positioning and clamping of various - sized parts in ultrasonic processing. Description of the drawings

[0057] Figure 1 is a three - dimensional structural schematic diagram of the flip - type ultrasonic vibration processing device for grinding of the present invention;

[0058] Figure 2 is the front view of the flip - type ultrasonic vibration processing device for grinding of the present invention;

[0059] Figure 3 It is a schematic diagram of the state where the reversible fixture 5 of the present invention clamps the to-be-machined tenon teeth 6;

[0060] Figure 4 It is a schematic diagram of the porous ultrasonic tooling 17 of the present invention;

[0061] Figure 5 It is the vibration mode diagram of the reversible fixture of the present invention; It can be seen that in the 21KHz frequency mode, the vibration amplitude in the tenon tooth area of the blade is the largest, and the utilization effect of ultrasonic vibration energy is good.

[0062] Figure 6 It is the vibration mode diagram of the porous ultrasonic tooling of the present invention; (a) Without holes; (b) With holes; It can be seen that the coupled vibration mode of the longitudinal full wave and the transverse half wave forms an enlarged single longitudinal vibration at the center of the platform. The amplitude in the central longitudinal vibration area is the largest and uniform. At this time, near-amplitude-free areas appear at the four corners of the rectangle in the longitudinal vibration area. Fixing the vibration platform using these weak amplitude nodes can minimize the dissipation of ultrasonic vibration and improve the ultrasonic-assisted processing effect. Compared with the vibration platform without holes, the amplitude is increased, the mass and volume are reduced, and the utilization rate of ultrasonic energy is improved.

[0063] Figure 7 It is a schematic diagram of the usage state of the ultrasonic vibration processing device for reversible grinding of the present invention;

[0064] In the figure: 1. Rear cover plate; 2. Piezoelectric ceramic; 3. Front cover plate; 4. Amplitude transformer; 5. Reversible fixture; 6. To-be-machined tenon teeth; 7. Fixture pressing plate; 8. Locking bolt; 9. Positioning bolt; 10. Fixture housing; 11. Upper positioning pin; 12. Center point; 13. Positioning block; 14. Top block; 15. Top block base; 16. Side positioning pin; 17. Porous ultrasonic tooling; 18. Optimized structure of side evenly distributed holes; 19. Optimized structure of top evenly distributed holes; 20. Tooling pressing plate; 21. Compression bolt; 22. Corundum grinding wheel; 23. Porous ultrasonic vibration platform; 24. Support feet. Specific embodiments

[0065] The following makes a detailed description of an ultrasonic vibration processing device for reversible grinding of blade tenon teeth of the present invention in combination with the embodiments and the drawings.

[0066] Refer to Figure 1As shown in the figure, an ultrasonic vibration processing device for flip-grinding of blade tenons includes: an ultrasonic component, a porous ultrasonic tooling, a flip-over ultrasonic fixture, and a tenon to be processed. The porous ultrasonic tooling 17 is installed on the machine tool base plate through feet 24. The feet are located at the vibration nodes of the ultrasonic platform, which can effectively reduce their impact on resonance. The ultrasonic component includes: an ultrasonic transducer and a horn; among them, the small end of the horn is connected to the porous ultrasonic tooling by bolts, which can effectively transmit vibration; the large end of the horn is connected to the ultrasonic transducer. After the tenon to be processed is clamped in the flip-over ultrasonic fixture, the whole is fixed in the central area of the ultrasonic vibration platform. The ultrasonic vibration generated by the ultrasonic transducer is transmitted and amplified through the horn and sent to the porous ultrasonic tooling 17 to achieve unidirectional ultrasonic vibration on the workpiece.

[0067] Referring to Figure 1 , 2 As shown in the figure, the ultrasonic transducer includes a rear cover plate 1, a piezoelectric ceramic 2, and a front cover plate 3; the rear cover plate 1 and the front cover plate 3 clamp the piezoelectric ceramic 2 tightly in the middle, and the front cover plate 3 is connected to the horn 4, and the horn is a conical horn.

[0068] A design method for a flip-over blade tenon ultrasonic vibration processing device. First, a three-dimensional model is established through Catia (as shown in Figure 1 ); then it is converted to the stp format and imported into the geometric structure of the Workbench component in the simulation software Ansys; then the corresponding auxiliary lines are drawn in the SpaceClaim component to prepare for subsequent data output and mesh generation; during the finite element modal analysis, the materials of each component of the model are assigned and the mesh is divided, and finally the analysis is carried out and the tenon expansion and contraction vibration modal frequency distribution diagram is output (as shown in Figure 5 ). Determine the optimal frequency for the tooling to transmit vibration to the tenon, so that the tenon part of the blade has a larger amplitude and better vibration uniformity. Then, based on the design method of the one-dimensional longitudinal vibration ultrasonic device (Formulas 1 - 15), and then based on the tenon resonance frequency obtained from the finite element analysis, the structural parameters of the ultrasonic transducer and the horn are initially determined (according to Frequency Equations 13 and 15). On this basis, the structural dimensions of the ultrasonic tooling are modified, and the finite element modal analysis and harmonic response analysis are carried out on the tooling with different parameters, and the structural parameters of the ultrasonic tooling are optimized according to the results, and the design of the tenon ultrasonic vibration device is initially completed.

[0069] Combined with Formulas 16 and 17, the uniformly distributed hole parameters are designed and the uniformly distributed hole structure is optimized in the vibration three-dimensional model to construct a parameter optimization model. Based on this, the finite element modal analysis is carried out to further optimize the structural parameters of the tenon ultrasonic vibration device.

[0070] Example 1

[0071] The diameters of the ultrasonic transducer and the horn are less than 1 / 4 wavelength. The radial vibration inside the transducer can be ignored, and the ultrasonic transducer and the horn can be simplified as the vibration of a slender rod. According to the one-dimensional vibration theory, the ultrasonic transducer can be regarded as a variable cross-section circular rod model, and the ultrasonic transducer can be regarded as a circular rod with a constant cross-section.

[0072] Under the condition of one-dimensional vibration, Newton's second law (F = ma) for the variable cross-section rod model can be expressed as:

[0073]

[0074] In the formula, S(x) represents the rod cross-sectional area function, and m, a, and V x represent mass, acceleration, and volume respectively. Based on Eqs. (1) and (2), a mechanical equation is established:

[0075]

[0076]

[0077] Substituting Eq. (4) into Eq. (3) gives:

[0078]

[0079] After simplification, the one-dimensional wave equation can be obtained:

[0080]

[0081] Under the condition of simple harmonic vibration, there is:

[0082]

[0083] Combining formula (6) and Eq. (7) gives the one-dimensional wave equation of simple harmonic vibration:

[0084]

[0085] where ω is the circular frequency of vibration, ω = 2πf, and c represents the one-dimensional longitudinal wave velocity.

[0086] For a circular rod with a constant cross-section, since the wave equation can be further simplified to obtain the one-dimensional wave equation of simple harmonic vibration for a circular rod with a constant cross-section:

[0087]

[0088] where The solution of this wave equation can be expressed as:

[0089] ε = Acos(kx) + Bsin(kx) (10)

[0090]

[0091] Among them, A and B are coefficients, which can be determined by boundary conditions under free vibration conditions. In this study, a half-wavelength ultrasonic transducer and a horn are used. According to the continuity requirement, under the free vibration condition of the ultrasonic transducer, the boundary conditions are satisfied as follows:

[0092]

[0093] Among them, the subscripts R and L represent the boundary conditions on the right and left sides of the interface respectively. According to the wave equation (11) and the boundary condition equation (12), the frequency equation of the transducer can be obtained:

[0094]

[0095] Among them, l 12 and l 23 represent the thickness of the rear cover plate and the total thickness of the piezoelectric ceramics respectively, Z represents the impedance of each part of the transducer, and Z = ρcS. According to the ultrasonic horn model, the boundary conditions during free vibration can be constructed:

[0096]

[0097] Construct the frequency equation of the conical horn according to the boundary conditions of equation (14):

[0098]

[0099] The rear cover plate 1 is made of C45 steel. Due to its large impedance, it can effectively increase the radiation ratio of ultrasonic energy forward, and at the same time, it can also adjust the ultrasonic bandwidth. The piezoelectric ceramic PZT-8 has large electromechanical coupling coefficient, permittivity, piezoelectric constant, tensile strength and stability, and is often used to make emission-type ultrasonic transducers with high mechanical amplitude. Considering the power requirements, the diameter of the piezoelectric ceramic 2 is 50 mm, the thickness is 5 mm, and the number is 6 pieces. The ultrasonic horn is made of TC4 titanium alloy. The sound attenuation coefficient of the titanium alloy is very small, which helps to increase the amplitude. According to the frequency equations (13) and (15), the parameters of the ultrasonic transducer are calculated as follows: the length of the rear cover plate l 12 = 19.3 mm; the piezoelectric ceramic l 23 = 6×5 mm; the front cover plate l 34 = 61.7 mm; the length of the horn l 45 = 125.2 mm.

[0100] Refer to Figure 4As shown in the figure, the porous ultrasonic tooling includes a clamping screw with an opening on the side and a tooling pressure plate 20 installed on the opening side. A flip-over fixture is placed inside the screw and fixed by means of a clamping bolt 21 after being pressed by the tooling pressure plate 20. Among them, the front section of the tooling pressure plate 20 is forked. Circular through-holes are evenly distributed on the surface and side of the clamping screw of the porous ultrasonic tooling. Vertically, the through-holes are evenly distributed on both sides of the horizontal threaded holes. All the through-holes have the same diameter, and the calculation of the hole diameter and hole pitch is obtained by the apparent elasticity method. On the one hand, it is used to control the vibration mode of the platform, and on the other hand, it can reduce the weight of the ultrasonic device and increase the amplitude without changing the resonant frequency (see Figure 6 ).

[0101] Specifically, based on the apparent elasticity method, the relationship between the parameters (hole diameter, hole pitch, number of holes) of the uniformly distributed porous structure and the resonant frequency is established, and a parameter optimization model of the ultrasonic transducer is constructed; the equivalent apparent elastic modulus E of the porous structure eff can be expressed as:

[0102]

[0103] where r s is the hole radius, l m and l n represent the hole pitches in the x and y directions, and E is the elastic modulus of the material.

[0104] Substitute the above formula (1) into the vibration model to construct a parameter optimization model. Based on this, perform a finite element modal analysis to further optimize the structural parameters of the tenon tooth ultrasonic vibration device.

[0105] Refer to Figure 3As shown, the reversible fixture cooperates with an external ultrasonic tooling, and it includes a locking bolt 8, a fixture pressing plate 7, a positioning bolt 9, a pair of top blocks 14 (below the tenon teeth), a top block base 15, two positioning pins (respectively located above and on the side), a positioning block 13 (behind the tenon teeth), a center point 12 (on the right side of the tenon teeth), and a fixture housing 10. The fixture housing 10 is fixedly matched with the clamping screw of the ultrasonic tooling; by rotating the locking bolt 8 at the top, the fixture pressing plate 7 drives the positioning bolt 9 and the upper positioning pin 11 to move downward to press and restrict the vertical displacement of the tenon teeth 6. The positioning block 13 is located behind the tenon teeth and is used to restrict the axial displacement of the tenon teeth. A pair of top blocks 14 are fixed to the base by bolts and are used to support the grinding process of the tenon teeth. The top blocks can be replaced according to the specifications of tenon teeth of different sizes. The center point 12 is horizontally arranged on the convex block in front of the fixture housing 10 and is used to restrict the horizontal displacement of the tenon teeth. The side positioning pin 16 is used to restrict the disturbance of the tail of the tenon teeth during processing. The above positioning parts cooperate to transfer ultrasonic vibration to the tenon teeth, fully positioning the tenon teeth. By restricting all six degrees of freedom of the tenon teeth 6 to be processed, reliable positioning and clamping of dimensions are achieved. The porous ultrasonic tooling with optimized dimensions through uniformly distributed holes transfers vibration to the tenon teeth, avoiding repeated installation of the tenon teeth during the processing. It is more flexible than traditional tooling, reduces auxiliary time, improves production efficiency, and has good working stability and a wide range of applications.

[0106] The reversible fixture is fixed at the central position of the porous ultrasonic tooling. The workpiece to be processed (blade tenon teeth) is clamped on the reversible ultrasonic fixture. The ultrasonic transducer is installed on the back of the porous ultrasonic tooling by bolts. In the working state, the ultrasonic transducer generates longitudinal vibration. After being amplified by the horn, it drives the porous ultrasonic tooling to drive the reversible fixture to resonate, and horizontal ultrasonic vibration is generated on the surface of the blade tenon teeth. On this basis, through the feeding movement of the tenon teeth, the rotational movement of the tenon teeth, the rotational movement of the grinding wheel, and the feeding movement of the grinding wheel, the assisted grinding of the tenon teeth with reversible ultrasonic vibration is realized.

[0107] Referring to Figure 6 、 7 As shown, it can be seen that the coupled vibration mode of the longitudinal full wave and the transverse half wave forms an enlarged single longitudinal vibration at the center (b) of the porous ultrasonic tooling. The amplitude of the central longitudinal vibration region is the largest and uniform. At this time, near-amplitude-free regions appear at the four corners of the rectangle in the longitudinal vibration region. Fixing the vibration platform using these weak amplitude nodes can minimize the dissipation of ultrasonic vibration to the greatest extent and improve the effect of ultrasonic-assisted processing. Compared with the non-porous vibration platform (a), the amplitude is increased, the mass and volume are reduced, and the utilization rate of ultrasonic energy is improved.

[0108] The above are only the preferred embodiments of the present invention and are not used to limit the present invention. For those skilled in the art, various changes and modifications can be made to the present invention. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims

1. A flip - type blade tenon ultrasonic vibration machining device, characterized in that, Including: An ultrasonic component, a porous ultrasonic tooling, a flip - over ultrasonic fixture, and a to - be - machined dovetail tooth; Among them, the porous ultrasonic tooling (17) is installed on the machine tool base plate through the feet (24) at the bottom, and the feet are located at the vibration nodes of the ultrasonic platform; the ultrasonic component is installed on the back of the porous ultrasonic tooling; After the to - be - machined blade dovetail tooth is clamped in the flip - over ultrasonic fixture, the whole is fixed in the central area of the ultrasonic vibration platform; the ultrasonic vibration generated by the ultrasonic component is transmitted to the porous ultrasonic tooling (17) to achieve an enlarged and uniform unidirectional ultrasonic vibration on the workpiece; through the dovetail tooth feeding and rotating motion and the grinding wheel rotating and feeding motion, the flip - over ultrasonic vibration - assisted grinding of the dovetail tooth is realized.

2. The ultrasonic vibration machining device for reversible blade tenon teeth according to claim 1, wherein The ultrasonic component includes an ultrasonic transducer and a horn; among them, the horn is a conical horn, the small end is connected to the porous ultrasonic tooling by bolts, and the large end of the horn is connected to the ultrasonic transducer; the ultrasonic transducer includes a rear cover plate (1), a piezoelectric ceramic (2), and a front cover plate (3); the rear cover plate (1) and the front cover plate (3) clamp the piezoelectric ceramic (2) tightly in the middle, and the front cover plate (3) is connected to the horn (4), and this horn is a conical horn.

3. The ultrasonic vibration machining device for reversible blade tenon teeth according to claim 1, characterized in that, The porous ultrasonic tooling includes a clamping screw with an opening on the side and a tooling pressure plate (20) installed on the opening side. The flip - over fixture is placed inside the clamping screw and is fixed by the tooling pressure plate (20) and then fixed with the help of a clamping bolt (21).

4. The ultrasonic vibration machining device for reversible blade tenon teeth according to claim 1 or 3, characterized in that, Through holes are evenly distributed on the surface and side of the top and bottom panels of the clamping screw of the porous ultrasonic tooling. Vertically, the through holes are evenly distributed on both sides of the horizontal threaded holes, and all the through hole diameters are equal. The hole diameter and hole pitch are calculated by the apparent elasticity method.

5. The ultrasonic vibration machining device for reversible vane tenon teeth according to claim 4, characterized in that, The top, bottom, surface and side of the clamping screw are evenly distributed with through holes. Based on the apparent elasticity method, the relationship between the parameters of the uniformly distributed porous structure and the resonance frequency is established. The equivalent apparent elastic modulus E of the porous structure eff can be expressed as: （1） wherein r s is the hole radius, l m and l n represents x, y the hole pitch in the direction, E is the elastic modulus of the material; The porous structure parameters include but are not limited to hole diameter, hole pitch, and number of holes.

6. The ultrasonic vibration machining device for reversible blade tenon teeth according to claim 1, wherein, The flip - over fixture cooperates with the external ultrasonic tooling. It includes a locking bolt (8), a fixture pressure plate (7), a positioning bolt (9), a pair of top blocks (14), a top block base (15), two positioning pins, a positioning block (13), a tip (12), and a fixture housing (10); the fixture housing (10) is fixedly matched with the clamping screw of the ultrasonic tooling; by rotating the locking bolt (8) at the top, the fixture pressure plate (7) drives the positioning bolt (9) and the upper positioning pin (11) to move downwards to press and limit the vertical displacement of the dovetail tooth (6); the positioning block (13) is located behind the dovetail tooth to limit the axial displacement of the dovetail tooth. A pair of top blocks (14) are fixed to the base by bolts and are used to support the grinding process of the dovetail tooth. The top blocks can be replaced according to different sizes of dovetail teeth; the tip (12) is horizontally arranged on the convex block in front of the fixture housing (10) to limit the horizontal displacement of the dovetail tooth, and the side positioning pin (16) is used to limit the disturbance of the dovetail tooth tail during processing. The above - mentioned positioning parts cooperate to transmit the ultrasonic vibration to the dovetail tooth and fully position the dovetail tooth; By restricting all six degrees of freedom of the to - be - machined dovetail tooth (6), reliable positioning and clamping of the dimensions are achieved.

7. The design method of a flip - blade tenon ultrasonic vibration machining device according to claim 1, characterized in that, First, an ultrasonic vibration model of the tenon is established based on the principle of ultrasonic vibration, and combined with finite element modal analysis, the relationship between the expansion and contraction vibration modal frequency and the geometric parameters of the tenon is obtained; then, based on the design method of the one-dimensional longitudinal vibration ultrasonic device, the structural parameters of the ultrasonic transducer are preliminarily determined according to the resonant frequency of the tenon. On this basis, finite element modal analysis and harmonic response analysis are carried out, and the structural parameters of the ultrasonic transducer are optimized according to the results; the size and weight of the tenon are in the range of 20-300 grams.

8. The design method of a flip - blade tenon - tooth ultrasonic vibration processing device according to claim 6, characterized in that, Firstly, a three-dimensional model of an ultrasonic vibration device for reversible grinding was established using Catia. The model was then converted into stp format and imported into the geometric structure of the Workbench component in the simulation software Ansys. The corresponding auxiliary lines were then drawn in the SpaceClaim component to prepare for subsequent data output and meshing. During the finite element modal analysis, the materials of the various components of the model were allocated and the meshes were divided. Finally, the frequency distribution diagram of the tenon expansion and contraction vibration mode was analyzed and output. The optimal frequency of the vibration transmitted from the tooling to the tenon was determined so that the tenon part of the blade had a larger amplitude and better vibration uniformity. Based on the one-dimensional longitudinal vibration ultrasonic device design method, the structural parameters of the ultrasonic transducer and the amplitude transformer were preliminarily determined according to the tenon resonant frequency obtained by finite element analysis. On this basis, the structural dimensions of the ultrasonic tooling were modified, and finite element modal analysis and harmonic response analysis were performed on tooling with different parameters. The structural parameters of the ultrasonic tooling were optimized based on the results, and the design of the tenon ultrasonic vibration device was preliminarily completed.

9. The operating method of a flip - blade tenon ultrasonic vibration machining device according to claim 1, characterized in that, The reversible fixture is fixed at the center of the porous ultrasonic tooling. The blade tenon to be machined is clamped on the reversible ultrasonic fixture. The ultrasonic transducer is bolted to the back of the porous ultrasonic tooling. In operation, the ultrasonic transducer generates longitudinal vibrations, which are amplified by the amplitude transformer and drive the porous ultrasonic tooling to resonate with the reversible fixture, generating horizontal ultrasonic vibrations on the blade tenon surface. Reversible ultrasonic vibration-assisted grinding of the tenon is achieved through the tenon feed motion, tenon rotation motion, grinding wheel rotation motion, and grinding wheel feed motion. The coupled vibration modes of the longitudinal full wave and transverse half wave form an expanded single longitudinal vibration at the center of the porous ultrasonic tooling. The central longitudinal vibration region has the largest and most uniform amplitude, while near-zero amplitude regions appear at the four corners of the rectangular longitudinal vibration region.

Images