An ultrasonic internal broaching broach vibration mode design and control method

Abstract

The present application belongs to the technical field of machining, and particularly relates to a method for designing and controlling the vibration mode of an ultrasonic internal broaching broach. First, the axial and radial vibration modes of the broach are accurately designed based on a modal isolation structure design method to meet the requirements of high-precision and high-efficiency broaching. Then, a signal processing method based on filter driving is proposed for the designed vibration mode of the broach to accurately drive the target vibration mode and solve the problem that the vibration mode bandwidth of the PZT changes with the working conditions such as temperature. Finally, since the broach frequency vibration mode will drift with the change of the working conditions in actual application, a dynamic frequency tracking system is developed to ensure that the signal can dynamically adjust the driving frequency when it is near the resonant frequency, so that the ultrasonic auxiliary broaching system always maintains the target vibration mode. Through the optimization and improvement of the above three aspects, the ultrasonic vibration broaching effect of high-strength and high-hardness workpieces is significantly improved.

Description

Technical Field

[0001] This invention relates to the field of machining technology, specifically to a method for designing and controlling the vibration mode of an ultrasonic internal broach. Background Technology

[0002] In recent years, Ultrasonic Assisted Machining (UAM) technology has been successfully introduced into the broaching field. This innovative integration has brought many significant advantages. On the one hand, it greatly improves the cutting performance of the tool, enabling it to remove material more efficiently during machining. On the other hand, it effectively alleviates the extreme loads and wear on the tool, extending its service life and reducing machining costs. More importantly, the application of UAM technology has significantly overcome the bottlenecks faced by traditional broaching when dealing with high-strength, high-hardness, and visco-tough materials, greatly expanding its material adaptability and machining capabilities. This not only brings new development opportunities to the broaching field but also provides more efficient and reliable machining methods for related industries, promoting the development and progress of the entire manufacturing industry.

[0003] The broach mode shape has a crucial impact on the broaching effect. However, in the actual machining process of ultrasonic-assisted broaching, the broach mode shape often changes significantly due to various factors, exhibiting multiple different modes. This can lead to multi-directional ultrasonic vibration effects, which in turn significantly affect machining accuracy and efficiency: on the one hand, intensified multi-directional vibration may increase the non-uniformity of the machined surface, significantly reducing surface quality and dimensional accuracy; on the other hand, changes in the distribution and direction of cutting forces affect machining efficiency and disrupt the stability of the cutting process. Studies have shown that the changes in the broach mode shape are closely related to the excitation mode shape characteristics of PZT, and the bandwidth of the PZT excitation mode shape varies with operating conditions such as temperature. The broach frequency mode shape also drifts with changes in operating conditions, making precise control of the target mode shape extremely complex.

[0004] To address this challenge, this invention aims to provide a method for designing and controlling the vibration mode of an ultrasonic internal broaching broach. This method can precisely design the broach's vibration mode and drive it accurately. It 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 of the Invention

[0005] The purpose of this invention is to overcome the above-mentioned shortcomings of the prior art and provide an ultrasonic internal broaching broach vibration mode design and control method. This method can accurately design the broach vibration mode and drive it precisely. It 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 objectives, the present invention provides a method for designing and controlling the vibration mode of an ultrasonic internal broach, comprising the following steps:

[0007] A. Broach vibration mode design;

[0008] A1. Modal simulation analysis;

[0009] A1-1. Establish a parametric model;

[0010] A parametric model of the broach was established using finite element analysis software (such as ANSYS / COMSOL), with the material set as cemented carbide with a density of 14.5 g / cm³ and an elastic modulus of 600 GPa.

[0011] A1-2. Conduct operational modal calculations;

[0012] 1) Determine the cutting time for each tooth of the broach;

[0013] The first tooth of the broach, starting from the entry point, is designated as No. 1, and the last tooth, when cutting out, is designated as No. M. The time period during which each tooth participates in the cutting is determined by the workpiece thickness L, the broach tooth spacing L1, and the broaching speed V.

[0014] 2) Determine the cutting force;

[0015] In this application, the standard is that 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 can be determined by single-tooth cutting force test; it will not be elaborated here.

[0016] 3) Obtaining mode shapes;

[0017] After the broach is clamped, the time-varying load determined in the previous steps is applied to each tooth of the broach, and the first n modes are calculated to obtain the mode shape near N kHz, not exceeding 1.1 N kHz; where n is the order and N is the preset modal frequency value; if the calculated maximum modal frequency is close to N kHz after n is selected, the axial (longitudinal) and radial (bending / torsional) natural frequencies of the broach near the N kHz frequency are extracted; if the obtained frequency does not reach 1.1 N kHz, the value of n is increased to 1.1n until the calculated maximum modal frequency is close to N kHz. In this application, "close" means that the difference in values ​​is within a specified range, such as ±3%.

[0018] 4) Mode selection;

[0019] From the previously obtained mode shapes, two modes with large axial vibration amplitude and small radial vibration amplitude are selected and labeled as S and K, respectively.

[0020] The specific selection criteria are as follows: the mode shape with the largest ratio of axial vibration amplitude to radial vibration amplitude is marked as mode S. Then, mode shapes with a frequency interval of not less than A Hz from mode S are selected. Among the multiple mode shapes that meet the interval requirement, the mode shape with the largest ratio of axial vibration amplitude to radial vibration amplitude is selected again and marked as mode K. The value of A is set according to actual needs, for example, it can be set to 500.

[0021] The advantage of using the above selection criteria is that, based on the S-mode with an axial vibration amplitude that is as large as possible compared to the radial vibration amplitude, and the K-mode with the minimum interval frequency (A) as the basic condition, there is a minimum range of modification when changing the mode shape to optimize the broach cross-section dimensions. Selecting a mode shape with an axial vibration amplitude that is as large as possible compared to the radial vibration amplitude within this range ensures the most significant effect of changing the mode shape when optimizing the cross-section dimensions.

[0022] A1-3. Conduct free modal calculations;

[0023] 1) With the broach in an unconstrained state, calculate the mode shapes around N KHz, and extract the mode shape, frequency, and amplitude when the vibration amplitude at the broach clamping point is 0.

[0024] 2) Denote the free mode shape that is close to the K mode shape frequency as K1 mode shape, and the free mode shape that is close to the S mode shape frequency as S1 mode shape; with the optimization goal of making 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, the energy loss of ultrasonic vibration can be reduced by making the frequency and mode shape close.

[0025] A2. Cross-section optimization design;

[0026] A2-1. At the axial intervals of the broach teeth and at the peaks or troughs of the mode shape, the axial stiffness is increased or decreased by increasing or decreasing the diameter, thereby increasing or decreasing the S-mode frequency.

[0027] A2-2. Add grooves at the circumferential intervals of the broach teeth to modify the radial stiffness of the broach and reduce the K-mode frequency;

[0028] A2-3. In the software, a combination optimization method is used to obtain the axial spacing diameter of multiple broach teeth and the circumferential groove depth and width of the broach teeth after optimization, and the optimal size is selected.

[0029] A3. Modal testing;

[0030] Using the existing broach as a sample, hammer impact modal tests were conducted based on the optimized dimensions. The simulated and measured frequencies were compared and analyzed. If the error was ≤3%, it was considered qualified; otherwise, further modifications were made. That is, based on the influence of the axial spacing diameter and circumferential spacing groove size of the broach teeth on the S and K mode shapes, the broach dimensions were modified until they met the expected requirements.

[0031] B. Design of filter drive signals;

[0032] Determine the bandwidth of the excitation S-mode and K-mode modal frequencies, including:

[0033] B1. Design a bandpass filter;

[0034] B1-1. Conduct frequency sweep tests to determine the axial modal bandwidth;

[0035] 1) Use a signal generator to output a sinusoidal sweep signal within the target frequency range to drive the piezoelectric ceramic, and use a laser vibrometer to record the amplitude of the broach cutting edge to determine the half-power bandwidth of the resonance peak;

[0036] 2) After testing, data post-processing was performed. The Python toolkit SciPy was used to detect the resonant peak position using the find_peaks function, and the bandwidth was calculated using the half-power bandwidth method.

[0037] B1-2, Perform thermal drift compensation;

[0038] B2. Digital filter implementation;

[0039] B2-1. Selection of Window Function;

[0040] The transition zone is optimized using the Kaiser Window.

[0041] B2-2, Fixed-point number optimization;

[0042] The filter coefficients are quantized into an 18-bit fixed-point format to improve computational efficiency during hardware implementation.

[0043] B2-3. Accelerating filters using FPGA;

[0044] Employing Xilinx's hardware acceleration architecture, it provides a processing throughput of 200MSPS by parallelizing eight DSP48E1 units; by inserting 12-stage shift registers, it compensates for the group delay of the filter, ensuring that the total latency remains within 0.6μs.

[0045] B2-4. Design an FIR filter;

[0046] Design an FIR filter with linear phase characteristics to ensure that the signal is not distorted due to the filtering process;

[0047] C. Dynamic frequency tracking;

[0048] To ensure the driving frequency can be dynamically adjusted when the signal is near the resonant frequency, including:

[0049] C1. Design a PLL system;

[0050] Design a hybrid PLL (Phase-Locked Loop) system that combines a digital phase detector and the CORDIC algorithm to calculate the phase difference and precisely adjust the drive frequency;

[0051] C2. Adopt a dual-mode tracking strategy;

[0052] During the locking phase, the system quickly locks the frequency using a coarse adjustment mode with a step size of 100Hz; during the steady-state phase, it enters a fine adjustment mode with a step size of 1Hz to achieve more precise frequency adjustment.

[0053] C3. Add a fault protection mechanism;

[0054] When the system detects a phase change exceeding 30°, it triggers an emergency stop and automatically switches to the backup analog filter.

[0055] C4. Adaptive bandwidth adjustment;

[0056] By designing precise bandpass filters, combining hardware deployment and dynamic frequency tracking technology, the position of the resonant peak is detected in real time, and the passband range of the filter is adjusted accordingly.

[0057] Furthermore, in the step of determining the cutting time of each tooth of the broach, if the initial cutting time is set to 0, then:

[0058] The cutting time for the first tooth is from 0 to L / V.

[0059] The cutting time period for the second tooth is from time L1 / V to time (L+L1) / V.

[0060] The cutting time period for the third tooth is from 2×L1 / V to (L+2×L1) / V.

[0061] …

[0062] Similarly, the cutting time of the qth tooth is from (q-1)×L1 / V to (L+(q-1)×L1) / V.

[0063] Let the total number of teeth on the broach be M. Then the cutting time of the Mth tooth is from (M-1)×L1 / V to (L+(M-1)×L1) / V.

[0064] Furthermore, during the acquisition of modal frequencies, if the maximum frequency value calculated after selecting a value for n does not reach 1.1 N kHz, then the value of n is increased to 1.1 n and the calculation continues until the calculated maximum modal frequency approaches N kHz.

[0065] Furthermore, during the acquisition of mode shapes, the obtained axial and radial mode shapes, natural frequencies, axial vibration amplitudes, and radial vibration amplitudes are denoted as follows:

[0066] 1, f1, f x1 f y1 ;

[0067] 2, f2, f x2 f y2 ;

[0068] …;

[0069] i, f i f xi f yi ;

[0070] …;

[0071] i+1, f i+1 f x(i+1) f y(i+1) ;

[0072] …;

[0073] j-1, f j-1 f x(j-1) f y(j-1) ;

[0074] j, f j f xj f vj ;

[0075] Where i represents the i-th mode shape, f i Let f represent the i-th natural frequency. xi f represents the amplitude of the axial vibration of the i-th order. yi Let represent the radial vibration amplitude of the i-th order, and j be the total number of mode shapes extracted that are close to N kHz.

[0076] Furthermore, when selecting mode shapes, if mode shape S is determined, but the frequency interval of mode shape K cannot meet the condition of not being lower than a specific value (A), then the mode shape with the largest possible frequency interval from mode shape S should be selected as mode shape K. This ensures that optimizing the cross-sectional dimensions minimizes the range of modifications required for mode shapes.

[0077] Furthermore, in step A2-1, let the diameter of the broach at the axial interval between the first broach tooth and the second broach tooth be D1, the diameter of the broach at the axial interval between the second broach tooth and the third broach tooth be D2, and so on, successively set as Di, with the last one being Dm. The optimization range of the broach diameter is set to 20-30mm, and the diameter increment during optimization is 1mm.

[0078] Furthermore, in step A2-2, the initial values ​​of the width and depth of the groove are 0.5mm and 1mm, respectively, with the width increment being 0.1mm and the maximum value being 1mm; the depth increment is 0.2mm and the maximum value being 3mm.

[0079] Furthermore, in step B1-1, when phase delay causes mode distortion, a minimum phase IIR filter is used or a pre-compensation delay is added.

[0080] Furthermore, in step B1-1, in order to further improve the bandwidth calibration accuracy, a logarithmic frequency sweep method is adopted to improve the low-frequency band resolution.

[0081] Furthermore, 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, in order to test the voltage-bandwidth correlation.

[0082] Furthermore, in step B1-2, thermal drift compensation specifically includes the following operations:

[0083] 1) Insert a calibration signal after every 5 frequency sweeps; the frequency value of the calibration signal is within the target frequency range;

[0084] 2) Use a temperature sensor to record the temperature rise data of 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.

[0085] Furthermore, establishing the correction relationship between bandwidth and temperature specifically includes the following process:

[0086] a. Design of the temperature monitoring system;

[0087] In order to monitor the temperature changes of PZT in real time, the temperature monitoring system includes multiple temperature sensors, which are precisely placed near the PZT to capture the temperature rise data generated by the PZT during operation.

[0088] b. Establishing the relationship between bandwidth and temperature;

[0089] The temperature rise data collected in real time by the temperature sensor is transmitted to the processing unit to establish a correction relationship between bandwidth and temperature.

[0090] c. Calculation of temperature correction factor;

[0091] Based on the correction relationship between bandwidth and temperature established in the previous step, the temperature correction coefficient is calculated.

[0092] d. Bandwidth correction and real-time adjustment;

[0093] When the temperature changes, the bandwidth value is adjusted in real time based on the previously established bandwidth-temperature relationship.

[0094] Furthermore, the temperature correction factor is obtained through the following steps:

[0095] 1) Experimental calibration;

[0096] By conducting multiple tests under different temperature conditions, the bandwidth and temperature values ​​were recorded for each test.

[0097] 2) Data fitting;

[0098] By fitting the experimental data, a mathematical expression for a correction coefficient is obtained. This relationship is usually presented as a linear or quadratic curve.

[0099] Furthermore, step B2 also includes: B2-5, alternative analog circuit design;

[0100] By using a parallel resonant circuit and an operational amplifier buffer circuit, filtering is achieved near a selected frequency, supplementing the digital filter and providing more redundancy and stability.

[0101] Furthermore, 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.

[0102] Furthermore, impedance matching was performed on the PZT drive circuit traces, and 50Ω microstrip lines were used to optimize signal transmission quality. A vapor chamber was added to the FPGA to ensure that its junction temperature was below 85℃. The PZT substrate was made of AlN ceramic, which effectively reduced the temperature rise of the device by utilizing the high thermal conductivity of AlN ceramic.

[0103] Furthermore, in step C, fault tree analysis (FTA) is used to identify faults, and countermeasures are developed for each fault mode.

[0104] Compared with the prior art, the beneficial effects of the present invention are as follows: The present invention provides a method for designing and controlling the vibration mode of an ultrasonic internal broaching broach. First, the vibration mode of the broach is precisely designed to meet the requirements of high-precision and high-efficiency broaching. Then, the driving signal is optimized for the target vibration mode of the broach to ensure that it can accurately drive the target vibration mode. Finally, through dynamic frequency tracking, the driving frequency can be dynamically adjusted when the signal is near the resonant frequency to ensure that the ultrasonic assisted broaching system always stays in the target vibration mode. Through the above three improvements, the ultrasonic vibration broaching effect of high-strength and high-hardness workpieces is significantly improved. Attached Figure Description

[0105] Figure 1 This is a flowchart illustrating the dual-mode tracking strategy used in this invention.

[0106] Figure 2 This is a flowchart illustrating the Fault Tree Analysis (FTA) method used in this invention. Detailed Implementation

[0107] To make the objectives, technical solutions, and advantages of this invention clearer, descriptions of well-known structures and techniques are omitted in the following description to avoid unnecessarily obscuring the concepts in this invention. Example

[0108] This embodiment provides a method for designing and controlling the vibration mode of an ultrasonic internal broach, including the following steps:

[0109] A. Broach vibration mode design;

[0110] A1. Modal simulation analysis;

[0111] A1-1. Establish a parametric model;

[0112] A parametric model of the broach was created using ANSYS / COMSOL, with the material set as cemented carbide (density 14.5 g / cm³, elastic modulus 600 GPa).

[0113] A1-2. Conduct operational modal calculations;

[0114] (1) Determine the cutting time of each tooth of the broach;

[0115] The broach is clamped at the connection point with the clamping sleeve. The broach teeth are counted starting from the entry point, with the first tooth designated as number 1 and the last tooth designated as number M upon exiting the broach. The time interval for each tooth to participate in the cutting process is determined by the workpiece thickness L, the broach tooth spacing L1, and the broaching speed V. With the initial cutting time set to 0, then:

[0116] The cutting time for the first tooth is from 0 to L / V.

[0117] The cutting time period for the second tooth is from time L1 / V to time (L+L1) / V.

[0118] The cutting time for the third tooth is from 2×L1 / V to (L+2×L1) / V,…

[0119] Similarly, the cutting time of the qth tooth is from (q-1)×L1 / V to (L+(q-1)×L1) / V; if the total number of teeth of the broach is M, then the cutting time of the Mth tooth is from (M-1)×L1 / V to (L+(M-1)×L1) / V.

[0120] (2) Determine the cutting force;

[0121] Since the vibration amplitude of the broach teeth cannot be determined, the cutting force value will significantly affect the ultrasonic vibration mode of the broach. In this application, the standard is that 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 can be determined by single-tooth cutting force test.

[0122] (3) Obtaining mode shapes;

[0123] After 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 mode shape near N kHz, not exceeding 1.1N kHz; where n is the order and N is the preset modal frequency value;

[0124] First, set n to 100 and N to 20. If the calculated maximum modal frequency is close to 20kHz, then extract the axial (longitudinal) and radial (bending / torsion) natural frequencies near the 20kHz frequency. If the obtained frequency does not reach 22kHz, then increase n to 1.1n until the calculated maximum modal frequency is close to 20kHz.

[0125] The extracted modal frequency range was set to 18kHz-22kHz. The axial (longitudinal) and radial (bending / torsional) mode shapes, natural frequencies, axial vibration amplitudes, and radial vibration amplitudes were denoted as follows:

[0126] 1, f1, f x1 f y1 ;

[0127] 2, f2, f x2 f y2 ;

[0128] …;

[0129] i, f i f xi fyi ;

[0130] …;

[0131] i+1, f i+1 f x(i+1) f y(i+1) ;

[0132] …;

[0133] j-1, f j-1 f x(j-1) f y(j-1) ;

[0134] j, f j f xj f vj ;

[0135] Where i represents the i-th mode shape, f i Let f represent the i-th natural frequency. xi f represents the amplitude of the axial vibration of the i-th order. yi Let represent the radial vibration amplitude of the i-th order, and j be the total number of mode shapes extracted that are close to N kHz.

[0136] (4) Selection of vibration mode;

[0137] Comparing the axial and radial vibration amplitudes and modal frequencies, since radial vibration is mainly caused by bending modes, this application selects two vibration modes with large axial vibration amplitude and small radial vibration amplitude from the vibration modes obtained in step (3) above, and labels them as S and K respectively.

[0138] The specific selection criteria are as follows: The mode shape with the largest ratio of axial to radial vibration amplitude is marked as the S-mode. Then, mode shapes with a frequency interval of at least 500 Hz from the S-mode are selected. Among the multiple mode shapes that meet the interval requirement, the mode shape with the largest ratio of axial to radial vibration amplitude is selected again and marked as the K-mode. Since the extracted mode shape frequencies range from 18 kHz to 22 kHz, it is generally possible to extract mode shapes with a frequency interval of at least 500 Hz. If, after determining the S-mode from the extracted mode shapes, selecting the K-mode does not meet the condition of a frequency interval of at least 500 Hz between the two mode shapes, then the mode shape with the largest possible frequency interval is selected as the K-mode.

[0139] The advantages of using the above selection criteria are as follows: First, based on the S-mode with an axial vibration amplitude that is as large as possible compared to the radial vibration amplitude, and with the minimum frequency interval of 500Hz as the basic condition, the K-mode can be determined. This allows for the smallest possible modification range when changing the mode shape to optimize the broach cross-section dimensions. Selecting a mode shape with an axial vibration amplitude that is as large as possible compared to the radial vibration amplitude within this range ensures the most significant effect of changing the mode shape when optimizing the cross-section dimensions. When the minimum frequency interval requirement cannot be met, the frequency interval is selected through finite element analysis to determine the mode shape with the largest interval as the reference S-mode, which ensures the smallest possible modification range for improving the mode shape when optimizing the cross-section dimensions.

[0140] A1-3. Conduct free modal calculations;

[0141] (1) Make the broach in an unconstrained state, calculate the mode shape around 20 KHz, and extract the mode shape, frequency and amplitude when the vibration amplitude at the broach clamping point is 0;

[0142] (2) Set optimization goals;

[0143] Free mode shapes close to the K-mode frequency are denoted as K1 mode shapes, and free mode shapes close to the S-mode frequency are denoted as S1 mode shapes. The optimization goal is to make the K1 mode shape as close to the K-mode frequency as possible, and the S1 mode shape frequency as close to the S-mode frequency as possible. By making the frequency and mode shapes as close as possible, the energy loss of ultrasonic vibration is reduced. The frequency interval between the S and K modes is kept as large as possible, with a minimum threshold set to 2000Hz.

[0144] A2. Cross-section optimization design;

[0145] A2-1. At the axial intervals of the broach teeth, and at the peaks or troughs of the mode shape, the axial stiffness is increased or decreased by increasing or decreasing the diameter. Let the broach diameter at the axial interval between the first and second broach teeth be D1, the broach diameter at the axial interval between the second and third broach teeth be D2, and so on, successively designated as Di, with the last being Dm. The optimized broach diameter range is set to 20~30mm, with each optimized diameter increment being 1mm. The main basis for this step is that by modifying the optimized stiffness at the peaks or troughs of the broach mode shape, the mode shape can be adjusted, i.e., the S-mode frequency can be increased.

[0146] A2-2. Add grooves at the circumferential intervals of the broach teeth to modify the radial stiffness of the broach, thereby reducing the K-mode frequency. Specifically, symmetrical grooves can be machined at 1 / 4 of the broach tooth interval (usually 1 / 4 of the distance from the clamping end). The initial width and depth of the symmetrical grooves are 0.5mm and 1mm respectively, with width increments of 0.1mm and a maximum value of 1mm. The depth increments are 0.2mm, with a maximum value of 3mm.

[0147] A2-3. In the software, a combination optimization method is used to obtain the axial spacing diameter and the circumferential groove depth and width of the broach teeth after optimization, and the optimal one is selected according to the previous criteria.

[0148] A3. Modal testing;

[0149] Using existing broaches as samples, hammer impact modal tests were conducted based on the optimized dimensions. The radius of the transition arc of the variable cross-section was not less than 5 mm to reduce stress concentration; the surface roughness was not more than 0.8 μm to reduce modal damping. The simulated and measured frequencies were compared and analyzed. If the error was ≤3%, it was considered qualified; otherwise, further modifications were made. Specifically, the broach dimensions were modified according to the influence of the axial spacing diameter and circumferential spacing groove size of the broach teeth on the S and K mode shapes until the expected requirements were met.

[0150] B. Design of filter drive signals;

[0151] This step is used to determine the bandwidth of the excitation S and K mode frequencies;

[0152] B1. Design a bandpass filter;

[0153] B1-1. Conduct frequency sweep tests to determine the axial modal bandwidth;

[0154] 1) A signal generator outputs an 18–22kHz sinusoidal sweep signal to drive the piezoelectric ceramic (PZT). A laser vibrometer records the amplitude of the broach cutting edge to determine the resonant peak half-power bandwidth, i.e., the resonant power curve is half of its original value, with the amplitude reduced to the peak power. The corresponding frequency bandwidth is specified, such as 19.8–20.2kHz. When phase delay causes mode shape distortion, a minimum-phase IIR filter is used or a pre-compensation delay is added. To further improve bandwidth calibration accuracy, a logarithmic frequency sweep method is used to improve low-frequency resolution. The frequency range is 18-22kHz, the duration is 500ms, the test voltage is increased from 50V to 150V, the step size is set to 0.5Vpp, and the voltage-bandwidth correlation is tested.

[0155] 2) After testing, data post-processing was performed. The Python toolkit SciPy was used to detect the resonant peak positions using the find_peaks function, and the bandwidth was calculated using the half-power bandwidth method.

[0156] The following is a Python code example:

[0157] from scipy.signal import find_peaks

[0158] peaks, _ = find_peaks(vibration_data, height=0.8×max_amp, width=5)

[0159] bandwidth = freq[peaks[-1]] - freq[peaks[0]] # Half-power bandwidth

[0160] B1-2, Thermal drift compensation;

[0161] When piezoelectric ceramics (PZT) are in operation, they generate heat, which causes changes in the excitation frequency and amplitude of the piezoelectric ceramic. Thermal drift compensation is required to address this phenomenon.

[0162] 1) Insert a 20kHz calibration signal after every 5 frequency sweeps;

[0163] 2) Real-time recording of PZT temperature rise data using a temperature sensor, and establishment of a correction coefficient between bandwidth and temperature based on the temperature rise data, thereby further improving the accuracy of bandwidth measurement. Specifically, this includes the following process:

[0164] a. Design of the temperature monitoring system;

[0165] To monitor the temperature changes of piezoelectric ceramics (PZTs) in real time, the temperature monitoring system includes multiple temperature sensors precisely positioned near the PZT to capture temperature rise data generated during operation. Common temperature sensors, such as thermocouples or RTDs (resistance temperature detectors), can be used, as they offer high accuracy and fast response, capable of capturing minute temperature changes in a short time. In practical applications, the operation of PZTs causes their surface temperature to rise continuously, especially under prolonged or high-power operation. This temperature rise effect can lead to changes in their frequency characteristics (including bandwidth). This is because the physical properties of piezoelectric materials change with increasing temperature, particularly near their critical temperature, where the bandwidth may expand or contract. Therefore, real-time monitoring by temperature sensors provides crucial data on temperature changes, providing a basis for subsequent bandwidth correction.

[0166] b. Establishing the relationship between bandwidth and temperature;

[0167] The temperature rise data collected in real time by the temperature sensor is transmitted to the processing unit. To ensure the accuracy of bandwidth measurement, a 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 these experimental data can be used to determine how the bandwidth changes with temperature. Assuming 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 experimentally and modeled as a temperature-dependent function. This relationship usually exhibits a linear or non-linear trend. For example, during the experiment, the temperature of PZT can be controlled by changing the driving voltage, and the bandwidth change can be recorded. Assuming that the bandwidth of PZT increases by a certain proportion at different temperatures (e.g., for every 5°C increase), then the functional relationship between bandwidth and temperature can be obtained using these data points through regression analysis or other fitting methods.

[0168] c. Calculation of temperature correction factor;

[0169] Based on 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:

[0170] 1) Experimental calibration: Under a controlled environment, the bandwidth and temperature values ​​were recorded during each test by conducting multiple tests under different temperature conditions.

[0171] 2) Data Fitting: By fitting the experimental data, a mathematical expression for a correction coefficient is obtained. This relationship is typically presented as a linear or quadratic curve.

[0172] BW(T) = BW0 + ΔBW(T);

[0173] 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);

[0174] For example, if the correction coefficient K(T) is a linear function, then:

[0175] ΔBW(T) = K(T) = aT+b;

[0176] Where a and b are constants obtained by fitting experimental data, and T is the temperature change; the temperature range is 0-500℃, the increment is 25, and a and b can be obtained by fitting bandwidth test data at different temperatures.

[0177] d. Bandwidth correction and real-time adjustment;

[0178] 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 drive system adjusts the bandwidth in real time according to the previously established bandwidth-temperature relationship.

[0179] For example, when a temperature monitoring system detects a temperature increase, the filter drive system can calculate a new bandwidth value in real time and adjust the filter's passband range based on the updated bandwidth. This is an adaptive process; the filter drive system can dynamically adjust the bandwidth to keep it within its optimal operating range. Specifically, the filter drive system can use a previously calculated correction coefficient K(T) to adjust the bandwidth value in real time. Assuming the temperature sensor detects a current temperature of T, the new bandwidth can be calculated using the following formula:

[0180] BWcurrent = BW0 + K(T) × T;

[0181] Then, the filter parameters are updated based on the corrected bandwidth to ensure that the signal processing always maintains optimal performance.

[0182] This temperature compensation mechanism ensures that bandwidth variations do not affect the overall accuracy of the ultrasonic machining system, allowing it to adaptively adjust to different temperature environments and guaranteeing signal processing stability and accuracy. This is of great significance for practical applications, especially in ultrasonic machining equipment. During ultrasonic machining, the temperature of PZT changes significantly. Therefore, compensating for bandwidth fluctuations caused by temperature variations using a temperature correction coefficient not only improves the accuracy of bandwidth measurement in the machining system but also effectively prevents machining errors caused by temperature fluctuations.

[0183] In summary, real-time recording of PZT temperature rise data by temperature sensors and establishing a correction coefficient between bandwidth and temperature based on this data is an effective measure to improve bandwidth measurement accuracy and system stability. This method enables the filter drive system to maintain high efficiency and stable performance under different environmental conditions, ensuring high-precision control and reliability of the system.

[0184] B2. Digital filter implementation;

[0185] The required frequency band (bandwidth) has been determined above, providing a basis for filter design. The next step is to implement it using a digital filter. The digital filter is the core component in the system used for frequency selection, and strengthening its design helps improve signal processing accuracy. To optimize the performance of the bandpass filter, the following operations were performed:

[0186] B2-1. Selection of Window Function;

[0187] A Kaiser window is employed to optimize the transition band. The use of a Kaiser window effectively reduces frequency response fluctuations and improves filter performance. In this design, a Kaiser window with a β value of 5 was selected, ensuring that the passband ripple is controlled within 0.1 dB and the stopband attenuation reaches 45 dB, further enhancing the filter's effectiveness.

[0188] B2-2, Fixed-point number optimization;

[0189] The filter implementation also considers fixed-point optimization, that is, the filter coefficients are quantized into an 18-bit fixed-point format (1 sign bit + 17 decimal bits) to improve computational efficiency in hardware implementation.

[0190] Simulation verification shows that the quantized filter can meet the requirement of a signal quality-to-noise ratio (SQNR) greater than 80dB, thus ensuring that the filtering effect maintains a high quality in the hardware.

[0191] B2-3. In terms of hardware implementation, in order to further accelerate the signal processing, FPGA is used to accelerate the filter.

[0192] Employing Xilinx's hardware acceleration architecture, the parallel processing of eight DSP48E1 units provides a processing throughput of 200 MSPS. By inserting 12-stage shift registers, the group delay of the filter is compensated, ensuring that the total delay is kept within 0.6 μs, which is crucial for real-time control.

[0193] B2-4. Design an FIR filter;

[0194] Considering the requirements of real-time processing, an FIR filter with linear phase characteristics is designed to ensure that the signal is not distorted during the filtering process. The specific implementation is as follows:

[0195] In MATLAB, design a bandpass filter using the `fir1` function. Assume a sampling rate of 100kHz, a center frequency of 20kHz, a bandwidth of 400Hz, and choose an FIR filter order of 100 to find a balance between the steepness of the filter response and the delay.

[0196] The following is a specific MATLAB code example:

[0197] fs = 100e3; % Sampling rate 100kHz

[0198] f_center = 20e3; % Center frequency 20kHz

[0199] bandwidth = 0.4e3; % Bandwidth 400Hz

[0200] b = fir1(100, [f_center-bandwidth / 2, f_center+bandwidth / 2] / (fs / 2), 'bandpass');

[0201] freqz(b, 1, 1024, fs); % Verify frequency response

[0202] The filter is designed to ensure a passband from 19.8kHz to 20.2kHz, allowing signals to pass through. Stopband attenuation, exceeding 40dB, ensures the filtering of noise signals outside the target frequency band. After design and verification, the filter effectively removes frequency components beyond 20kHz, preserving the desired signal.

[0203] B2-5, Design of backup analog circuits;

[0204] Using a parallel resonant circuit and an operational amplifier buffer circuit, filtering is achieved near a specific frequency, which can supplement digital filters and provide more redundancy and stability. The specific frequency corresponds to the target frequency.

[0205] C. Dynamic frequency tracking;

[0206] C1. Design a PLL system;

[0207] Design a hybrid PLL (Phase-Locked Loop) system that combines a digital phase detector and the CORDIC algorithm to calculate the phase difference and precisely adjust the drive frequency. The PLL technology allows for 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 of the PZT and adjusts the drive frequency via the VCO to maintain consistency with the resonant frequency. The VCO dynamically adjusts the drive frequency to maintain resonance locking. The digital phase detector employs the CORDIC algorithm, enabling phase difference calculation with an accuracy of ±0.1°, significantly improving the system's tracking accuracy in practical applications. The FPGA using the CORDIC algorithm effectively avoids the accuracy loss associated with traditional calculation methods, resulting in more precise phase difference calculations and ensuring accurate target frequency locking.

[0208] C2. Adopt a dual-mode tracking strategy;

[0209] To improve the efficiency of frequency tracking, a dual-mode tracking strategy was designed. During the locking phase, the system quickly locks the frequency in coarse adjustment mode with a step size of 100Hz. In the steady-state phase, it enters fine adjustment mode with a step size of 1Hz to achieve more precise frequency adjustment. This dual-mode tracking strategy not only improves the tracking speed but also ensures that the system maintains high accuracy during long-term operation.

[0210] C3. Add a fault protection mechanism;

[0211] To prevent system failures, a fault protection mechanism was added. When the PLL system detects a phase change exceeding 30°, it triggers an emergency stop and automatically switches to the backup analog filter. This design effectively improves the reliability of the entire system.

[0212] Fault Tree Analysis (FTA) was employed to identify potential failure modes, and countermeasures were developed for each failure mode. FTA not only helps optimize the reliability design of the system but also provides a valuable reference for future fault diagnosis and repair.

[0213] C4. Adaptive bandwidth adjustment;

[0214] Under varying loads or environmental conditions, the resonant frequency may shift, necessitating real-time updates to the passband of the bandpass filter. This can be achieved by detecting the position of the resonant peak in real time and adjusting the filter's passband accordingly. By designing a precise bandpass filter, combined with hardware deployment and dynamic frequency tracking technology, efficient signal processing and control can be achieved. Both the real-time implementation of the digital filter and the dynamic frequency adaptation mechanism ensure that the system can cope with various frequency changes and interferences in real-world operating environments, providing stable and reliable performance.

[0215] In practical applications, the hardware devices used in the method can be optimized. For example, impedance matching can be performed on the traces of the PZT driving circuit, and 50Ω microstrip lines can be used to optimize signal transmission quality. A heat spreader can be added to the FPGA to ensure that its junction temperature is below 85℃. The PZT substrate can be made of AlN ceramic with excellent thermal conductivity, which can effectively reduce the temperature rise of the entire device.

[0216] The above are only some embodiments of the present invention and are not intended to limit the present invention. For those skilled in the art, the present invention can have various combinations and modifications of the aforementioned technical features. Any improvements, modifications, equivalent substitutions, or applications of the structure or method of the present invention to other fields to achieve the same effect without departing from the spirit and scope of the present invention shall fall within the protection scope of the present invention.

Claims

1. A method for designing and controlling the vibration mode of an ultrasonic internal broach, characterized in that, Includes the following steps: A. Broach vibration mode design; A1. Modal simulation analysis; A2. Cross-section optimization design; At the axial intervals of the broach teeth, and at the peaks or troughs of the mode shape, the diameter is increased or decreased, thereby increasing or decreasing the axial stiffness to improve the S-mode frequency. Grooves are added at the circumferential intervals of the broach teeth to modify the radial stiffness of the broach and reduce the K-mode frequency. A combined optimization method is used to obtain the optimized diameters at the axial intervals of multiple broach teeth and the depth and width of the circumferential grooves of the broach teeth, and the optimal dimensions are selected according to the set standards. A3. Modal testing; Using the existing broach as a sample, hammer impact modal tests were conducted based on the optimized dimensions. The simulated and measured frequencies were compared and analyzed. If the error was ≤3%, it was considered qualified; otherwise, further modifications were made. That is, based on the influence of the axial spacing diameter and circumferential spacing groove size of the broach teeth on the S and K mode shapes, the broach dimensions were modified until they met the expected requirements. B. Design of filter drive signals; B1. Design a bandpass filter; B2. Digital filter implementation; C. Dynamic frequency tracking; To ensure the driving frequency can be dynamically adjusted when the signal is near the resonant frequency, including: C1. Design a PLL system; C2. Adopt a dual-mode tracking strategy; During the locking phase, the system quickly locks the frequency using coarse adjustment mode; during the steady-state phase, it enters fine adjustment mode. C3. Add a fault protection mechanism; C4. Adaptive bandwidth adjustment; By designing precise bandpass filters, combining hardware deployment and dynamic frequency tracking technology, the position of the resonant peak is detected in real time, and the passband range of the filter is adjusted accordingly. Step A1 specifically includes the following operations: 1) Determine the cutting time for each tooth of the broach; The first tooth of the broach, starting from the entry point, is designated as No. 1, and the last tooth, when cutting out, is designated as No. M. The time period during which each tooth participates in the cutting is determined by the workpiece thickness L, the broach tooth spacing L1, and the broaching speed V. 2) Determine the cutting force; When ultrasonic-assisted cutting is effective, the ultrasonic-assisted cutting force should not exceed 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 by single-tooth cutting force test. 3) Obtaining mode shapes; After 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 mode shape near NKHz; where n is the order and N is the preset modal frequency value; if the maximum modal frequency calculated after n is taken is close to N kHz, the axial and radial natural frequencies of the broach near the N kHz frequency are extracted. 4) Mode selection; From the previously obtained mode shapes, two modes with large axial vibration amplitude and small radial vibration amplitude are selected and labeled as S and K, respectively. In the process of selecting mode shapes, the specific selection criteria for S-mode and K-mode are as follows: the mode shape with the largest ratio of axial vibration amplitude to radial vibration amplitude is designated as S-mode. Then, multiple mode shapes with a frequency interval of not less than a specific value from S-mode are selected. Among the multiple mode shapes that meet the interval requirement, the mode shape with the largest ratio of axial to radial vibration amplitude is selected as K-mode. If S-mode is determined, but the condition that the frequency interval of mode shapes is not less than a specific value cannot be met when selecting K-mode, then the mode shape with the largest frequency interval from S-mode is selected as K-mode.

2. The ultrasonic internal broaching tool vibration mode design and control method according to claim 1, characterized in that, Step A1 specifically includes the following operations: 1) With the broach in an unconstrained state, calculate the modes around N KHz, and extract the mode shape, frequency, and amplitude when the vibration amplitude at the broach clamping point is 0. 2) Set optimization goals; Free mode shapes close to the K-mode frequency are denoted as K1 mode shapes, and free mode shapes close to the S-mode frequency are denoted as S1 mode shapes. The optimization goal is to make the K1 mode shape as close as possible to the K-mode frequency and the S1 mode shape frequency as close as possible to the S-mode frequency. By making the frequency and mode shapes closer, the energy loss of ultrasonic vibration is reduced.

3. The ultrasonic internal broaching tool vibration mode design and control method according to claim 1, characterized in that: During the process of obtaining the modal frequency, if the maximum frequency value calculated after n is selected does not reach 1.1N kHz, then the value of n is increased to 1.1n and the calculation continues until the maximum modal frequency calculated is close to N kHz.

4. The ultrasonic internal broaching tool vibration mode 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 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.

5. The ultrasonic internal broaching tool vibration mode design and control method according to claim 4, characterized in that, Establishing the correction relationship between bandwidth and temperature specifically includes the following process: a. Design of a temperature monitoring system; In order to monitor the temperature changes of PZT in real time, the temperature monitoring system includes multiple temperature sensors, which are precisely placed near the PZT to capture the temperature rise data generated by the PZT during operation. b. Establishing the relationship between bandwidth and temperature; The temperature rise data collected in real time by the temperature sensor is transmitted to the processing unit to establish a correction relationship between bandwidth and temperature. c. Calculation of temperature correction factor; Based on the correction relationship between bandwidth and temperature established in the previous step, the temperature correction coefficient is calculated. 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-temperature relationship.

6. The ultrasonic internal broaching tool vibration mode design and control method according to claim 1, characterized in that: In step C1, the PLL system includes a phase detector, a voltage-controlled oscillator, and a frequency adjustment module. 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.

7. The ultrasonic internal broaching tool vibration mode design and control method according to claim 1, characterized in that: Impedance matching was performed on the traces of the PZT drive circuit, and a 50Ω microstrip line was used to optimize signal transmission quality. A heat spreader was added to the FPGA to ensure that its junction temperature is below 85℃. The PZT substrate was made of AlN ceramic, which effectively reduced the temperature rise of the device by utilizing the high thermal conductivity of AlN ceramic.

8. The ultrasonic internal broaching tool vibration mode design and control method according to claim 1, characterized in that: In step C3, fault tree analysis is used to identify faults and develop countermeasures for each fault mode.

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