High load gear forming grinding method based on ultrasonic-assisted liquid gallium phase transformation strengthening

Abstract

This invention proposes a high-load gear forming grinding method based on the local phase transition strengthening effect of liquid gallium assisted by ultrasonic rapid cooling. When room-temperature liquid gallium is transported from a constant-temperature storage tank to an ultrasonic atomizing device, the liquid gallium metal is vibrated by ultrasonic waves into atomized particles, which are then propelled forward. Due to the rapid increase in kinetic energy and decrease in internal energy, the ejected liquid gallium atomized particles quickly condense, forming a solid-liquid transition state. The direction of movement of the ejected liquid gallium droplets is controlled by charging electrodes and deflection electrodes, focusing the precise ejection of liquid gallium droplets into the core grinding area. During the solid-liquid transition process of the liquid gallium particles, a large amount of heat energy is rapidly absorbed on the gear processing surface. After thermal melting, gallium atoms react with titanium atoms to form a metastable gallium titanate compound, achieving local phase transition strengthening of the high-dynamic-load gear. This method utilizes the local phase transition strengthening effect of the liquid gallium solid-liquid transition process to significantly enhance the metal strength and toughness of the high-dynamic-load gear, which is in line with the concept of green development.

Description

Technical Field

[0001] This invention relates to the field of machining technology, specifically a high-load gear forming grinding method based on the ultrasonic rapid cooling-assisted local phase change strengthening effect of liquid gallium. It is applicable to the precision machining of high-load gears in aerospace, heavy machinery, and other fields. This invention utilizes the local phase change effect of liquid gallium and ultrasonic rapid cooling technology to optimize the grinding cooling process, improve the metal strength, toughness, and corrosion resistance of the gear, and adapt to high dynamic load working environments. Background Technology

[0002] Form grinding is a crucial method for manufacturing high-precision gears, effectively improving the geometric accuracy of gear teeth, reducing surface roughness, and eliminating deformation after heat treatment of the gear blank. However, traditional gear form grinding technology still faces numerous challenges under high-load conditions, such as heat accumulation during processing, grinding burns, surface microcracks, and accelerated abrasive wear. These problems severely impact the service life and reliability of gears. During the grinding of high-load gears (such as titanium alloy TC4 gears), the intense friction between the workpiece and the grinding wheel can rapidly raise the local temperature to over 1000℃, causing a large amount of the α-phase on the surface of the titanium alloy to transform into the β-phase, reducing the strength and corrosion resistance of the high-load gear. If cooling is not timely, thermal damage can also occur, such as rehardened layers, decarburized layers, and microcracks.

[0003] To reduce grinding heat, traditional methods typically employ large amounts of water-based or oil-based coolants. However, traditional coolants have low heat transfer efficiency, making it difficult to rapidly reduce the temperature in high-load grinding zones within a very short time. This leads to localized heat accumulation and can still cause grinding thermal damage. Newer methods such as supercritical CO2 cooling, cold air jet cooling, and cryogenic refrigerant cooling have seen some application in high-efficiency grinding in recent years. However, these methods either involve complex and costly equipment or have limited precision in controlling grinding temperature, making it difficult to meet the stringent temperature control requirements of high-load gear forming grinding and contradicting the current environmental and low-carbon development trends.

[0004] Liquid metals, due to their excellent thermal conductivity and fluidity, have been extensively studied in fields such as microelectronic packaging, flexible electronics, and thermal management. Gallium (Ga), as a typical liquid metal, has a low melting point (approximately 29.8℃), high thermal conductivity (approximately 40 W / m·K), and good wettability and chemical stability, showing great potential in high-temperature heat transfer and cooling applications. The thermal conductivity of liquid gallium is much higher than that of traditional coolants, allowing for faster heat absorption and transfer during solid-liquid transitions. This significantly reduces the temperature in the processing area and promotes the transformation of the large amount of metallic β-phase formed on the surface of titanium alloys at high temperatures into a metastable phase structure. After molten gallium atoms react chemically with titanium atoms to form metastable gallium titanate compounds, achieving localized phase transformation strengthening of gears under high dynamic loads.

[0005] The invention patent with publication number "CN107405753A" entitled "A Gas-Liquid Two-Phase Jet Cooling Device" discloses a gas-liquid two-phase jet cooling device. Its principle is to spray the liquid at high speed into the machining area through a specially designed nozzle. The high-speed airflow atomizes the liquid into tiny droplets, increasing its surface area and thus improving cooling efficiency. Simultaneously, the impact of the airflow helps remove chips, prevents secondary cutting, and improves machining quality. However, this technical solution still has the following problems: while gas-liquid two-phase jets can improve cooling efficiency, the cooling effect may still be insufficient under high-temperature, high-speed cutting conditions, making it difficult to effectively control the temperature of the tool and workpiece, leading to thermal damage; under certain special machining conditions, its cooling and lubrication effects may be unsatisfactory, limiting its application range. Summary of the Invention

[0006] To address the above problems, this invention provides a high-load gear forming and grinding method based on the ultrasonic rapid cooling assisted local phase transformation strengthening effect of liquid gallium. This method solves the problem that during the forming and manufacturing process of high-dynamic load gears for aerospace applications, the surface metal layer of titanium alloy is affected by high temperature, causing most of the microscopic α metal phase to transform into the β metal phase, thereby reducing the gear's strength and corrosion resistance.

[0007] This invention discloses a high-load gear forming and grinding method based on ultrasonic-assisted liquid gallium phase change enhancement, the high-load gear forming and grinding method based on ultrasonic-assisted liquid gallium phase change enhancement includes the following steps:

[0008] Step 1: Drive the liquid gallium liquid into the reservoir of the ultrasonic atomizer;

[0009] Step 2: The ultrasonic atomizer's liquid storage chamber generates strong resonant oscillations to atomize liquid gallium into atomized liquid gallium droplets;

[0010] Step 3: Deliver the atomized liquid gallium droplets to the atomizing nozzle;

[0011] Step 4: The atomized liquid gallium droplets are charged with uniform positive / negative charges by the charging electrode and enter the deflection control area;

[0012] Step 5: Precision grinding of the gear surface using a grinding wheel;

[0013] Step 6: The atomizing nozzle sprays atomized liquid gallium droplets, and adjusts the electric field distribution according to the temperature distribution data of the grinding contact area to spray the atomized liquid gallium droplets onto the grinding contact area.

[0014] Step 7: Atomized liquid gallium droplets react with titanium alloy to generate a metastable gallium titanate compound;

[0015] Step 8: Liquid gallium particles are effectively filtered and recovered through coarse and fine vibrating filter membranes.

[0016] Furthermore, in step 1, the liquid gallium is driven by a segmented spiral low-frequency electromagnetic coil to flow along a heat-resistant polymer pipe to the ultrasonic atomizer's storage chamber by a pulsating magnetic field generated by the liquid gallium.

[0017] The heat-resistant polymer pipe is equipped with a spiral high-frequency electromagnetic coil for precise temperature control of the pipe through inductive heating, ensuring the fluidity and liquid state of liquid gallium during transportation.

[0018] Furthermore, in step 2, a PLL algorithm is used to monitor the feedback impedance characteristics of the transducer resonant point and adjust the output frequency of the drive signal in real time, so that the output frequency f out Continuously and automatically approximate the actual resonant frequency f r This enables efficient excitation of liquid gallium.

[0019]

[0020] Where, Δθ(t)=θ measured (t)-θ target (0)≈tan -1 (X / R), Δθ(t) represents the phase difference at time t, indicating the deviation between the currently measured phase and the target phase, used for PLL feedback adjustment calculations; θ measured (t) represents the actual operating phase angle calculated at time t by detecting the transducer voltage and current signals; θ target (0) represents the target phase angle set by the system, taken as 0°; X represents the imaginary part of the transducer's equivalent impedance, used to characterize the degree to which the system deviates from the resonant point; R represents the real part of the transducer's equivalent impedance, used to characterize the energy loss in the resonant state; t represents the current discrete time step, used for iterative calculation and real-time control; n represents the historical sampling sequence number in the integral operation, all accumulated data points from the initial time n = 0 to the current time n = t; K p K i For the proportional and integral gain coefficients of the PLL controller;

[0021] By combining the pressure, heat flow, and impact feedback among the grinding wheel, liquid gallium, and workpiece, a coupled feedback control equation of "grinding load-impedance feedback" is designed, and a composite load factor L is established. dyn :

[0022] L dyn =α·F g +β·Q t +γ·ΔT

[0023] Among them, F g Q is the normal force during grinding; tdenoted as transient heat flux density; ΔT is the temperature difference between liquid gallium and the grinding zone; α, β, γ are coupling coefficients obtained through modeling or experimental fitting.

[0024] Then introduce it into the frequency control formula:

[0025]

[0026] Among them, f opt f0 is the current optimal operating frequency, which serves as the reference input value for the PLL controller; k is the current operating frequency; k is the adjustment gain. This indicates the sensitivity of the frequency response to load coupling; the system can automatically adjust the excitation frequency according to the real-time changes in grinding load to ensure optimal efficiency of liquid gallium excitation and avoid oscillation or overload.

[0027] Furthermore, in step 3, the atomized liquid gallium droplets are enveloped in nitrogen gas to reduce gallium oxidation.

[0028] Furthermore, in step 6, the droplets formed by the liquid gallium being charged by the atomizing electrode will be deflected in the electrostatic field formed between the deflecting electrodes, and their trajectory can be approximated as obeying the simplified form of the Lorentz force equation:

[0029] F = qE = ma

[0030] F is the Lorentz force, E is the electric field strength, m is the droplet mass, q is the charge, and a is the acceleration of the droplet under the influence of the electrostatic field.

[0031] The deflection angle θ of the droplet is related to the applied electric field strength E, the droplet mass m, the charge q, and the flight time t as follows:

[0032]

[0033] Where L is the jet length, and t can be calculated from the flight path and initial velocity;

[0034] Real-time temperature distribution maps of the workpiece surface are obtained using thermal imaging or thermocouple matrices. Assume the hotspot appears in the x, y plane with coordinates (x, y). h y h If the origin is (0,0) at the center nozzle, then the target deflection angle is:

[0035]

[0036] Where d is the distance from the nozzle to the workpiece surface;

[0037] Based on the target deflection angle and the characteristics of the droplets, the deflection voltage can be deduced:

[0038]

[0039] Where, d e It is the deflection electrode spacing, and the final high voltage U applied to the system. x and U y Control the deflection electrode to achieve precise control of targeted spraying.

[0040] Furthermore, in step 8, the coarse and fine vibrating filter membranes effectively filter and recover liquid gallium particles, and unused gallium particles are recovered by an electromagnet block and a recovery box.

[0041] The beneficial effects achieved by this invention are:

[0042] This invention utilizes the local phase transition strengthening effect of liquid gallium to form a metastable gallium titanate compound on the surface of loaded gears, significantly improving the gear's metallic strength, toughness, and corrosion resistance. The strengthening phase generated during the phase transition effectively improves the gear's mechanical properties and extends its service life, making it suitable for grinding high-load gears.

[0043] By employing ultrasonic-assisted liquid gallium atomization technology, the liquid gallium droplets can rapidly condense and absorb a large amount of grinding heat in the core grinding region, forming a significant temperature gradient. This effectively avoids the impact of excessive grinding heat on gear surface performance. A precise temperature control system ensures that the entire grinding process remains within the optimal temperature range, optimizing grinding efficiency and gear surface quality.

[0044] This invention utilizes nitrogen to encapsulate liquid gallium droplets, significantly reducing oxidation and ensuring that the liquid gallium rapidly absorbs heat during the solid-liquid transition, thus improving cooling efficiency. The liquid gallium particles quickly absorb heat and complete the phase transition, greatly enhancing cooling efficiency and avoiding the uneven heat distribution and oxidation problems common in traditional cooling methods.

[0045] Employing a highly efficient recovery module, liquid gallium particles are filtered through coarse and fine vibrating filter membranes, and unused gallium particles are recovered by an electromagnet. An external magnetic field further enhances the recovery effect, ensuring efficient resource utilization and reducing waste, aligning with green development principles, reducing environmental pollution, and making it suitable for applications in high-end manufacturing fields such as aerospace.

[0046] This method is highly efficient, rapidly enhances the phase transition of liquid gallium atomized nanoparticles, can be automated, and is low in cost, meeting the requirements of industrial production. Attached Figure Description

[0047] Figure 1 : Flowchart of a high-load gear forming and grinding method based on ultrasonic-assisted liquid gallium phase transition enhancement;

[0048] Figure 2 Schematic diagram of a high-load gear forming grinding device;

[0049] Figure 3 Schematic diagram of heat-resistant polymer pipe and segmented high and low frequency electromagnetic coils;

[0050] Figure 4 Schematic diagram of an ultrasonic atomizer.

[0051] In the diagram, 1. Main controller, 4. Atomizing plate, 5. Piezoelectric ceramic, 10. Charging electrode, 11. High voltage power supply, 13. Nitrogen source, 14. Nitrogen pipe, 15. Pressure detector, 16. Ultrasonic atomizer reservoir, 17. Ultrasonic atomizer, 19. Heat-resistant polymer pipe, 20. Segmented spiral low-frequency electromagnetic coil, 23. One-way valve, 24. Pressure reducing valve, 25. Temperature controller, 26. Infrared temperature sensor, 27. Deflection electrode, 28. Coarse vibrating filter, 29. Fine vibrating filter, 30. Electromagnetic block, 31. Recycling box, 32. External magnetic field, 33. Grinding wheel, 35. Workpiece fixing plate. Detailed Implementation

[0052] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0053] This invention provides a high-load gear forming grinding method based on the ultrasonic rapid cooling-assisted local phase transformation strengthening effect of liquid gallium. The essence lies in using ultrasonic atomization technology to spray liquid gallium into the gear grinding area, and utilizing the solid-liquid transformation of liquid gallium during rapid cooling to quickly absorb a large amount of heat energy, thereby achieving efficient cooling. Liquid gallium particles are formed into fine droplets by ultrasonic vibration and sprayed onto the gear surface. While absorbing grinding heat, this promotes the transformation of the β-metallic phase of the titanium alloy into a metastable phase. This process generates gallium titanate compounds through the reaction of liquid gallium with titanium atoms, improving the gear's metallic strength, toughness, and corrosion resistance. Furthermore, a temperature control system and a recycling module ensure the high efficiency and precision of the entire processing and the recycling of liquid gallium. This method effectively solves the problem of thermal damage in high-load gear processing and improves the overall performance of the gear.

[0054] High-load gear forming grinding method based on ultrasound-assisted liquid gallium phase change enhancement, such as Figure 1-4 As shown, the specific steps are as follows:

[0055] Step 1: By starting the main controller 1, the segmented spiral low-frequency electromagnetic coil 20 and the segmented spiral high-frequency electromagnetic coil 21 are controlled in coordination. The segmented spiral low-frequency electromagnetic coil 20 generates a pulsating magnetic field to drive the liquid gallium liquid to flow along the heat-resistant polymer pipe 19. The segmented spiral high-frequency electromagnetic coil 21 precisely controls the internal temperature of the pipe through inductive heating to ensure the fluidity and liquid state of the liquid gallium during the transportation process and prevent it from solidifying during transportation.

[0056] As liquid gallium flows through pressure reducing valve 24 into the ultrasonic atomizer reservoir 16, the flow rate is precisely controlled. One-way flow via check valve 23 ensures that liquid gallium enters the reservoir and maintains a stable level.

[0057] Step 2: Unlike conventional water-based or oil-based liquid ultrasonic atomization methods, this method designs a dedicated temperature control-ultrasound-assisted spraying-electric control atomization system specifically for the high surface tension, low melting point, and easy oxidation characteristics of liquid gallium. A heating element is introduced into the atomization chamber to continuously heat the liquid gallium, ensuring its stable flow. A high-frequency piezoelectric ceramic transducer system generates strong resonant oscillations. An integrated frequency tracking module employs a PLL (Phase Locked Loop) algorithm, which monitors the feedback impedance characteristics of the transducer's resonant point to adjust the output frequency of the drive signal in real time, achieving efficient excitation of the liquid gallium. Under the influence of factors such as temperature fluctuations, load changes, and changes in gallium flow rate, the resonant frequency will drift slightly. The PLL detects the current impedance phase difference Δθ and feeds it back to the frequency modulator to adjust the output frequency f. out Continuously and automatically approximate the actual resonant frequency f r This achieves dynamic closed-loop regulation. The mathematical essence of the regulation mechanism is:

[0058]

[0059] Where, Δθ(t)=θ measured (t)-θ target (0)≈tan -1 (X / R), while the target phase is 0 degrees (pure resistive state), K p K i These are the proportional and integral gain coefficients of the PLL controller.

[0060] Δθ(t) represents the phase difference at time t, which is the deviation between the currently measured phase and the target phase, and is used for PLL feedback adjustment calculation;

[0061] θ measured (t) represents the actual operating phase angle calculated at time t by detecting the voltage and current signals of the transducer;

[0062] θ target(0) represents the target phase angle set by the system, which is 0° (i.e., the voltage and current are in phase under pure resistance).

[0063] X represents the imaginary part (reactance) of the transducer's equivalent impedance, used to characterize the degree to which the system deviates from its resonant point (unit: ohms).

[0064] R represents the real part (resistance) of the transducer's equivalent impedance, used to characterize the energy loss in the resonant state (unit: ohms);

[0065] t represents the current discrete-time step, used for iterative calculation and real-time control;

[0066] The historical sampling sequence number in the n-integral operation refers to all the cumulative data points from the initial time n=0 to the current time n=t.

[0067] By combining the pressure, heat flow, and impact feedback among the grinding wheel, liquid gallium, and workpiece, a coupled feedback control equation of "grinding load-impedance feedback" is designed, and a composite load factor L is established. dyn :

[0068] L dyn =α·F g +β·Q t +γ·ΔT

[0069] Among them, F g Grinding normal force;

[0070] Q t Transient heat flux density;

[0071] ΔT: Temperature difference between liquid gallium and the grinding zone;

[0072] α, β, γ: Coupling coefficients obtained through modeling or experimental fitting.

[0073] Then introduce it into the frequency control formula:

[0074]

[0075] Where f0: current operating frequency;

[0076] k: Adjust the gain;

[0077] This indicates the sensitivity of the frequency response to load coupling.

[0078] f opt The current optimal operating frequency is used as the reference input value for the PLL controller.

[0079] The system can automatically adjust the excitation frequency according to the real-time changes in grinding load to ensure optimal excitation efficiency of liquid gallium and avoid idling or overload; nitrogen-encased spraying further enhances droplet delivery capacity and effectively prevents oxidation.

[0080] Step 3: Ultrasonic oscillation causes liquid gallium to form nano- to micron-sized fine particles after passing through atomizing plate 4. As the liquid gallium particles are enveloped by nitrogen gas, the pressurized airflow provided by nitrogen source 13 is delivered to atomizing nozzle 17 through air pressure detector 15 and nitrogen pipe 14. This airflow envelops the liquid gallium particles, effectively reducing gallium oxidation and quickly delivering them to the grinding core area.

[0081] Step 4: After atomization, the liquid gallium droplets first pass through the charging electrode 10, acquiring a uniform positive / negative charge, and then enter the deflection control region. This region consists of multiple sets of deflection electrodes 27, arranged in the circumferential and radial directions of the spray path. These electrodes are independently connected to the high-voltage power supply module, enabling the construction of a non-uniform controllable electric field in two or three dimensions.

[0082] Step 5: The grinding wheel 33 is responsible for precision grinding the surface of the gear 30, while the workpiece fixing plate 35 ensures that the workpiece maintains a stable position during the grinding process, thereby ensuring the machining accuracy of the gear surface.

[0083] Step 6: During the grinding process, the control system applies high-voltage electrical signals (100–3000 VDC) of different polarities between different electrodes, generating a spatially directional electric field distribution and forming a "potential gradient path". Because the charged droplets are subjected to Coulomb forces in the electric field, their trajectories undergo controllable deflection, with the deflection angle precisely controlled within the range of 1°–20°, thereby achieving high-precision control of the droplet ejection direction.

[0084] The injection of liquid gallium droplets directly acts on the gear surface, achieving not only efficient cooling but also significantly improving surface quality through a local phase transition enhancement effect.

[0085] To achieve intelligent response, the main controller pre-establishes a thermal field model and an electric field control function library, and communicates with a 26-array infrared temperature sensor. The sensors collect temperature distribution data of the grinding contact area every second and upload it to the main control system. Liquid gallium droplets, after being charged by the atomizing electrodes, will deflect in the electrostatic field between the deflecting electrodes; their trajectory can be approximated as obeying a simplified form of the Lorentz force equation:

[0086] F = qE = ma

[0087] F is the Lorentz force, E is the electric field strength, m is the droplet mass, q is the charge, and a is the acceleration of the droplet under the influence of the electrostatic field.

[0088] The deflection angle θ of the droplet is related to the applied electric field strength E, the droplet mass m, the charge q, and the flight time t as follows:

[0089]

[0090] Where L is the jet length, and t can be calculated from the flight path and initial velocity. This model provides a basis for deflection voltage design. Real-time temperature distribution maps of the workpiece surface are obtained through thermal imaging or a thermocouple matrix. It is assumed that the hotspot appears in the x, y plane with coordinates (x...). h y h If the origin is (0,0) at the center nozzle, then the target deflection angle is:

[0091]

[0092] Where d is the distance from the nozzle to the workpiece surface.

[0093] Based on the target deflection angle, and considering the droplet characteristics (mass m, initial velocity v, and charge q), the deflection voltage can be derived:

[0094]

[0095] Among them, E x E represents the electric field strength in the x-direction. y d represents the electric field intensity in the y-direction. e It is the deflection electrode spacing, and the final high voltage U applied to the system. x U y Control the deflection electrode to achieve precise control of targeted spraying.

[0096] Step 7: When the liquid gallium droplets in the solid-liquid transition state enter the core grinding region, they absorb a large amount of heat energy, creating a significant temperature gradient. This promotes the high-temperature-induced transformation of the titanium alloy's β-metal phase into a metastable phase. Under the strengthening effect of the local phase transformation of liquid gallium, the molten gallium atoms react with titanium atoms in a high-temperature environment to form a metastable gallium titanate compound. This effectively improves the metallic strength, toughness, and corrosion resistance of the titanium alloy, ensuring a longer service life for the gears under high-load conditions.

[0097] Temperature controller 25 and main control controller 1 precisely control the temperature of the entire system, ensuring that the optimal temperature range for liquid gallium is maintained at different stages. The temperature control system can automatically adjust the temperature control equipment of each part according to real-time feedback to ensure the continuous and stable atomization effect of liquid gallium and prevent temperature fluctuations from adversely affecting the processing.

[0098] Step 8: The coarse vibrating filter membrane 28 and the fine vibrating filter membrane 29 effectively filter and recover liquid gallium particles, and unused gallium particles are recovered by the electromagnet block 30 and the recovery box 31. The recovery effect is further enhanced by the external magnetic field 32, ensuring the effective recycling of resources.

[0099] The above are merely specific steps of the present invention and do not constitute any limitation on the scope of protection of the present invention; all technical solutions formed by equivalent transformation or equivalent substitution fall within the scope of protection of the present invention; the parts of the present invention not described in detail are common knowledge to those skilled in the art.

Claims

1. A high-load gear forming grinding method based on ultrasonic-assisted liquid gallium phase transformation strengthening, characterized in that, The high-load gear forming and grinding method based on ultrasonic-assisted liquid gallium phase change enhancement includes the following steps: Step 1: Drive the liquid gallium liquid into the reservoir of the ultrasonic atomizer; Step 2: The ultrasonic atomizer's liquid storage chamber generates strong resonant oscillations to atomize liquid gallium into atomized liquid gallium droplets; Step 3: Deliver the atomized liquid gallium droplets to the atomizing nozzle; Step 4: The atomized liquid gallium droplets are charged with uniform positive / negative charges by the charging electrode and enter the deflection control area; Step 5: Precision grinding of the gear surface using a grinding wheel; Step 6: The atomizing nozzle sprays atomized liquid gallium droplets, and adjusts the electric field distribution according to the temperature distribution data of the grinding contact area to spray the atomized liquid gallium droplets onto the grinding contact area. Step 7: Atomized liquid gallium droplets react with titanium alloy to generate a metastable gallium titanate compound; Step 8: Liquid gallium particles are effectively filtered and recovered through coarse and fine vibrating filter membranes. In step 2, the PLL algorithm is used to monitor the feedback impedance characteristics of the transducer resonant point and adjust the output frequency of the drive signal in real time to make the output frequency... Continuously and automatically approximate the actual resonant frequency This enables efficient excitation of liquid gallium. ； in, , This represents the phase difference at time t, indicating the deviation between the currently measured phase and the target phase, and is used for PLL feedback adjustment calculations. This represents the actual operating phase angle calculated at time t by detecting the transducer voltage and current signals; This represents the target phase angle set by the system, which is 0°. The imaginary part of the transducer's equivalent impedance is used to characterize the degree to which the system deviates from its resonant point. The real part of the equivalent impedance of the transducer is used to characterize the energy loss in the resonant state. This represents the current discrete-time step count, used for iterative calculations and real-time control. The historical sampling sequence number in the integration operation, representing all accumulated data points from the initial time n=0 to the current time n=t; , For the proportional and integral gain coefficients of the PLL controller; By combining the pressure, heat flow, and impact feedback among the grinding wheel, liquid gallium, and workpiece, a coupled feedback control equation of "grinding load-impedance feedback" is designed, and a composite load factor is established. : ； in, For grinding normal force; This refers to the transient heat flux density; α represents the temperature difference between liquid gallium and the grinding zone; α, β, and γ are coupling coefficients obtained through modeling or experimental fitting. Then introduce it into the frequency control formula: ； in, The current optimal operating frequency is used as the reference input value for the PLL controller. This is the current operating frequency; To adjust the gain; This indicates the sensitivity of the frequency response to load coupling; the system can automatically adjust the excitation frequency according to the real-time changes in grinding load to ensure optimal efficiency of liquid gallium excitation and avoid oscillation or overload.

2. The high-load gear forming grinding method based on ultrasonic-assisted liquid gallium phase transition strengthening according to claim 1, characterized in that, In step 1, the liquid gallium is driven by a segmented spiral low-frequency electromagnetic coil to flow along a heat-resistant polymer pipe to the storage chamber of the ultrasonic atomizer by a pulsating magnetic field generated by the liquid gallium. The heat-resistant polymer pipe is equipped with a spiral high-frequency electromagnetic coil for precise temperature control of the pipe through inductive heating, ensuring the fluidity and liquid state of liquid gallium during transportation.

3. The high-load gear forming grinding method based on ultrasonic-assisted liquid gallium phase change strengthening according to claim 1, characterized in that, In step 3, the atomized liquid gallium droplets are enveloped in nitrogen gas to reduce gallium oxidation.

4. The high-load gear forming grinding method based on ultrasonic-assisted liquid gallium phase transition strengthening according to claim 1, characterized in that, In step 6, the droplets formed by the liquid gallium being charged through the atomizing electrode will be deflected in the electrostatic field formed between the deflecting electrodes. Their trajectory can be approximated as obeying the simplified form of the Lorentz force equation: ； Let E be the Lorentz force, E be the electric field strength, m be the droplet mass, and q be the charge. This is the acceleration of the droplets under the influence of an electrostatic field; The deflection angle θ of the droplet is related to the applied electric field strength E, the droplet mass m, the charge q, and the flight time t as follows: ； Where L is the jet length, and t can be calculated from the flight path and initial velocity; Real-time temperature distribution maps of the workpiece surface are obtained through thermal imaging or thermocouple matrix. Assume the hotspot appears at coordinates (x, y) in the x, y plane. , If the origin is (0,0) at the center nozzle, then the target deflection angle is: ， ； Where d is the distance from the nozzle to the workpiece surface; Based on the target deflection angle and the characteristics of the droplets, the deflection voltage can be deduced: ， ； ， ； in, It is the deflection electrode spacing, and the final high voltage applied to the system. and Control the deflection electrode to achieve precise control of targeted spraying.

5. The high-load gear forming grinding method based on ultrasonic-assisted liquid gallium phase change strengthening according to claim 1, characterized in that, In step 8, the coarse and fine vibrating filter membranes effectively filter and recover liquid gallium particles, and unused gallium particles are recovered by an electromagnet block and a recovery box.

Images