Indirect measurement method of ultrasonic bone cutting force based on anti-node vibration displacement
By establishing an indirect measurement method for anti-node vibration displacement, and utilizing an eddy current displacement sensor and Matlab-Simulink simulation program, a simplified detection method for the cutting force of ultrasonic bone scalpels was achieved. This solved the problem of cutting force detection in orthopedic robots and promoted bone layer sensing and cutting force control.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- NORTHEASTERN UNIV CHINA
- Filing Date
- 2022-08-05
- Publication Date
- 2026-06-05
AI Technical Summary
The detection of cutting force in orthopedic robots using ultrasonic bone cutters is not yet mature, which affects cutting stability and surgical outcomes. Existing technologies make it difficult to achieve bone layer sensing and cutting force control.
By establishing an indirect measurement method based on the vibration displacement of the reverse node, the vibration displacement of the reverse node is measured using an eddy current displacement sensor. Combined with the Matlab-Simulink simulation program, the relationship between cutting force and vibration displacement is calculated, thereby realizing the indirect detection of cutting force.
A simplified model for detecting the cutting force of ultrasonic bone scalpels is provided, which is easy to establish a dataset, improves the detection speed, promotes the application of ultrasonic bone scalpels in orthopedic robots, and provides a theoretical basis for bone layer sensing and cutting force control.
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Figure CN115438533B_ABST
Abstract
Description
[0001] Invention Name
[0002] An indirect method for measuring ultrasonic bone cutting force based on anti-node vibration displacement. Technical Field
[0003] This invention belongs to the field of robotic ultrasonic bone cutting applications, specifically involving an indirect measurement method for ultrasonic bone cutting force based on anti-node vibration displacement. Background Technology
[0004] As a novel surgical instrument, the ultrasonic bone scalpel converts high-frequency electrical signals into high-frequency mechanical vibrations via a magnetostrictive transducer or piezoelectric ceramic transducer. This excites the high-frequency longitudinal vibration mode of the scalpel, achieving ultrasonic vibration with amplitudes in the hundreds of micrometers for cutting. Compared to traditional bone cutting tools, the ultrasonic bone scalpel offers advantages such as low cutting force, low cutting temperature, and tissue selectivity. In recent years, it has been widely used by surgeons as a handheld tool in spinal surgery, maxillofacial surgery, and plastic surgery. However, its application in orthopedic robots has not yet been reported. The ultrasonic bone scalpel is sensitive to the end-effector cutting force; the magnitude of the cutting force affects cutting stability (changing the bone scalpel's resonant frequency and vibration amplitude), cutting quality, and consequently, surgical outcomes. Therefore, developing a detection model for the ultrasonic bone scalpel's cutting force is a crucial problem to be solved in its application in robot-assisted surgery, and it is of great significance for achieving bone layer sensing and cutting force control during surgery. Summary of the Invention
[0005] To address the problems existing in the prior art, this invention provides an indirect method for measuring ultrasonic bone cutting force based on anti-node vibration displacement.
[0006] The technical solution of this invention is:
[0007] An indirect method for measuring ultrasonic bone cutting force based on anti-nodal vibration displacement includes the following steps:
[0008] Step 1: Determine the node positions of the ultrasonic bone scalpel to obtain a simplified model of the ultrasonic bone scalpel.
[0009] Step 2: Establish a piezoelectric transducer model, calculate the model parameters, and obtain the vibration displacement of the piezoelectric transducer.
[0010] Step 3: Establish a stepped amplitude transformer model and calculate the dynamic parameters based on eigenvalues, eigenvectors, and the principle of energy conservation.
[0011] Step 4: Establish a force load model of bone tissue and identify model parameters.
[0012] Step 5: Establish an ultrasonic bone scalpel-bone tissue interaction model and build a Matlab-Simulink simulation program.
[0013] Step 6: Based on the Matlab-Simulink simulation program, using the data-driven modeling method, the effective value of the inverse nodal vibration displacement x1 is obtained. 1rms Vibration frequency f x1 The input is the effective value of the cutting force F. rms The relationship between the anti-node vibration displacement x1 and the cutting force F is obtained.
[0014] Step 7: Measure the effective value x of the vibration displacement of the inverse node using an eddy current displacement sensor. 1rms and vibration frequency f x1 Calculate the effective value F of the cutting force based on the relationship obtained in step 6. rms .
[0015] Beneficial effects
[0016] This invention simplifies the complex continuous system (with infinitely many degrees of freedom) of an ultrasonic bone scalpel into a discrete system with two degrees of freedom. This model retains the properties of the original system and can be used for simulation. The developed one-dimensional numerical calculation model processes the required information much faster than finite element methods and experiments, and it is easy to establish datasets. The indirect detection method of ultrasonic bone scalpel cutting force will promote the application of ultrasonic bone scalpels in orthopedic robots, providing a theoretical basis for orthopedic robots to achieve bone layer sensing and cutting force control during surgery. Attached Figure Description
[0017] Figure 1 This is a simplified model diagram of the ultrasonic bone scalpel according to a specific embodiment of the present invention;
[0018] Figure 2 This is a schematic diagram illustrating the acquisition of feature values and feature vectors in a specific embodiment of the present invention;
[0019] Figure 3 This is a force load model diagram of bone tissue according to a specific embodiment of the present invention;
[0020] Figure 4 This is a schematic diagram of the Matlab-Simulink simulation model of a specific embodiment of the present invention;
[0021] Figure 5 This is a schematic diagram of the reverse node vibration displacement measurement according to a specific embodiment of the present invention;
[0022] Figure 6 This is a flowchart of an indirect measurement method for ultrasonic bone cutting force based on anti-node vibration displacement according to a specific embodiment of the present invention. Detailed Implementation
[0023] The specific embodiments of the present invention will now be described in detail with reference to the accompanying drawings.
[0024] Indirect measurement method of ultrasonic bone cutting force based on anti-nodal vibration displacement, such as Figure 6 As shown, it includes the following steps:
[0025] Step 1: Determine the node positions of the ultrasonic bone scalpel to obtain a simplified model of the ultrasonic bone scalpel.
[0026] A simplified model of an ultrasonic bone scalpel is as follows: Figure 1 When the ultrasonic bone scalpel operates in longitudinal modal vibration, the entire ultrasonic bone scalpel (excluding the scalpel head) has two nodes: one located between two piezoelectric ceramics and the other located at the step of the amplitude transformer. Since there is a node between the two piezoelectric ceramics, it can prevent the ultrasonic waves from propagating backward. Therefore, the left side of the node is ignored. The simplified model of the ultrasonic bone scalpel consists of two parts: the piezoelectric transducer model and the stepped amplitude transformer model.
[0027] Based on the number of inverse nodes, the amplitude transformer is simplified into a 2-DOF mass-spring-damped (MSD) system with two resonant frequencies. The first resonant frequency corresponds to the in-phase vibration of m1 and m2, and the second resonant frequency corresponds to the out-of-phase vibration of m1 and m2.
[0028] Step 2: Establish a piezoelectric transducer model, calculate the model parameters, and obtain the vibration displacement of the piezoelectric transducer.
[0029] The working principle of a piezoelectric transducer is to apply an alternating voltage excitation across the piezoelectric ceramic, utilizing the inverse piezoelectric property of the material to induce longitudinal vibration, resulting in compression or expansion deformation. Without considering the nonlinearity of the piezoelectric material, the interaction between the electrical and mechanical behavior of the piezoelectric ceramic can be described by the following linear relationship:
[0030]
[0031] In the formula: S is strain, T is stress, and S E It is the elastic compliance under a constant electric field, where d is the piezoelectric charge constant, D is the dielectric displacement, E is the electric field strength, and ε is the elastic compliance under a constant electric field. T It is the dielectric constant under constant stress.
[0032]
[0033] In the formula: S0 is the cross-sectional area of the piezoelectric ceramic, l0 is the thickness of the piezoelectric ceramic, x0 is the vibration displacement of the piezoelectric ceramic, F0 is the force applied to the piezoelectric transducer by the amplitude transformer, and u is the excitation voltage.
[0034] Substituting equation (2) into equation (1), we can obtain the vibration displacement of the piezoelectric transducer as follows:
[0035]
[0036] In the formula: For elastic flexibility, d33 Where is the charge constant. is the dielectric constant.
[0037] Step 3: Establish a stepped amplitude transformer model and calculate the dynamic parameters based on eigenvalues, eigenvectors, and the principle of energy conservation.
[0038] Step 3-1: Dynamic Modeling
[0039] According to the Euler-Lagrange equation, the dynamic equation of the unloaded ultrasonic bone scalpel can be written as:
[0040]
[0041] The interaction force F0 between the piezoelectric ceramic and the 2-DOF model can be expressed as:
[0042]
[0043] In the formula: m1, m2, k1, k2, c1, and c2 are the equivalent mass, equivalent stiffness, and equivalent damping, respectively. x0 is the vibration displacement of the piezoelectric ceramic, and x1 and x2 are the vibration displacements of m1 and m2, respectively.
[0044] Based on the boundary conditions, the longitudinal vibration displacement of the ultrasonic bone scalpel can be expressed as:
[0045]
[0046] In the formula: V1 and V2 are the vibration amplitudes of m1 and m2, κ is the circular wave number, l0 is the length of the large cylindrical part of the amplitude transformer, and l1 is the total length of the amplitude transformer.
[0047] Step 3-2: Identification of dynamic parameters
[0048] The mass matrix, stiffness matrix, eigenvalues, and eigenvectors of the system can be represented as:
[0049]
[0050] In the formula: ω1 is the first natural frequency, ω2 is the second natural frequency, ψ1 is the amplitude ratio corresponding to ω1, and ψ2 is the amplitude ratio corresponding to ω2.
[0051] From the characteristic equation MλΨ=KΨ, we can obtain
[0052]
[0053] However, for equation (8), with four unknown parameters (m1, m2, k1, k2), there are only three independent equations, resulting in an infinite number of solutions (infinite combinations). Based on the principle of energy conservation, the equation can be supplemented.
[0054]
[0055] By combining equations (8) and (9), we can obtain
[0056]
[0057] Therefore, the system dynamic parameters (m1, m2, k1, k2) can be solved.
[0058] System eigenvalue measurement: Modal analysis of the ultrasonic bone scalpel was performed using the Modal module in ANSYS Workbench 20.0 software to obtain the vibration frequencies ω1 and ω2 corresponding to the two longitudinal vibration modes.
[0059] System eigenvector measurement: such as Figure 2 A schematic diagram of eigenvalue and eigenvector acquisition is shown. Two reference points are created at the front and rear ends of the ultrasonic bone scalpel model. The reference points are connected to form a path. Harmonic response analysis is performed on the ultrasonic bone scalpel using the MEMS ACT plugin in ANSYS Workbench 20.0 software. Voltages with frequencies of ω1 and ω2 are applied to the ultrasonic bone scalpel to obtain the axial vibration displacement distribution curve of the ultrasonic bone scalpel along the path. The eigenvector can be obtained by calculating the amplitude ratios ψ1 and ψ2 at the corresponding frequencies.
[0060] By adjusting coefficients c1 and c2, the simulated ultrasonic vibration amplitudes x1 and x2 are matched with the experimentally measured values V1 and V2.
[0061] Step 4: Establish a force load model of bone tissue and identify model parameters.
[0062] Step 4-1: Establish the force load model.
[0063] During ultrasonic bone scalpel cutting, the interaction between the scalpel and bone tissue generates a force load on the vibration system, which can be represented by the Kelvin-Voigt model. Figure 3 The load can be modeled as a linear spring with elastic coefficient k and a damper with damping coefficient c. The dynamic response of the load model can be expressed by the following equation:
[0064]
[0065] In the formula: k is the stiffness coefficient; c is the damping coefficient; x2 is the vibration displacement of the tool; Δ is the initial interference.
[0066] Step 4-2: Identification of Force Load Model Parameters
[0067] The values of the initial interference, stiffness coefficient, and damping coefficient were adjusted to match the cutting force obtained in the ultrasonic bone cutting finite element simulation.
[0068] Step 5: Establish an ultrasonic bone scalpel-bone tissue interaction model and build a Matlab-Simulink simulation program.
[0069] The dynamic equation of a loaded ultrasonic bone scalpel can be written as:
[0070]
[0071] In the formula: ψ2(ω F ) is related to ω F The corresponding amplitude ratio.
[0072] As can be seen from equation (12), changes in the cutting force F will cause changes in the resonant frequency and mode shape of the ultrasonic bone scalpel, which in turn will cause changes in the vibration displacement x1 or x2. There is a certain correspondence between the cutting force F and the vibration displacement x1 or x2. Therefore, the cutting force F can be reflected by measuring the changes in vibration displacement x1 or x2. However, on the one hand, the narrow cutting zone makes it difficult to fix and install the sensor; on the other hand, the working environment is harsh, with cooling water mist, blood, etc. These two factors make it impossible to measure the vibration displacement x2. Therefore, this paper proposes an indirect measurement method of ultrasonic bone cutting force based on the anti-node vibration displacement x1.
[0073] Based on equations (3), (5), and (11), a MATLAB-Simulink simulation model is established as follows: Figure 4 The cutting force will cause the resonant frequency of the ultrasonic bone scalpel to drift. To ensure that the bone scalpel operates at the resonant frequency, frequency tracking is required. By inputting a 50kHz pulse excitation to the system and measuring the system output with a time step of 1e-6 and a sampling frequency resolution of 1Hz, the input and output data are Fourier transformed and then divided according to the definition of the frequency response function to obtain the frequency response function of the ultrasonic bone scalpel, thereby determining the resonant frequency. During the simulation, the ultrasonic bone scalpel employs a constant voltage drive strategy, ensuring that the drive voltage frequency equals the resonant frequency to simulate the frequency tracking function of the bone scalpel.
[0074] Step 6: Based on the Matlab-Simulink simulation program, using the data-driven modeling method, the effective value of the inverse nodal vibration displacement x1 is obtained. 1rms Vibration frequency f x1 The input is the effective value of the cutting force F. rms The relationship between the anti-node vibration displacement x1 and the cutting force F is obtained.
[0075] First, the stiffness coefficient was set to level m, and the damping coefficient to level n. An m*n set of simulation experiments was designed using a full factorial design. Next, based on the designed experiments, the stiffness and damping coefficients were changed in the MATLAB-Simulink simulation model, and the driving voltage frequency was reset to match the resonant frequency corresponding to the stiffness and damping coefficients. Then, the effective value x1 of the anti-node vibration displacement was recorded. 1rms Vibration frequency f x1 (equal to the resonant frequency) and the effective value F of the cutting force F rms Finally, the relationship between the anti-nodal vibration displacement x1 and the cutting force F is obtained using a data-driven modeling method.
[0076] Step 7: Measure the effective value x of the vibration displacement of the inverse node using an eddy current displacement sensor. 1rms and vibration frequency f x1 Calculate the effective value F of the cutting force based on the relationship obtained in step 6. rms .
[0077] like Figure 5 A schematic diagram of the reverse node vibration displacement measurement includes a housing 1, an eddy current displacement sensor 2, a marker 3, an amplitude transformer 4, a computer 5 with analysis software installed, a signal generator 6, and a power amplifier 7. A marker is installed at the reverse node x1 position of the amplitude transformer, and the marker vibrates axially along with the amplitude transformer. The eddy current displacement sensor is installed on the bone cutter housing; the housing is connected to the amplitude transformer node and remains stationary.
[0078] The eddy current displacement sensor 2 uses a Keyence EX-305V with a sampling frequency of 40KHz and is used to measure the reverse node vibration displacement x1 signal.
[0079] Signal acquisition system 5 uses an NI 9234 acquisition card to acquire signals from the displacement sensor;
[0080] Computer 1, equipped with analysis software, is used to analyze the displacement signal obtained by the signal acquisition system to obtain the effective value x of the anti-nodal vibration displacement x1. 1rms Vibration frequency f x Then, the effective value F of the cutting force F is calculated. rms .
Claims
1. An indirect measurement method for ultrasonic bone cutting force based on anti-nodal vibration displacement, characterized in that, Includes the following steps: Step 1: Determine the node positions of the ultrasonic bone scalpel to obtain a simplified model of the ultrasonic bone scalpel; Step 2: Establish a piezoelectric transducer model, calculate the model parameters, and obtain the vibration displacement of the piezoelectric transducer; Step 3: Establish the stepped amplitude transformer model and calculate the dynamic parameters based on eigenvalues, eigenvectors, and the principle of energy conservation; Step 4: Establish a force load model of bone tissue and identify model parameters; Step 5: Establish an ultrasonic bone scalpel-bone tissue interaction model and build a Matlab-Simulink simulation program; Step 6: Based on the Matlab-Simulink simulation program, use the data-driven modeling method to calculate the inverse nodal vibration displacement. x Valid value of 1 x 1rms Vibration frequency f x1 Input is the effective value of the cutting force. Output is the effective value of the cutting force. F rms Obtain the inverse node vibration displacement x 1 and cutting force F Relationship; Step 7: Measure the effective value of the vibration displacement of the inverse node using an eddy current displacement sensor. x 1rms and vibration frequency f x1 Calculate the effective value of the cutting force based on the relationship obtained in step 6. F rms ; The working principle of a piezoelectric transducer is to apply an alternating voltage excitation across the piezoelectric ceramic, utilizing the inverse piezoelectric properties of the material to induce longitudinal vibration, compression, or expansion deformation. Without considering the nonlinearity of the piezoelectric material, the interaction between the electrical and mechanical behaviors of the piezoelectric ceramic is described by the following linear relationship: (1) In the formula: S It is a response. T It is stress. S E It is the elastic compliance under a constant electric field. d It is the piezoelectric charge constant. D It is dielectric displacement. E It is the electric field strength. ε T It is the dielectric constant under constant stress; (2) In the formula: S 0 represents the cross-sectional area of the piezoelectric ceramic. l 0 represents the thickness of the piezoelectric ceramic. x 0 represents the vibrational displacement of the piezoelectric ceramic. F 0 is the force applied to the piezoelectric transducer by the amplitude transformer. u It is the excitation voltage; Substituting equation (2) into equation (1), we can obtain the vibration displacement of the piezoelectric transducer as follows: (3) In the formula: For elasticity and flexibility, Where is the charge constant. It is the dielectric constant; Step 3-1: Dynamic Modeling According to the Euler-Lagrange equation, the dynamic equation of the unloaded ultrasonic bone scalpel can be written as: (4) Interaction forces between piezoelectric ceramics and the 2-DOF model F 0 can be represented as: (5) In the formula: m 1, m 2, k 1, k 2, c 1, c 2 represents equivalent mass, equivalent stiffness, and equivalent damping, respectively; x 0 represents the vibration displacement of the piezoelectric ceramic. x 1, x 2 are respectively m 1, m 2. Vibration displacement; Based on the boundary conditions, the longitudinal vibration displacement of the ultrasonic bone scalpel can be expressed as: (6) In the formula: V 1, V 2 is m 1, m The vibration amplitude of 2, κ For the circular wave number, l 0 represents the length of the large cylinder of the amplitude transformer. l 1 represents the total length of the amplitude transformer; Step 3-2: Identification of dynamic parameters The mass matrix, stiffness matrix, eigenvalues, and eigenvectors of the system are represented as follows: (7) In the formula: ω 1 represents the first-order natural frequency. ω 2 is the second-order natural frequency. ψ 1 is with ω The amplitude ratio corresponding to 1 ψ 2 is with ω The amplitude ratio corresponding to 2; From the characteristic equation MλΨ = KΨ , can be obtained (8) However, there are four unknown parameters for equation (8) m 1, m 2, k 1, k 2) There are only three independent equations, therefore the solutions are infinitely combinable; the equations are supplemented according to the principle of energy conservation. (9) By combining equations (8) and (9), we can obtain (10) Therefore, the system dynamic parameters can be solved. m 1, m 2, k 1, k 2); Step 4-1: Establish the force load model; During ultrasonic bone scalpel cutting, the interaction between the tool and bone tissue generates a force load on the vibration system, which can be represented by the Kelvin-Voigt model. This load is equivalent to an elastic coefficient of... k A linear spring and a damping coefficient of c The model of the damper; the dynamic response of the load model is expressed by the following equation: (11) In the formula: k This is the stiffness coefficient; c The damping coefficient; x 2 represents the vibration displacement of the cutting tool; Δ For the initial interference; Step 4-2: Identification of Force Load Model Parameters The values of the initial interference, stiffness coefficient, and damping coefficient were adjusted to match the cutting force obtained in the ultrasonic bone cutting finite element simulation. The dynamic equation of a loaded ultrasonic bone scalpel can be written as follows: (12) In the formula: ψ 2( ω F ) for and ω F The corresponding amplitude ratio.
2. The indirect measurement method for ultrasonic bone cutting force based on anti-node vibration displacement according to claim 1, characterized in that, Step 1 describes simplifying the ultrasonic bone scalpel into two parts based on the location and number of nodes: a piezoelectric transducer model and a stepped amplitude transformer model.
3. The indirect measurement method for ultrasonic bone cutting force based on anti-node vibration displacement according to claim 1, characterized in that, Step 2 describes the use of linear relationships to describe the interaction between the electrical and mechanical behaviors of piezoelectric ceramics without considering the nonlinearity of piezoelectric materials, thus establishing a piezoelectric transducer model.
4. The indirect measurement method for ultrasonic bone cutting force based on anti-node vibration displacement according to claim 1, characterized in that, Step 3 describes establishing a stepped amplitude transformer model based on the Euler-Lagrange equations, and calculating its dynamic parameters according to eigenvalues, eigenvectors, and the principle of energy conservation.
5. The indirect measurement method for ultrasonic bone cutting force based on anti-node vibration displacement according to claim 1, characterized in that, Step 4 describes how, during the ultrasonic bone scalpel cutting process, the interaction between the scalpel and the bone tissue generates a force load on the vibration system, which is equivalent to an elastic coefficient of... k A linear spring and a damping coefficient of c The model of the damper.
6. The indirect measurement method for ultrasonic bone cutting force based on anti-node vibration displacement according to claim 1, characterized in that, Step 5 describes the establishment of an ultrasonic bone scalpel-bone tissue interaction model based on the piezoelectric transducer model, stepped amplitude transformer model, and force load model, and the development of a Matlab-Simulink simulation program.
7. The indirect measurement method for ultrasonic bone cutting force based on anti-node vibration displacement according to claim 1, characterized in that, Step 6 describes establishing an inverse nodal vibration displacement model based on the MATLAB-Simulink simulation program. x Valid value of 1 x 1rms Vibration frequency f x1 As input, the effective value of the cutting force F rms For the output dataset, a data-driven modeling method is used to obtain the inverse nodal vibration displacement. x 1 and cutting force F The relationship.
8. The indirect measurement method for ultrasonic bone cutting force based on anti-node vibration displacement as described in claim 1, characterized in that, The anti-node vibration displacement measurement platform described in step 7 comprises a shell, an eddy current displacement sensor, markers, an amplitude transformer, a computer with analysis software installed, a signal generator, a power amplifier, and an amplitude transformer anti-node... x A marker is installed at position 1. The marker reciprocates axially along with the amplitude transformer. An eddy current displacement sensor is installed on the shell of the bone cutter. The shell is connected to the amplitude transformer node and does not move.