Ultrasonic internal broaching broach vibration mode design and control method

Abstract

The invention belongs to the technical field of machining, and particularly relates to an ultrasonic internal broaching broach vibration mode design and control method, which comprises the following steps: firstly, based on a modal isolation structure design method, accurately designing axial and radial vibration modes of a broach so as to meet the requirements of high-precision and high-efficiency broaching machining; a signal processing method based on filtering driving is provided, a designed target vibration mode is accurately driven, the problem that the vibration mode bandwidth of PZT changes along with working conditions such as temperature is solved, finally, due to the fact that the broach frequency vibration mode drifts along with working condition changes in practical application, a dynamic frequency tracking system is developed, and it is ensured that when signals are close to the resonant frequency, the vibration mode bandwidth of the PZT changes along with the working condition changes. The driving frequency can be dynamically adjusted, and it is ensured that the ultrasonic-assisted broaching system is always kept in the target vibration mode. Through optimization and improvement in the three aspects, the ultrasonic vibration broaching effect of the high-strength and high-hardness workpiece is remarkably improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of machining, in particular to an ultrasonic internal broaching broach vibration mode design and control method. BACKGROUND

[0002] In recent years, ultrasonic assisted machining (UAM) technology has been successfully introduced into the field of broaching. This innovative integration brings many significant advantages. On the one hand, it greatly improves the cutting performance of the tool, enabling the tool to remove material more efficiently during the machining process. On the other hand, it effectively alleviates the extreme load and wear experienced by the tool, prolonging the tool's service life and reducing machining costs. More importantly, the application of UAM technology has greatly broken through the bottleneck faced by traditional broaching in dealing with high-strength, high-hardness and sticky-tough difficult-to-machine materials, greatly expanding the material adaptability and processing capacity boundaries. This not only brings new development opportunities to the broaching field, but also provides more efficient and reliable processing methods for related industries, promoting the development and progress of the entire manufacturing industry.

[0003] The vibration mode of the broach has a crucial impact on the broaching effect. However, in the actual processing of ultrasonic assisted broaching, the vibration mode of the broach often changes significantly due to various factors, presenting multiple different modes. This can lead to multi-directional ultrasonic vibration effects, which in turn have a significant impact on processing precision and efficiency: on the one hand, the multi-directional vibration intensifies, which can lead to an increase in surface unevenness, significantly reducing surface quality and dimensional accuracy; on the other hand, the change in cutting force distribution and direction affects processing efficiency and disrupts the stability of the cutting process. Research shows that the change in broach vibration mode is closely related to the excitation vibration mode characteristics of the PZT, while the excitation vibration mode bandwidth of the PZT varies with temperature and other working conditions. The frequency vibration mode of the broach also drifts with changes in working conditions, making precise control of the target vibration mode extremely complex.

[0004] To solve this problem, the present application aims to provide an ultrasonic internal broaching broach vibration mode design and control method that can accurately design the vibration mode of the broach and accurately drive it, and can also dynamically adjust the driving frequency to ensure that the ultrasonic assisted broaching system always maintains the target vibration mode, thereby achieving stable broaching of high-strength and high-hardness workpieces. SUMMARY

[0005] The present application aims to overcome the above-mentioned deficiencies of the prior art and provide an ultrasonic internal broaching broach vibration mode design and control method that can accurately design the vibration mode of the broach and accurately drive it, and can also dynamically adjust the driving frequency to ensure that the ultrasonic assisted broaching system always maintains the target vibration mode, thereby achieving stable broaching of high-strength and high-hardness workpieces.

[0006] To achieve the above object, the present application provides an ultrasonic internal broaching broach vibration mode design and control method, comprising the following steps: A. Broach vibration mode design; A1. Modal simulation analysis; A1-1. Establish a parameterized model; Use finite element analysis software (such as ANSYS / COMSOL) to establish a broach parameterized model, and set the material as cemented carbide with a density of 14.5 g / cm³ and an elastic modulus of 600 GPa.

[0007] A1-2. Perform working mode calculation; 1) Determine the cutting time of each tooth of the broach; The first tooth of the broach tooth from the cutting-in end is set as No. 1, and the last tooth when cutting out is set as No. M. Through the workpiece thickness L and the broach tooth spacing distance L1, the broach cutting speed V, the time period of each tooth participating in cutting during broaching is determined.

[0008] 2) Determine the cutting force; In this application, when the ultrasonic auxiliary process is effective, the ultrasonic auxiliary cutting force is not higher than 80% of the conventional cutting force. The cutting force applied to each tooth is set as 80% of the conventional single-tooth cutting force. The conventional single-tooth cutting force can be determined by a single-tooth cutting force test. Herein, no further description is made.

[0009] 3) Vibration mode acquisition; When the broach is clamped, the time-varying load determined in the previous step is applied to each tooth of the broach, and the first n modes are calculated to obtain the vibration mode near NKHz, not more than 1.1NKHz; wherein n is the order number, and N is the numerical value of the preset modal frequency; if after n is taken, the maximum modal frequency calculated is close to NKHz, the axial (longitudinal) and radial (bending / torsion) natural frequencies of the broach near NKHz frequency are extracted; if the obtained frequency does not reach 1.1NKHz, the value of n is increased to 1.1n, until the maximum modal frequency calculated is close to NKHz. In this application, "close" means that the difference between the index values is within a specified range, such as ±3%.

[0010] 4) Vibration mode selection; In the vibration mode obtained in the previous step, two vibration modes with large axial vibration amplitude and small radial vibration amplitude are selected and marked as S and K, respectively. The specific selection criteria are: mark the mode shape with the largest ratio of axial vibration amplitude to radial vibration amplitude as S mode shape, then screen out mode shapes with a frequency interval of no less than A Hz from the S mode shape, and in the multiple mode shapes meeting the interval requirement, select the mode shape with the largest ratio of axial vibration amplitude to radial vibration amplitude again, and mark it as K mode shape. The value of A is set according to actual requirements, for example, it can be set to 500.

[0011] The benefits of using the above selection criteria are: the S mode shape is based on the mode shape with the axial vibration amplitude as large as possible compared to the radial vibration amplitude, and the K mode shape is determined based on the minimum interval frequency (A), so that the modification range is minimized when optimizing the cross-sectional size of the broach to change the mode shape. Selecting the mode shape with the axial vibration amplitude as large as possible compared to the radial vibration amplitude within this range can ensure that the effect of optimizing the cross-sectional size to change the mode shape is most significant.

[0012] A1-3, carry out free modal calculation; 1) Put the broach in an unconstrained state, calculate the mode shape modal near N KHz, and extract the mode shape and vibration frequency and amplitude when the vibration amplitude of the broach clamping is 0; 2) Record the free modal mode close to the K mode shape frequency as K1 mode shape, and record the free modal mode close to the S mode shape frequency as S1 mode shape; the optimization target is to make the K1 mode shape as close as possible to the K mode shape frequency and the S1 mode shape frequency as close as possible to the S mode shape frequency, so as to reduce the ultrasonic vibration energy loss through the frequency mode shape.

[0013] A2, cross-sectional optimization design; A2-1, at the axial interval of the broach teeth and at the mode shape peak or trough, increase or decrease the diameter to increase or decrease the axial stiffness, so as to improve the S mode shape frequency; A2-2, increase grooves at the circumferential interval of the broach teeth to modify the radial stiffness of the broach to reduce the K mode shape frequency; A2-3, in the software, use a combination optimization method to obtain the diameters at the axial intervals of the optimized multiple broach teeth and the depths and widths of the circumferential grooves of the broach teeth, and select the optimal size.

[0014] A3, modal test; Take the existing broach as a sample, carry out hammer modal test according to the optimized size, compare and analyze the simulation and actual test frequencies, if the error is ≤3%, it is qualified, otherwise further modification; that is, according to the influence law of the increase of the axial interval diameter of the broach teeth and the circumferential interval groove size change on the S and K mode shapes, modify the broach size until the desired requirements are met.

[0015] B, filter driving signal design; Determine the bandwidth of exciting the S mode shape and the K mode shape modal frequency, including: B1, Designing a band-pass filter; B1-1, Conducting a sweep test to determine the axial modal bandwidth; 1) Use a signal generator to output a sinusoidal sweep signal in the target frequency range to drive the piezoelectric ceramic, and use a laser vibration meter to record the amplitude of the cutter blade to determine the resonance peak half-power bandwidth; 2) After testing, perform data post-processing, use the Python toolkit SciPy, use the find_peaks function to detect the resonance peak position, and calculate the bandwidth by the half-power bandwidth method; B1-2, Thermal drift compensation; B2, Digital filter implementation; B2-1, Selection of window function; Use Kaiser Window to optimize the transition band; B2-2, Fixed-point optimization; Quantize the filter coefficients to 18-bit fixed-point format to improve computational efficiency when implemented in hardware; B2-3, Use FPGA to accelerate the filter; Use Xilinx's hardware acceleration architecture, process 8 DSP48E1 units in parallel, provide 200MSPS processing throughput; by inserting a 12-stage shift register, compensate for the group delay of the filter, ensure that the total delay is kept within 0.6μs; B2-4, Design of FIR filter; Design a FIR filter with linear phase characteristics to ensure that the signal will not be distorted due to the filtering process; C, Dynamic frequency tracking; Ensure that the signal can dynamically adjust the driving frequency when it is near the resonance frequency, including: C1, Design of PLL system; Design a hybrid PLL (Phase-Locked Loop) system that combines a digital phase discriminator and CORDIC algorithm to calculate the phase difference and accurately adjust the driving frequency; C2, Use dual-mode tracking strategy; In the locking phase, the system performs fast frequency locking through the coarse adjustment mode, with a step size of 100Hz; in the steady state phase, enter the fine adjustment mode, with a step size of 1Hz, to achieve more precise frequency adjustment; C3, Add fault protection mechanism; When the system detects a phase mutation of more than 30°, trigger an emergency stop and automatically switch to a backup analog filter; C4, Adaptive bandwidth adjustment; By designing an accurate band-pass filter, combining hardware deployment and dynamic frequency tracking technology, the position of the resonance peak is detected in real time, and the passband range of the filter is adjusted accordingly.

[0016] Further, in the step of determining the cutting time of each tooth of the broach, taking the initial cutting time as 0, then: The cutting time period of the first tooth is 0 to L / V time, The cutting time period of the second tooth is L1 / V time to (L+L1) / V time, The cutting time period of the third tooth is 2×L1 / V time to (L+2×L1) / V time, … By analogy, the cutting time period of the qth tooth is (q-1)×L1 / V time to (L+(q-1)×L1) / V time. Let the total number of teeth of the broach be M, then the cutting time period of the Mth tooth is (M-1)×L1 / V time to (L+(M-1)×L1) / V time.

[0017] Further, in the process of obtaining the mode shape, if the maximum frequency value calculated after n is taken reaches 1.1N KHz, then the value of n is increased to 1.1n and the calculation is continued; until the maximum modal frequency calculated approaches N KHz.

[0018] Further, in the process of obtaining the mode shape, the obtained axial and radial mode shapes, natural frequencies, axial vibration amplitudes and radial vibration amplitudes are respectively recorded as: 1, f1, f x1 , f y1 ; 2, f2, f x2 , f y2 ; …; i, f i , f xi , f yi ; …; i+1, f i+1 , f x(i+1) , f y(i+1) ; …; j-1, f j-1 , f x(j-1) , f y(j-1) ; j, f j , f xj , f vj ; Where i represents the i-th mode shape, f iωi represents the i-th order natural frequency, f xi ωi represents the i-th order axial vibration amplitude, f yi ωi represents the i-th order radial vibration amplitude, j is the total number of modes extracted to near NKHz.

[0019] Further, in the mode selection, if the S mode is determined, but in the selection of the K mode, the condition that the mode frequency interval is not less than a certain value (A) cannot be met, then the mode with the largest frequency interval from the S mode is selected as the K mode. Ensure the minimum modification range of optimizing the cross-sectional size to improve the mode.

[0020] Further, in step A2-1, the diameter of the first broach tooth and the second broach tooth at the axial interval is D1, the diameter of the second broach tooth and the third broach tooth at the axial interval is D2, and so on, and the last one is Di, and the optimization interval of the broach diameter is set to 20-30mm, and the increment of the diameter is 1mm.

[0021] Further, in step A2-2, the initial values of the width and depth of the groove are 0.5mm and 1mm respectively, wherein the width increment is 0.1mm, and the maximum value is 1mm; the depth increment is 0.2mm, and the maximum value is 3mm.

[0022] Further, in step B1-1, when the phase delay causes mode distortion, a minimum phase IIR filter is used or a pre-compensation delay is added.

[0023] Further, in step B1-1, in order to further improve the bandwidth calibration accuracy, a logarithmic frequency sweep is used to improve the low frequency resolution.

[0024] Further, in step B1-1, the target frequency range is set to 18-22kHz, the duration is 500ms, the test voltage is increased from 50V to 150V, and the step size is set to 0.5Vpp, which is used to test the voltage-bandwidth correlation.

[0025] Further, in step B1-2, the thermal drift compensation specifically includes the following operations: 1) Insert a calibration signal after every 5 sweeps; the frequency value of the calibration signal is in the target frequency range; 2) Use a temperature sensor to record the temperature rise data of the PZT in real time, and establish a correction relationship between the bandwidth and the temperature based on the temperature rise data, which is used to adjust the bandwidth value in real time.

[0026] Further, the correction relationship between the bandwidth and the temperature specifically includes the following process: a. Design of temperature monitoring system; In order to monitor the temperature change of PZT in real time, the temperature monitoring system includes a plurality of temperature sensors which are precisely placed near the PZT for capturing the temperature rise data generated by the PZT during operation; b. Establishing the relationship between bandwidth and temperature; The temperature rise data collected by the temperature sensor in real time is transmitted to the processing unit to establish the correction relationship between bandwidth and temperature; c. Calculation of temperature correction coefficient; The temperature correction coefficient is calculated through the correction relationship between bandwidth and temperature established in the previous step; d. Bandwidth correction and real-time adjustment; When the temperature changes, the bandwidth value is adjusted in real time according to the previously established relationship between bandwidth and temperature.

[0027] Further, the temperature correction coefficient is obtained through the following steps: 1) Experimental calibration; By testing multiple times under different temperature conditions, record the bandwidth and temperature value at each test time; 2) Data fitting; Through fitting the experimental data, a mathematical expression of the correction coefficient is obtained, and this relationship usually presents as linear or quadratic curve.

[0028] Further, step B2 further includes: B2-5, backup analog circuit design; Use parallel resonance circuit and operational amplifier buffer circuit to realize filtering near the selected frequency, as a supplement to digital filter, provide more redundancy and stability.

[0029] Further, in step C1, the PLL system includes a phase detector, a voltage-controlled oscillator and a frequency adjustment module, wherein the phase detector is used to compare the phase difference of the current and voltage of the PZT, and the voltage-controlled oscillator is used to adjust the driving frequency so that it is always consistent with the resonance frequency.

[0030] Further, the impedance matching is performed on the wiring of the PZT driving circuit, 50Ω microstrip line is adopted to optimize the signal transmission quality, the uniform temperature plate is added to the FPGA to ensure that the junction temperature is lower than 85℃; AlN ceramic is selected for the PZT substrate, and the high thermal conductivity of AlN ceramic is used to effectively reduce the temperature rise of the equipment.

[0031] Further, in step C, the fault tree analysis (FTA) method is adopted to identify faults, and countermeasures are formulated for each fault mode.

[0032] Compared with the prior art, the beneficial effects of the present application are: the ultrasonic internal broaching broach vibration mode design and control method provided by the present application firstly accurately designs the vibration mode of the broach, so that the broach vibration mode meets the needs of high-precision and high-efficiency broaching machining, then, for the target vibration mode of the broach, the driving signal is optimized so that it can accurately drive the target vibration mode, finally, through dynamic frequency tracking, it is ensured that the signal can dynamically adjust the driving frequency when it is near the resonance frequency, so that the ultrasonic auxiliary broaching system always maintains the target vibration mode, through the above three improvements, the ultrasonic vibration broaching effect of high-strength and high-hardness workpieces is significantly improved. BRIEF DESCRIPTION OF DRAWINGS

[0033] Figure 1 is a flowchart of the dual-mode tracking strategy used in the present application; Figure 2 is a flowchart of the fault tree analysis (FTA) method used in the present application. DETAILED DESCRIPTION

[0034] In order to make the purpose, technical scheme and advantages of the present application more clear and explicit, in the following description, the description of known structures and technologies is omitted to avoid unnecessary confusion of the concepts in the present application. EMBODIMENT

[0035] An ultrasonic internal broaching broach vibration mode design and control method is provided in this embodiment, which includes the following steps: A, broach vibration mode design; A1, modal simulation analysis; A1-1, establishing a parameterized model; Use ANSYS / COMSOL to establish a broach parameterized model, and set the material as hard alloy (density 14.5 g / cm³, elastic modulus 600 GPa).

[0036] A1-2, carrying out working mode calculation; (1) Determine the cutting time of each tooth of the broach; The broach is clamped at the connection with the clamping sleeve, the broach teeth are counted from the cutting-in end, the first tooth is set as No. 1, and the last tooth is set as No. M when cutting out, the cutting time of each tooth during broaching is determined through the workpiece thickness L, the broach tooth spacing distance L1 and the broaching speed V; taking the initial cutting time as 0, then: the cutting time of the first tooth is 0 to L / V, the cutting time of the second tooth is L1 / V to (L+L1) / V, the cutting time of the third tooth is 2×L1 / V to (L+2×L1) / V,… Similarly, the cutting time period of the qth tooth is (q-1) x L1 / V moment to (L+(q-1) x L1) / V moment; if the total number of teeth of the broach is M, the cutting time period of the Mth tooth is (M-1) x L1 / V moment to (L+(M-1) x L1) / V moment.

[0037] (2) Determine the cutting force; Since the vibration amplitude of the broach tooth cannot be determined, the cutting force value will significantly affect the ultrasonic vibration mode of the broach. In this application, when the ultrasonic auxiliary process is effective, the ultrasonic auxiliary cutting force is not higher than 80% of the conventional cutting force. The cutting force applied to each tooth is set to be 80% of the conventional single-tooth cutting force. The conventional single-tooth cutting force can be determined by a single-tooth cutting force test.

[0038] (3) Vibration mode acquisition; When the broach is clamped, the time-varying load determined in the previous step is applied to each tooth of the broach, and the first n modes are calculated to obtain the vibration mode near NKHz, not exceeding 1.1NKHz; wherein n is the order, and N is the number of preset modal frequencies; First, set n to 100 and N to 20. If the maximum modal frequency calculated is close to 20KHz, extract the axial (longitudinal) and radial (bending / torsional) natural frequencies near 20KHz. If the frequency does not reach 22KHz, increase n to 1.1n until the maximum modal frequency calculated is close to 20KHz.

[0039] Set the extracted vibration mode frequency range to 18KHz-22KHz, and record the axial (longitudinal) and radial (bending / torsional) vibration modes, natural frequencies, axial vibration amplitudes, and radial vibration amplitudes as follows: 1, f1, f x1 , f y1 ; 2, f2, f x2 , f y2 ; …; i, f i , f xi , f yi ; …; i+1, f i+1 , f x(i+1) , f y(i+1) ; …; j-1, f j-1 , f x(j-1) , f y(j-1) ; j, f j , f xj , fvj ; where i represents the i-th order mode, f i represents the i-th order natural frequency, f xi represents the i-th order axial vibration amplitude, f yi represents the i-th order radial vibration amplitude, j is the total number of modes extracted to the mode close to N KHz.

[0040] (4) Mode selection; By comparing the axial and radial vibration amplitudes and the modal frequency, since the radial vibration is mainly caused by the bending mode, the two modes with large axial vibration amplitude and small radial vibration amplitude are selected from the modes obtained in the previous step (3) and are marked as S and K respectively.

[0041] The specific selection criteria are as follows: the mode with the largest ratio of axial vibration amplitude to radial vibration amplitude is marked as S mode, then modes with a frequency interval of no less than 500 Hz from the S mode are selected, and among the modes meeting the interval requirement, the mode with the largest ratio of axial vibration amplitude to radial vibration amplitude is selected again and is marked as K mode. Since the extracted mode frequencies are from 18 KHz to 22 KHz, modes with a frequency interval of no less than 500 Hz can usually be extracted. If after determining the S mode, the K mode cannot be selected to meet the condition that the frequency interval of the two modes is no less than 500 Hz, the mode with the largest frequency interval is selected as the K mode.

[0042] The benefits of using the above selection criteria are as follows: first, the S mode is based on the mode with the axial vibration amplitude as large as possible and the radial vibration amplitude as small as possible, and the K mode is determined based on the minimum interval of 500 Hz frequency, so that the modification range is minimized when optimizing the cross-sectional size to change the mode. Within this range, selecting the mode with the axial vibration amplitude as large as possible and the radial vibration amplitude as small as possible can ensure that the effect of optimizing the cross-sectional size to change the mode is most significant. When the minimum frequency interval requirement cannot be met, the frequency interval is selected by finite element to determine the K mode as the mode with the largest interval based on the S mode, which can ensure the minimum modification range of optimizing the cross-sectional size to change the mode.

[0043] A1-3, perform free modal calculation; (1) The broach is in an unconstrained state, and the mode modal is calculated near 20 KHz, and the mode and the vibration frequency and amplitude when the vibration amplitude of the broach clamping part is 0 are extracted; (2) Set the optimization target; The free mode shape close to the K mode shape frequency is denoted as K1 mode shape, and the free mode shape close to the S mode shape frequency is denoted as S1 mode shape; the optimization target is that the K1 mode shape is as close as possible to the K mode shape frequency, and the S1 mode shape frequency is as close as possible to the S mode shape frequency, so as to reduce the ultrasonic vibration energy loss through the frequency mode shape proximity. The interval between the S mode shape frequency and the K mode shape frequency is ensured to be as large as possible, and the minimum threshold is set to 2000 Hz.

[0044] A2, cross-section optimization design; A2-1, at the axial interval of the broach teeth and at the mode shape crest or trough, the axial stiffness is increased or decreased by increasing or decreasing the diameter, the diameter of the first broach tooth and the second broach tooth is denoted as D1, the diameter of the second broach tooth and the third broach tooth is denoted as D2, and so on, and the diameter of the last broach tooth is denoted as Dm, the optimization interval of the broach diameter is set to 20-30 mm, and the optimization diameter interval is increased by 1 mm. The main basis of this operation is that the mode shape can be adjusted by modifying the optimization stiffness at the crest or trough of the broach mode shape, that is, the S mode shape frequency can be improved.

[0045] A2-2, grooves are added at the circumferential interval of the broach teeth to modify the radial stiffness of the broach, so as to reduce the K mode shape frequency. That is, symmetric grooves can be machined at 1 / 4 of the length interval of the broach teeth (usually at 1 / 4 of the length from the clamping end). The initial values of the width and depth of the symmetric grooves are 0.5 mm and 1 mm respectively, wherein the width is increased by 0.1 mm, and the maximum value is 1 mm. The depth is increased by 0.2 mm, and the maximum value is 3 mm.

[0046] A2-3, in the software, a combination optimization method is used to obtain the diameters of the axial intervals of the optimized multiple broach teeth and the depths and widths of the circumferential grooves of the broach teeth, and the optimal one is selected according to the previous standard.

[0047] A3, modal test; The existing broach is used as a sample, and the modal test is carried out according to the optimized size, wherein the transition arc radius of the variable cross-section is not less than 5 mm to reduce the stress concentration value, and the surface roughness is not more than 0.8 um to reduce the modal damping. The simulation and actual test frequency are compared and analyzed, if the error is less than or equal to 3%, it is qualified, otherwise it is further modified, that is, the size of the broach is modified according to the change of the axial interval diameter of the broach teeth and the circumferential interval groove size, and the influence law of the S and K mode shapes, until the desired requirements are met.

[0048] B, filter driving signal design; This step is used to determine the bandwidth of the excitation S and K mode shape modal frequency; B1, design a band-pass filter; B1-1, Conduct sweep test to determine the axial modal bandwidth; 1) Use a signal generator to output an 18-22 kHz sinusoidal sweep signal to drive the piezoelectric ceramic (PZT), and use a laser vibration meter to record the amplitude of the cutting edge of the broach, to determine the half-power bandwidth of the resonance peak, i.e. the resonance power curve is half of the original, the amplitude is reduced to the corresponding frequency bandwidth, such as 19.8-20.2 kHz; when the phase delay causes distortion of the vibration mode, use a minimum phase IIR filter or add pre-compensation delay. In order to further improve the accuracy of bandwidth calibration, use logarithmic sweep to improve the resolution of the low frequency band. The frequency range is 18-22 kHz, the duration is 500 ms, the test voltage increases from 50 V to 150 V, the step size is set to 0.5 Vpp, and the test voltage-bandwidth correlation is tested.

[0049] 2) After testing, perform data post-processing, use the Python toolkit SciPy to detect the resonance peak position using the find_peaks function, and calculate the bandwidth by the half-power bandwidth method, The Python code is as follows: from scipy.signal import find_peaks peaks, _ = find_peaks(vibration_data, height=0.8×max_amp, width=5) bandwidth = freq[peaks[-1]] - freq[peaks[0]] # Half-power bandwidth B1-2, Thermal drift compensation; When the piezoelectric ceramic (PZT) is working, it will generate heat and cause the piezoelectric ceramic excitation frequency and amplitude to change, which needs to be compensated for thermal drift: 1) Insert a 20 kHz calibration signal every 5 sweeps; 2) Use a temperature sensor to record the temperature rise data of the PZT in real time, and based on the temperature rise data, establish a correction coefficient between bandwidth and temperature, to further improve the accuracy of bandwidth measurement. Specifically, the following processes are included: a. Design of temperature monitoring system; In order to monitor the temperature change of piezoelectric ceramic (PZT) in real time, a temperature monitoring system includes multiple temperature sensors that are precisely placed near the PZT to capture the temperature rise data generated by the PZT during operation. Common temperature sensors such as thermocouples or RTDs (resistance temperature detectors) can be used, which have high precision and fast response characteristics, and can capture small changes in temperature in a short time. In practical applications, the operation of PZT will cause its surface temperature to rise continuously, especially under long-time driving or high-power driving, the temperature rise effect may cause the frequency characteristics (including bandwidth) to change. This is because the physical properties of piezoelectric materials will change as the temperature rises, especially near its critical temperature, the bandwidth will expand or shrink. Therefore, real-time monitoring of temperature sensors can provide key data on temperature changes, providing a basis for subsequent bandwidth correction.

[0050] b. Establishing the relationship between bandwidth and temperature; The temperature rise data collected by the temperature sensor in real time is transmitted to the processing unit, in order to ensure the accuracy of the bandwidth measurement, the correction relationship between bandwidth and temperature needs to be established. This relationship is usually modeled based on experimental data, the bandwidth of PZT can be measured at different temperatures, and then through these experimental data, how the bandwidth changes with temperature changes can be determined. Assuming that the bandwidth of PZT at room temperature is BW_0, and the bandwidth at high temperature is BW_T, the difference between the two can be obtained through experiments, and modeled as a temperature-dependent function, usually this relationship shows a linear or nonlinear change trend. For example, during the experiment, the temperature of the PZT can be controlled by changing the driving voltage, and the bandwidth change at that time is recorded. Assuming that the bandwidth of PZT increases by a certain percentage at different temperatures (such as every 5°C), then through these data points, the function relationship between bandwidth and temperature can be obtained by regression analysis or other fitting methods.

[0051] c. Calculation of temperature correction coefficient; Through the correction relationship between bandwidth and temperature established in the previous step, the temperature correction coefficient can be calculated; specifically, the correction coefficient K(T) can be obtained through the following steps: 1) Experimental calibration: in a controllable environment, by testing multiple times at different temperature conditions, record the bandwidth and temperature values at each test time; 2) Data fitting: through fitting the experimental data, a mathematical expression of the correction coefficient is obtained, usually this relationship will show as a linear or quadratic curve: BW(T) = BW0 + ΔBW(T) ; Where BW0 is the bandwidth at room temperature, and ΔBW(T) is the bandwidth change caused by temperature, which can be represented by the temperature correction coefficient K(T). For example, if the correction coefficient K(T) is a linear function, then: ΔBW(T) = K(T) = aT+b ; where a and b are constants obtained by fitting experimental data, and T is the temperature change; the temperature range is 0-500℃ with an increment of 25, and the bandwidth test data is detected at different temperatures to obtain a and b by fitting.

[0052] d. Bandwidth correction and real-time adjustment; During the operation of the piezoelectric ceramic PZT, the temperature sensor continuously records the temperature rise data of the PZT in real time; once the temperature changes, the filter driving system adjusts the bandwidth in real time according to the previously established relationship between the bandwidth and the temperature.

[0053] For example, when the temperature monitoring system detects a temperature rise, the filter driving system can calculate a new bandwidth value in real time, and adjust the passband range of the filter through the real-time updated bandwidth. This is an adaptive process, and the filter driving system can dynamically adjust the bandwidth to keep it within the optimal working range at all times. Specifically, the filter driving system can use the previously calculated correction coefficient K(T) to adjust the bandwidth value in real time. Assuming that the temperature sensor detects the current temperature as T, the new bandwidth can be calculated by the following formula: BWcurrent = BW0 + K(T) × T ; Then, update the filter parameters according to the corrected bandwidth to ensure that the signal processing process always maintains optimal performance.

[0054] Through this temperature compensation mechanism, the change in bandwidth will not affect the working accuracy of the entire ultrasonic machining system, allowing the system to adaptively adjust in different temperature environments and ensure the stability and accuracy of signal processing. This is of great significance for practical applications, especially in ultrasonic machining equipment. During ultrasonic machining, the temperature change of PZT is very obvious, so by using the temperature correction coefficient to compensate for the bandwidth fluctuation caused by temperature change, not only can the accuracy of the bandwidth measurement of the machining system be improved, but also the machining error caused by temperature fluctuation can be effectively prevented.

[0055] In summary, the temperature sensor records the PZT temperature rise data in real time and establishes the correction coefficient between the bandwidth and the temperature based on these data, which is an effective measure to improve the accuracy of bandwidth measurement and system stability. This method can make the filter driving system maintain high efficiency and stability under different environmental conditions, ensuring the high-precision control and reliability of the system.

[0056] B2. Digital filter implementation; The required frequency band (bandwidth) is determined above, which provides the basis for filter design. The next step is to implement it using a digital filter. The digital filter is the core component of the system for frequency selection, and intensive design helps to improve signal processing accuracy. To optimize the performance of the band-pass filter, the following operations are performed: B2-1, selection of window function; The Kaiser window is used to optimize the transition band; the use of the Kaiser window can effectively reduce the fluctuations in the frequency response and improve the performance of the filter. In the design, a Kaiser window with a beta value of 5 is selected, which can ensure that the passband fluctuation is controlled within 0.1 dB, and the attenuation of the stop band reaches 45 dB, further improving the effectiveness of the filter.

[0057] B2-2, fixed-point optimization; The implementation of the filter also considers fixed-point optimization, i.e., quantizing the filter coefficients to 18-bit fixed-point format (1-bit sign + 17-bit decimal), to improve the computational efficiency in hardware implementation.

[0058] Through simulation verification, the quantized filter can meet the requirement of signal quality noise ratio (SQNR) greater than 80 dB, thereby ensuring that the filtering effect still maintains high quality in hardware.

[0059] B2-3, in terms of hardware implementation, to further accelerate the signal processing process, FPGA is used for filter acceleration; Xilinx's hardware acceleration architecture is used, which provides a processing throughput of 200 MSPS by parallelizing 8 DSP48E1 units; by inserting a 12-stage shift register, the group delay of the filter is compensated, ensuring that the total delay is maintained within 0.6 μs, which is crucial for real-time control.

[0060] B2-4, design of FIR filter; Considering the requirement of real-time processing, a FIR filter is designed, which has the characteristic of linear phase to ensure that the signal will not be distorted due to the filtering process. The specific implementation is as follows: In MATLAB, a band-pass filter is designed using the fir1 function. Assuming the sampling rate is 100 kHz, the center frequency is 20 kHz, the bandwidth is 400 Hz, and the order of the FIR filter is selected as 100 to find a balance between the steepness of the filter response and the delay.

[0061] The specific MATLAB code is as follows: fs = 100e3; % Sampling rate 100 kHz f_center = 20e3; % Center frequency 20 kHz bandwidth = 0.4e3; % bandwidth 400Hz b = fir1(100, [f_center-bandwidth / 2, f_center+bandwidth / 2] / (fs / 2), 'bandpass'); freqz(b, 1, 1024, fs); % Verify frequency response The filter's design ensures a passband from 19.8kHz to 20.2kHz, allowing signals to pass. The stopband attenuation, exceeding 40dB, effectively filters out noise signals in the non-target frequency band. After design and verification, the filter effectively removes frequency components beyond 20kHz, retaining the desired signal.

[0062] B2-5, spare analog circuit design; Using a parallel resonant circuit and an operational amplifier buffer circuit to implement filtering near a corresponding frequency, which corresponds to a target frequency, can serve as a supplement to the digital filter and provide more redundancy and stability.

[0063] C. Dynamic frequency tracking; C1. Design the PLL system; A hybrid PLL (Phase-Locked Loop) system was designed, combining a digital phase detector and a CORDIC algorithm to calculate phase differences and precisely adjust the drive frequency. This phase-locked loop (PLL) technology allows real-time adjustment of the drive signal frequency, ensuring it remains synchronized with the resonant frequency. The PLL configuration includes a phase detector, a voltage-controlled oscillator (VCO), and a frequency adjustment module. The phase detector compares the phase difference between the current and voltage across the PZT and, through the VCO, adjusts the drive frequency to maintain alignment with the resonant frequency. The VCO dynamically adjusts the drive frequency to maintain resonant lock. The digital phase detector utilizes a CORDIC algorithm, capable of calculating phase differences with an accuracy of ±0.1°, significantly improving the tracking accuracy of the system in practice. The FPGA, using the CORDIC algorithm, effectively avoids the accuracy loss associated with traditional calculation methods, resulting in more accurate phase difference calculation and ensuring the system can precisely lock onto the target frequency.

[0064] C2, adopt dual-mode tracking strategy; To improve the efficiency of frequency tracking, a dual-mode tracking strategy was designed. During the locking phase, the system uses the coarse-tuning mode to quickly lock the frequency with a step size of 100Hz. During the steady-state phase, it enters the fine-tuning mode with a step size of 1Hz to achieve finer frequency adjustment. This dual-mode tracking strategy not only improves the tracking speed but also ensures that the system maintains high precision during long-term operation.

[0065] C3, adding a fault protection mechanism; In order to prevent the system from malfunctioning, a fault protection mechanism is added, which triggers an emergency stop when the PLL system detects a phase mutation exceeding 30°, and automatically switches to a backup analog filter; this design effectively improves the reliability of the entire system.

[0066] And the fault tree analysis (FTA) method is used to identify possible failure modes, and countermeasures are formulated for each failure mode. FTA not only helps to optimize the reliability design of the system, but also provides an effective reference for future fault diagnosis and repair.

[0067] C4, adaptive bandwidth adjustment; In the case of load or environmental changes, the resonant frequency may shift, so the passband of the bandpass filter needs to be updated in real time; specifically, the position of the resonance peak can be detected in real time, and the passband range of the filter can be adjusted accordingly. By designing an accurate bandpass filter, combined with hardware deployment and dynamic frequency tracking technology, efficient signal processing and control can be achieved; whether in the real-time implementation of the digital filter or in the dynamic frequency adaptation mechanism, the system can cope with various frequency changes and disturbances in the actual working environment, providing stable and reliable performance.

[0068] In the actual application process, the hardware devices applied in the method can be optimized, such as: impedance matching for the wiring of the PZT driving circuit, using 50Ω microstrip line to optimize the signal transmission quality; adding a heat sink to the FPGA to ensure that its junction temperature is below 85℃; the PZT substrate is made of AlN ceramic with excellent thermal conductivity, which can effectively reduce the temperature rise of the entire device.

[0069] The above is only some embodiments of the present application and is not intended to limit the present application. For those skilled in the art, the present application can have combinations and variations of the foregoing technical features, and those skilled in the art can make improvements, variations, equivalent replacements of the present application without departing from the spirit and scope of the present application, or use the structure or method of the present application in other fields to achieve the same effect, which all belong to the protection scope of the present application.

Claims

1. A vibration shape design and control method for ultrasonic internal broaching broaches, characterized in that: The following steps are involved: A. Broach vibration shape design; A1. Modal simulation analysis; A2. Cross-section optimization design; At the axial intervals between the broach teeth and at the peaks or troughs of the vibration mode, the diameter is increased or decreased, thereby increasing or decreasing the axial stiffness to increase or decrease the S vibration mode frequency; grooves are added at the circumferential intervals between the broach teeth to modify the broach radial stiffness to reduce the K vibration mode frequency; a combined optimization method is used to obtain the optimized diameters at the axial intervals between the broach teeth and the depth and width of the circumferential grooves of the broach teeth, and the optimal size is selected according to the set standards; A3. Modal testing; Using the existing broach as a specimen, hammer modal testing was conducted based on the optimized dimensions. The simulated and measured frequencies were compared and analyzed. If the error was ≤3%, the broach passed. Otherwise, further modifications were required. That is, based on the effect of increasing the axial spacing diameter of the broach teeth and the change in the circumferential spacing groove size on the S and K vibration modes, the broach dimensions were modified until they met the expected requirements. B. Filter drive signal design; B1. Design a bandpass filter; B2, digital filter implementation; C. Dynamic frequency tracking; Ensure that the driving frequency can be dynamically adjusted when the signal is near the resonant frequency, including: C1. Design the PLL system; C2, adopt dual-mode tracking strategy; C3. Add fault protection mechanism; C4, adaptive bandwidth adjustment; By designing a precise bandpass filter, combined with hardware deployment and dynamic frequency tracking technology, the position of the resonance peak is detected in real time and the passband range of the filter is adjusted accordingly.

2. The ultrasonic internal broaching broach vibration shape design and control method according to claim 1, characterized in that: Step A1 specifically includes the following operations: 1) Determine the cutting time of each tooth of the broach; The first tooth of the broach from the cutting end is set as number 1, and the last tooth when cutting out is set as number M. The time period for each tooth to participate in cutting during broaching is determined by the workpiece thickness L, the distance between the broach teeth L1 and the broaching speed V. 2) Determine cutting forces; When the ultrasonic-assisted process is effective, the ultrasonic-assisted cutting force is no higher than 80% of the conventional cutting force. The cutting force applied to each tooth is set to 80% of the conventional single-tooth cutting force. The conventional single-tooth cutting force is determined through the single-tooth cutting force test. 3) Obtaining vibration mode; After the broach is clamped, the time-varying load determined in the previous step is applied to each tooth of the broach. The first n modes are calculated to obtain vibration shapes near NKHz, where n is the order and N is the value of the preset modal frequency. If the maximum modal frequency calculated after the value of n is close to NKHz, the axial and radial natural frequencies of the broach near the NKHz frequency are extracted. 4) Mode selection; Among the vibration modes obtained above, two vibration modes with large axial vibration amplitude and small radial vibration amplitude are selected and marked as S and K respectively.

3. The ultrasonic internal broaching broach vibration shape design and control method according to claim 1, characterized in that: Step A1 specifically includes the following operations: 1) Place the broach in an unconstrained state, calculate the modes near N kHz, and extract the vibration mode, frequency, and amplitude when the vibration amplitude at the broach clamping point is 0; 2) Setting optimization goals; The free mode vibration mode close to the K mode frequency is recorded as K1 vibration mode, and the free mode vibration mode close to the S mode frequency is recorded as S1 vibration mode. The optimization goal is to make the K1 vibration mode as close to the K mode frequency as possible and the S1 vibration mode frequency as close to the S mode frequency as possible. By making the frequency vibration mode close, the ultrasonic vibration energy loss is reduced.

4. The ultrasonic internal broaching broach vibration shape design and control method according to claim 2, characterized in that: During the process of obtaining the vibration mode, if the calculated maximum frequency value does not reach 1.1N KHz after n is taken, the value of n is increased to 1.1n and the calculation is continued until the calculated maximum modal frequency is close to N KHz.

5. The ultrasonic internal broaching broach vibration shape design and control method according to claim 2, characterized in that: In the vibration mode selection process, the specific selection criteria for the S vibration mode and the K vibration mode are as follows: the vibration mode with the largest ratio of axial vibration amplitude to radial vibration amplitude is set as the S vibration mode, and then multiple vibration modes with a frequency interval of not less than a specific value from the S vibration mode are screened out, and among the multiple vibration modes that meet the interval requirements, the vibration mode with the largest ratio of axial to radial vibration amplitude is selected again and set as the K vibration mode; if the S vibration mode is determined, but when selecting the K vibration mode, the condition that the vibration mode frequency interval is not less than a specific value cannot be met, then the vibration mode with the largest frequency interval from the S vibration mode is selected as the K vibration mode.

6. The ultrasonic internal broaching broach vibration shape design and control method according to claim 1, characterized in that: In step B1, thermal drift compensation specifically includes the following operations: 1) Insert a calibration signal after every 5 frequency sweeps; the frequency value of the calibration signal is within the target frequency range; 2) Use a temperature sensor to record the temperature rise data of the PZT in real time, and establish a correction relationship between bandwidth and temperature based on the temperature rise data to adjust the bandwidth value in real time.

7. The ultrasonic internal broaching broach vibration shape design and control method according to claim 6, characterized in that: Establishing a corrected relationship between bandwidth and temperature The following processes are included: a. Design of temperature monitoring system; In order to monitor the temperature changes of PZT in real time, the temperature monitoring system includes multiple temperature sensors that are precisely placed near the PZT to capture the temperature rise data generated by the PZT during operation; b. Establishment of the relationship between bandwidth and temperature; The temperature rise data collected by the temperature sensor in real time is transmitted to the processing unit to establish a correction relationship between bandwidth and temperature; c. Calculation of temperature correction coefficient; Calculate the temperature correction coefficient using the correction relationship between bandwidth and temperature established in the previous step; d. Bandwidth correction and real-time adjustment; When the temperature changes, the bandwidth value is adjusted in real time based on the previously established bandwidth and temperature relationship.

8. The method for designing and controlling vibration shapes of ultrasonic internal broaching broaches according to claim 1, wherein: In step C1, the PLL system includes a phase detector, a voltage-controlled oscillator, and a frequency adjustment module, wherein the phase detector is used to compare the phase difference between the current and voltage of the PZT, and the voltage-controlled oscillator is used to adjust the driving frequency so that it is always consistent with the resonant frequency.

9. The ultrasonic internal broaching broach vibration shape design and control method according to claim 1, characterized in that: Impedance matching is performed on the PZT drive circuit traces, and 50Ω microstrip lines are used to optimize signal transmission quality. A temperature equalizer is installed for the FPGA to ensure that its junction temperature is below 85°C. AlN ceramic is used as the PZT substrate, and its high thermal conductivity effectively reduces the temperature rise of the equipment.

10. The ultrasonic internal broaching broach vibration shape design and control method according to claim 8, characterized in that: In step C, fault tree analysis is used to identify faults and countermeasures are developed for each failure mode.

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