Method, device, medium and equipment for constructing mechanical model for ultrasonic bone grinding, drilling and grinding of mechanical arm

Abstract

The invention relates to a mechanical arm ultrasonic grinding and drilling bone grinding mechanical model construction method and device, a medium and equipment, and the method comprises the steps: obtaining an ultrasonic machining motion model of ultrasonic grinding and drilling bone grinding according to the motion process of ultrasonic grinding and drilling grinding; according to the ultrasonic machining motion model, a finite element analysis model of ultrasonic abrasive drill bone grinding is established, and then the bone density, the vibration amplitude of a cylindrical abrasive drill of ultrasonic equipment and the influence rule of the feeding speed on the grinding force are obtained; and according to the finite element analysis model, a mechanical model of ultrasonic bone grinding and drilling is established, and then mathematical characterization among the grinding force, the vibration amplitude and the feeding speed is obtained. According to the mechanical arm ultrasonic grinding, drilling and grinding mechanical model, the dynamic relation among ultrasonic vibration parameters, mechanical arm motion parameters and grinding force can be accurately quantified, the situation that bone tissue is excessively damaged due to the fact that the grinding force is too large or the grinding efficiency is low due to the fact that the grinding force is insufficient is effectively avoided, and the safety of clinical operation is guaranteed.

Description

TECHNICAL FIELD

[0001] The application relates to a mechanical arm ultrasonic drill bone grinding mechanical model construction method, device, medium and equipment, and belongs to the field of robot bone grinding. BACKGROUND

[0002] The mechanical arm ultrasonic drill bone grinding mechanical model is constructed by virtue of the synergistic effect of ultrasonic vibration and mechanical feeding, and has the advantages of small trauma and high precision in the field of bone grinding, and construction of the mechanical model is a core basis for efficient application of the technology. The model can reveal the internal relationship between the ultrasonic amplitude, bone density, mechanical arm feeding rate and the cutting force and friction force generated in the bone grinding process, provide quantitative basis for avoiding excessive or insufficient grinding, and can be used as a key feedback element in the robot closed-loop control to ensure the stability of the operation process. Obviously, construction of the precise mechanical arm ultrasonic drill bone grinding mechanical model has an important value for promoting the development of the orthopedic surgery robot to a higher degree of automation.

[0003] At present, construction of the mechanical arm ultrasonic drill bone grinding mechanical model mainly depends on multi-physical field coupling analysis. The multi-physical field coupling analysis needs to integrate knowledge of acoustics, mechanics, materials science and other disciplines, involves complex processes such as ultrasonic energy conversion and dynamic response of bone tissue, and the model established has the problems of too many parameters and large amount of calculation, and is difficult to be quickly applied to the real-time decision system of the mechanical arm. In summary, it is of important academic research significance and clinical transformation value to explore a mechanical arm ultrasonic drill bone grinding mechanical model construction method that takes into account the mechanism accuracy and engineering practicability. SUMMARY

[0004] In view of the above technical problems, the application provides a mechanical arm ultrasonic drill bone grinding mechanical model construction method, device, medium and equipment, which provides a model basis for optimization and control of the mechanical arm ultrasonic drill grinding, and provides a theoretical basis for research of the mechanical arm ultrasonic drill grinding system.

[0005] To achieve the above purpose, the application adopts the following technical solutions:

[0006] A mechanical arm ultrasonic drill bone grinding mechanical model construction method, comprising:

[0007] S1: obtaining an ultrasonic machining motion model of ultrasonic drill bone grinding according to a motion process of ultrasonic drill grinding;

[0008] S2: establishing a finite element analysis model of ultrasonic drill bone grinding according to the ultrasonic machining motion model, and then obtaining the influence law of bone density, vibration amplitude of the cylindrical drill of the ultrasonic device and the feeding speed on the grinding force;

[0009] S3: According to the finite element analysis model, a mechanical model of ultrasonic bone grinding of the ultrasonic drill is established, and then mathematical representations between the grinding force and the vibration amplitude, the feed speed are obtained.

[0010] The mechanical model construction method of the ultrasonic drill bone grinding of the mechanical arm, preferably, step S1 comprises the following specific steps:

[0011] According to the processing movement process of the single abrasive grain on the cylindrical drill tool, X-axis displacement X t , Y-axis displacement Y t and Z-axis displacement Z t are obtained.

[0012] According to the processing movement process of the cylindrical drill tool, X-axis displacement S x and Z-axis displacement S z are obtained.

[0013] Based on X-axis displacement S x and Z-axis displacement S z , X-axis and Z-axis velocities V x and V z , i.e. the ultrasonic processing movement model, are obtained.

[0014] Based on the ultrasonic processing movement model, the relationship between the radial and axial velocities and the feed speed, the ultrasonic amplitude and the ultrasonic frequency is analyzed, and serves as the basis for setting the motion parameters of the finite element analysis model.

[0015] The mechanical model construction method of the ultrasonic drill bone grinding of the mechanical arm, preferably, X-axis and Z-axis velocities V x and V z are as follows:

[0016]

[0017] In the formula, V0 is the speed in the feed direction, F x is the radial amplitude of the ultrasonic drill, F z is the axial amplitude of the ultrasonic drill, ω is the ultrasonic vibration angular frequency, φ is the phase difference between the radial amplitude and the axial amplitude, and t is time.

[0018] The mechanical model construction method of the ultrasonic drill bone grinding of the mechanical arm, preferably, step S2 comprises the following specific steps:

[0019] A three-dimensional modeling software is used to construct the solid geometric model of the cylindrical drill and the bone, and the generated solid geometric model is imported into the finite element simulation software.

[0020] According to the material parameter library of the bone model and the cylindrical drill, parameters including density elasticity, material model and damage model are set, and the solid geometric model is assigned values by setting the cross section.

[0021] According to the relative position relationship under the real grinding scene, the entity geometric model is instantiated and assembled into a complete model, i.e. a finite element analysis model;

[0022] According to the geometric characteristics, material properties, analysis step and mechanical properties of the finite element analysis model, the conditions of the bone model and the cylindrical grinding head are set;

[0023] According to the ultrasonic machining motion model, the load parameters of the finite element analysis model are set to realize the simulation of the ultrasonic grinding motion process of the bone grinding.

[0024] According to the condition setting, the dynamic behavior of the bone model and the cylindrical grinding head is analyzed by using explicit dynamic analysis, and the feed direction grinding force of multiple simulation results is analyzed.

[0025] According to the finite element analysis model, the data of the feed direction grinding force under different bone densities, ultrasonic amplitudes and feed speeds are collected to provide data support for the mechanical model.

[0026] The mechanical model construction method of the mechanical arm ultrasonic grinding bone grinding, preferably, step S3 comprises the following specific steps:

[0027] According to the finite element analysis model, a response surface analysis experiment is designed, and data processing is performed according to the experimental results to draw a response surface.

[0028] According to the response surface analysis experiment, the sum of squares significance analysis, the loss of fitting term analysis and the fitting degree analysis of different order models are performed to construct the mechanical model of the ultrasonic grinding bone grinding, specifically:

[0029] F=-29.83658+0.27510*ρ+0.62448*A+4.51561*v

[0030] +2.80472*10 -4 *ρ*A-0.024785*ρ*v-0.026459*A*v

[0031] -8.66684*10 -4 *ρ 2 -4.41860*10 -3 *A 2 +0.25692*v 2

[0032] Wherein, ρ, A, v respectively represent the actual values of bone density, ultrasonic grinding amplitude and ultrasonic grinding feed speed.

[0033] According to the mechanical model, the mathematical representation between the grinding force and the vibration amplitude, the feed speed is obtained, and is used as the basis for the optimization and control of the ultrasonic grinding motion parameters of the mechanical arm;

[0034] According to the mechanical model, the fitting degree and significance of the mechanical model are evaluated by using a residual analysis method.

[0035] The mechanical model construction method of the mechanical arm ultrasonic grinding bone grinding provided by the embodiment of the application is preferably as follows:

[0036]

[0037] Wherein, sigma is the flow stress, A, B and C are the initial yield stress, hardening modulus and strain rate sensitive coefficient of the material; epsilon, And The equivalent plastic strain, the equivalent plastic strain rate and the reference plastic strain rate; n is the strain hardening index; m is the temperature softening index; T * The normalized temperature, Wherein, T is the temperature of the bone grinding part; T r The melting point of the material; T m The room temperature.

[0038] The mechanical model construction method of the mechanical arm ultrasonic grinding bone grinding provided by the embodiment of the application is preferably as follows:

[0039]

[0040] Wherein, epsilon f The failure strain; D1, D2, D3 and D4 are the coefficients related to the material damage; The normalized strain rate, sigma * The stress triaxiality.

[0041] The application has the following advantages due to the above technical scheme:

[0042] The mechanical model of the mechanical arm ultrasonic grinding bone grinding provided by the application can accurately quantify the dynamic relationship between the ultrasonic vibration parameters, the mechanical arm motion parameters and the grinding force, effectively avoid the excessive damage of the bone tissue caused by the excessive grinding force, or the low grinding efficiency caused by the insufficient grinding force, and ensure the safety of the clinical operation. BRIEF DESCRIPTION OF DRAWINGS

[0043] Figure 1 The mechanical model construction method of the mechanical arm ultrasonic grinding bone grinding provided by the embodiment of the application is preferably as follows:

[0044] Figure 2 The ultrasonic machining motion model schematic diagram provided by the embodiment of the application is as follows:

[0045] Figure 3 The bone model provided in this embodiment of the application and the schematic diagram of the cylindrical grinding head, wherein figure (a) is the cylindrical grinding head, figure (b) is the bone model;

[0046] Figure 4 The finite element analysis provided in this embodiment of the application, wherein figure (a) is the three-dimensional model of grinding; figure (b) is the bone model and the cylindrical grinding head grid; figure (c) is the interaction between the bone model and the cylindrical grinding head; figure (d) is the load constraint of the bone model and the cylindrical grinding head;

[0047] Figure 5 The space-time distribution of the finite element simulation provided in this embodiment of the application, wherein figure (a) is the cutting state diagram; figure (b) is the stable state diagram;

[0048] Figure 6 The response surface diagram of the grinding mechanics model provided in this embodiment of the application, wherein figure (a) is the response surface diagram of the grinding force when the feed speed is 1 mm / s, figure (b) is the response surface diagram of the grinding force when the feed speed is 2 mm / s, figure (c) is the response surface diagram of the grinding force when the feed speed is 3 mm / s, and figure (d) is the response surface diagram of the grinding force when the feed speed is 4 mm / s;

[0049] Figure 7 The smoothing treatment of the physical experiment provided in this embodiment of the application;

[0050] Figure 8 The diagram of the grinding force in the feed direction varying with time under different feed speeds in the finite element simulation provided in this embodiment of the application;

[0051] Figure 9 The diagram of the grinding force in the feed direction varying with time under different ultrasonic amplitudes in the finite element simulation provided in this embodiment of the application;

[0052] Figure 10 The diagram of the grinding force in the feed direction varying with time under different bone densities in the finite element simulation provided in this embodiment of the application;

[0053] Figure 11 The residual analysis diagram of the mechanics model provided in this embodiment of the application, wherein figure (a) is the normal probability distribution diagram of the residual; figure (b) is the distribution diagram of the predicted value and the actual value; figure (c) is the distribution diagram of the residual and the predicted value; and figure (d) is the distribution diagram of the residual and the actual value. DETAILED DESCRIPTION

[0054] In order to make the objects, technical solutions and advantages of the present application clearer, the technical solutions in the present application are clearly and completely described below. Obviously, the described embodiments are part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor fall within the protection scope of the present application.

[0055] Unless otherwise defined, the technical terms or scientific terms used in the present application shall have the meanings commonly understood by those skilled in the art to which the present application belongs. The "first", "second", "third", "fourth" and similar words used in the present application do not represent any order, number or importance, but are only used to distinguish different components. "Include" or "contain" and similar words mean that the elements or objects before the words cover the elements or objects listed after the words and their equivalents, without excluding other elements or objects. "Connected" or "connected" and similar words are not limited to physical or mechanical connection, but can include electrical connection, whether direct or indirect.

[0056] In order to facilitate the description, spatial relative terms can be used in the description to describe the relationship of one element or feature relative to another element or feature as shown in the figure, such as "inner", "outer", "inboard", "outboard", "under", "above", etc. Such spatial relative terms are intended to include different orientations of the device in use or operation in addition to the orientation depicted in the figure.

[0057] At present, the construction of the mechanical arm ultrasonic drill bone grinding mechanical model mainly depends on the multi-physical field coupling analysis. The multi-physical field coupling analysis needs to integrate the knowledge of acoustics, mechanics, materials science and other disciplines, involves complex processes such as ultrasonic energy conversion and bone tissue dynamic response, and the model established often has the problems of too many parameters and large amount of calculation, which is difficult to quickly apply to the real-time decision system of the mechanical arm. In summary, it is of important academic research significance and clinical transformation value to explore a mechanical arm ultrasonic drill bone grinding mechanical model construction method which takes into account the mechanism accuracy and engineering practicability.

[0058] Based on the above technical problems, the present application provides a mechanical arm ultrasonic drill bone grinding mechanical model construction method, which provides a model basis for the optimization and control of the mechanical arm ultrasonic drill grinding, and provides a theoretical basis for the research of the mechanical arm ultrasonic drill grinding system.

[0059] As shown in Figure 1 The mechanical arm ultrasonic drill bone grinding mechanical model construction method provided by the present application comprises the following specific steps:

[0060] Step S1: According to the movement process of the ultrasonic drill grinding, the ultrasonic machining motion model of the ultrasonic drill bone grinding is obtained;

[0061] Specifically, as shown in the figure, Figure 2 The processing motion of the ultrasonic drill tool of the embodiment is to apply periodic high-frequency harmonic vibration in the cutting direction and the depth direction while maintaining the grinding direction feeding motion, and simultaneously apply a low-speed rotary swing.

[0062] According to the processing motion process of a single abrasive grain on the cylindrical drill tool, the X-axis displacement X t , Y-axis displacement Y t and Z-axis displacement Z t are obtained as follows:

[0063]

[0064] Wherein, V0 is the speed in the feeding direction, r is the radius of the grinding head, F x is the radial amplitude of the ultrasonic drill, F z is the axial amplitude of the ultrasonic drill, ω is the angular frequency of the ultrasonic vibration, φ is the phase difference between the radial amplitude and the axial amplitude, θ is the rotation angle of the ultrasonic drill, Wherein n is the spindle speed, t is the time.

[0065] According to the processing motion process of the cylindrical drill tool, the X-axis displacement S x and the Z-axis displacement S z are obtained as follows:

[0066]

[0067] Wherein, V0 is the speed in the feeding direction, F x is the radial amplitude of the ultrasonic drill, F z is the axial amplitude of the ultrasonic drill, ω is the angular frequency of the ultrasonic vibration, φ is the phase difference between the radial amplitude and the axial amplitude, t is the time.

[0068] Thus, the X-axis and Z-axis speeds V x and V z can be expressed as:

[0069]

[0070] In this example, the ultrasonic vibration frequency is 40khz, ω = 251200, the radial amplitude F x is fixed at 10μm, the axial amplitude F z and the feeding speed V0 are variable.

[0071] According to the ultrasonic machining motion model, the relationship between the radial and axial velocities and the feed speed, ultrasonic amplitude and ultrasonic frequency is analyzed, which serves as the basis for setting the motion parameters of the finite element analysis model.

[0072] Step S2: According to the ultrasonic machining motion model, a finite element analysis model of ultrasonic bone grinding of the ultrasonic drill is established, and the influence of bone density, vibration amplitude of the cylindrical drill of the ultrasonic device and the feed speed on the grinding force is obtained.

[0073] Specifically, the finite element analysis model is established using Abaqus software. First, the entity geometric model of the component to be analyzed needs to be established, as shown in Figure 3 In the Solidworks three-dimensional CAD software, the entity geometric model of the bone block and the cylindrical grinding head is constructed, and is imported into the Abaqus finite element simulation software.

[0074] Further, the material parameter library of the bone model and the cylindrical grinding head is constructed in the attribute module, and the density elasticity, material model and damage model are set, and the entity geometric model is assigned by setting the section. The setting of the density elasticity of the bone model and the cylindrical grinding head is specifically shown in Table 1 and Table 2.

[0075] Table 1 Physical properties of the bone model

[0076]

[0077] Table 2 Physical properties of the cylindrical grinding head

[0078]

[0079] Further, the material model can approximately describe the plastic deformation of the material under high strain rate, and by reasonably adjusting the material model parameters, the elastic-plastic behavior of the bone tissue under high strain rate can be approximately simulated.

[0080] Specifically, the basic formula of the Johnson-Cook material model is:

[0081]

[0082] Where σ is the flow stress, A, B and C are the initial yield stress, hardening modulus and strain rate sensitivity coefficient of the material; ε, and are the equivalent plastic strain, equivalent plastic strain rate and reference plastic strain rate; n is the strain hardening index; m is the temperature softening index; T * is the normalized temperature, where T is the temperature of the bone grinding site; T r is the melting point of the material; T m is the room temperature, and the specific setting is shown in Table 3.

[0083] Table 3 Johnson-Cook material model main parameters

[0084]

[0085] Further, a damage model is set to describe the damage evolution of the bone material in the grinding process. Specifically, the basic formula of the Johnson-Cook damage model is:

[0086]

[0087] wherein ε f is the failure strain; D1, D2, D3, D4 are coefficients related to material damage; is the normalized strain rate, σ * is the stress triaxiality, which is specifically set as shown in Table 4.

[0088] Table 4 John-Cook damage model parameters

[0089]

[0090] Further, according to the relative position relationship in the real grinding scene, multiple components are instantiated and combined into a complete model in the assembly, wherein the cylindrical grinding head is simplified as a rigid body with a reference point (RP), as shown in Fig. (a) of Figure 4 ;

[0091] Further, the bone model and the cylindrical grinding head are meshed. First, as shown in Fig. (b) of Figure 4 , the C3D8R type linear eight-node hexahedral element is used to mesh the bone model, and the global size is set to 0.5mm, and the division result is 256000 element cells. The C3D4 type four-node linear tetrahedral element is used to mesh the cylindrical drill head, and the global size is set to 0.02mm, and the division result is 71888 element cells. In order to improve the solving accuracy and reduce the solving time, the multi-grid density method is used to mesh the bone model. In this method, the grinding area is meshed with high-density element, and the local grid design rule is set to 0.1mm in the feed direction and 0.1mm in the depth direction, and the other areas are meshed with low-density element.

[0092] Further, the grinding contact constraint of the bone model and the cylindrical grinding head is set. As shown in Fig. (c) of Figure 4 , first, the rigid body constraint is set on the reference point (RP), and then the contact properties of the cylindrical grinding head and the bone model are set, wherein the tangential behavior is added, the friction rule is selected as penalty, and the friction factor is set to 0.15; the normal behavior is added by default. Finally, the grinding contact area of the bone model and the cylindrical grinding head is set.

[0093] Further, the load of the bone model and the cylindrical grinding head is set. First, as shown in (d) of FIG. 1, the bone model is fixed, and the boundary conditions of the bone model are six degrees of freedom of the constrained bottom surface (U1=U2=U3=UR1=UR2=UR3=0), wherein U1, U2, U3 are respectively the velocities in the X, Y, Z directions, and UR1, UR2, UR3 are respectively the rotational velocities around the X, Y, Z axes, which are all set to 0. Second, different feed speeds in the negative direction of the X axis are applied on the reference point (RP) of the cylindrical grinding head, and periodic high-frequency harmonic vibrations in the radial direction and the axial direction are applied, and at the same time, a low-speed rotational swing is applied. Figure 4

[0094] According to the above condition setting, the dynamic behavior of the complex bone model and the cylindrical grinding head is analyzed by explicit dynamics. The time and space distribution diagram of the finite element simulation is shown in (a) and (b) of FIG. 2, and the grinding force in the feed direction is collected. Figure 5

[0095] Step S3: According to the finite element analysis model, a mechanical model of ultrasonic bone grinding is established, and a mathematical representation between the grinding force and the vibration amplitude, the feed speed is obtained.

[0096] According to the above finite element analysis model, the BBD method is used to design the response surface analysis experiment, and the simulation results are processed to draw the response surface as shown in FIG. 3. Figure 6

[0097] According to the above response surface analysis experiment, the linear model, the second-order interaction model, and the quadratic model are respectively evaluated, including the sum of squares significance analysis, the loss of fitting term analysis, and the goodness of fit analysis.

[0098] Further, the sum of squares significance analysis is performed, and the results of the sum of squares significance analysis are shown in Table 5. The P values of the linear model and the quadratic model are both less than 0.0001, indicating that the model is extremely significant and has strong data explanation ability. The P value of the second-order interaction model is 0.0002, which is slightly less than that of the linear model and the quadratic model, indicating that the data explanation ability is slightly weaker than that of the linear model and the quadratic model.

[0099] Table 5 Sum of squares significance analysis results

[0100]

[0101] ​​​Further, the results of the lack of fit term analysis are shown in Table 6. The lack of fit term P values of the linear model and the second-order interaction model are 0.0073 and 0.0071, respectively, both of which are less than 0.05, indicating that the lack of fit terms are significant, and that the current model misses key factors such as high-order terms and needs a more complex model. The lack of fit term P value of the quadratic model is 0.1462, which is greater than 0.05, indicating that the lack of fit term is not significant, and that the model fits well and does not miss important terms.

[0102] Table 6 Results of lack of fit term analysis

[0103]

[0104] Further, the results of the goodness of fit analysis are shown in Table 7. The R-Squared values of the linear model, the second-order interaction model, and the quadratic model are 0.8622, 0.9021, and 0.9883, respectively, and the higher the value (the closer to 1), the better. The R-Square value of the quadratic model is the highest, representing that the overall fitting effect of the quadratic model is the best. The Adj R-Squared values of the linear model, the second-order interaction model, and the quadratic model are 0.8305, 0.8433, and 0.9732, respectively, and the Adj R-Squared value of the quadratic model is closest to the R-Square value, representing that the quadratic model has strong real explanation ability and does not have overfitting phenomenon. The Pred R-Squared values of the linear model, the second-order interaction model, and the quadratic model are 0.7370, 0.6024, and 0.8626, respectively, and the Pred R-Squared value of the quadratic model is within 0.2 of the Adj R-Squared value and has the largest value, representing that the quadratic model does not have overfitting phenomenon and has strong model prediction ability.

[0105] Table 7 Results of goodness of fit analysis

[0106]

[0107]

[0108] Based on the results of the sum of squares significance analysis, the lack of fit term analysis, and the goodness of fit analysis, the quadratic model is selected as the optimal model, and the model regression equation is obtained.

[0109] Specifically, the coding factor equation is:

[0110] F = 12.74 + 3.10*A - 2.52*B + 2.55*C

[0111] + 0.18*A*B - 1.19*A*C - 0.79*B*C

[0112] - 0.89*A 2 - 1.77*B2 +0.58*C 2

[0113] wherein A, B, C represent the coding factors of bone density, ultrasonic bur amplitude and ultrasonic bur feed speed, respectively.

[0114] Specifically, the actual factor equation (i.e. the mechanical model) is:

[0115] F = -29.83658 + 0.27510 * p + 0.62448 * A + 4.51561 * v

[0116] + 2.80472 * 10 -4 * p * A - 0.024785 * p * v - 0.026459 * A * v

[0117] - 8.66684 * 10 -4 * p 2 - 4.41860 * 10 -3 * A 2 + 0.25692 * v 2

[0118] wherein p, A, v represent the actual values of bone density, ultrasonic bur amplitude and ultrasonic bur feed speed, respectively.

[0119] Further, to evaluate the effectiveness of the model, physical experiments are conducted to change the force signals in the grinding process of different parameters, and the changes of the grinding force in the feed direction under different parameters are collected.

[0120] It can be understood that the signals collected by the six-dimensional force sensor in the physical experiment have many noises, and need to be denoised and smoothed, as shown in Figure 7 .

[0121] In the first case, under the condition of keeping the bone density and ultrasonic bur amplitude constant, the grinding force in the feed direction increases with the increase of the ultrasonic bur feed speed, as shown in Figure 8 .

[0122] In the second case, under the condition of keeping the bone density and ultrasonic bur feed speed constant, the grinding force in the feed direction decreases with the increase of the ultrasonic bur amplitude, as shown in Figure 9 .

[0123] In the third case, under the condition of keeping the ultrasonic bur amplitude and feed speed constant, the grinding force in the feed direction increases with the increase of the bone density, as shown in Figure 10 .

[0124] Further, the residual analysis method is used to evaluate the fitting degree and significance of the model, and the external studentized residual method is used in this example, and its expression is:

[0125]

[0126] where e i is the ordinary residual of the ith observation, S -i is the residual standard deviation of the model refitted after deleting the ith observation, h ii is the leverage of the ith observation of the model.

[0127] It should be noted that the external studentized residual approximately obeys t distribution with degrees of freedom of n-p-1, where n is the sample size and p is the number of prediction variables. The absolute value 3 is used as a threshold to determine whether the observation is an outlier.

[0128] Further, four residual distribution diagrams are used to evaluate the fitting effect of the model. The residual normal probability distribution diagram is shown in Fig. (a) of Figure 11 , the residual is basically distributed on a straight line, indicating that the residual basically obeys the normal distribution. The distribution diagram of the predicted value and the actual value is shown in Fig. (b) of Figure 11 , the distribution points are basically distributed on a straight line, the predicted value is approximately equal to the actual value, indicating that the prediction effect of the model is good. The distribution diagram of the residual and the predicted value and the distribution diagram of the residual and the actual value are shown in Figs. (c) and (d) of Figure 11 and Figure 11 , respectively, the residual is randomly distributed in the range, there is no obvious relationship, and the absolute value of all residuals is less than 3, indicating that there is no outlier, and the fitting effect of the ultrasonic drill grinding mechanics model is good.

[0129] The second aspect of the present application provides a mechanical arm ultrasonic drill bone grinding mechanics model construction device, comprising:

[0130] A first processing unit is configured to obtain an ultrasonic machining motion model of ultrasonic drill bone grinding according to the motion process of ultrasonic drill grinding.

[0131] A second processing unit is configured to establish a finite element analysis model of ultrasonic drill bone grinding according to the ultrasonic machining motion model, and further obtain the influence law of bone density, vibration amplitude of the cylindrical drill of the ultrasonic equipment and feed speed on the grinding force.

[0132] A third processing unit is configured to establish a mechanics model of ultrasonic drill bone grinding according to the finite element analysis model, and further obtain the mathematical representation between the grinding force and the vibration amplitude and the feed speed.

[0133] The third aspect of the present application provides a computer readable storage medium having a computer program stored thereon, wherein the computer program is executed by a processor to implement the steps of the mechanical arm ultrasonic drill bone grinding mechanics model construction method described in any one of the above aspects.

[0134] The fourth aspect of the present application provides a computer device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the steps of the method for constructing a mechanical model of bone grinding by an ultrasonic drill of a mechanical arm according to any one of the preceding aspects when executing the computer program.

[0135] The present application is described according to flowcharts and / or block diagrams of the methods, devices (systems), and computer program products of the embodiments. It should be understood that each flow and / or block in the flowcharts and / or block diagrams, and the combination of the flows and / or blocks in the flowcharts and / or block diagrams can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing devices to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing devices generate a device that implements the flowcharts and / or block diagrams. Figure 1 one or more flows and / or blocks Figure 1 an apparatus that implements the functions specified in one or more flows and / or blocks.

[0136] These computer program instructions can also be stored in a computer-readable memory that can direct the computer or other programmable data processing devices to work in a specific manner, so that the instructions stored in the computer-readable memory produce a manufactured product comprising instruction apparatus that implements the flowcharts and / or block diagrams. Figure 1 one or more flows and / or blocks Figure 1 an apparatus that implements the functions specified in one or more flows and / or blocks.

[0137] These computer program instructions can also be loaded into a computer or other programmable data processing device, so that a series of operation steps are performed on the computer or other programmable device to produce a computer-implemented process, so that the instructions executed on the computer or other programmable device provide a process for implementing the flowcharts and / or block diagrams. Figure 1 one or more flows and / or blocks Figure 1 an apparatus that implements the functions specified in one or more flows and / or blocks.

[0138] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present application, and not to limit them; although the present application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that they can still modify the technical solutions recorded in the foregoing embodiments, or make equivalent replacements for some technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the present application.

Claims

1. A method for constructing a mechanical model for ultrasonic drilling and bone grinding using a robotic arm, characterized in that, include: S1: Based on the motion process of ultrasonic drilling, obtain the ultrasonic machining motion model of ultrasonic drilling bone grinding; S2: Based on the ultrasonic machining motion model, a finite element analysis model for ultrasonic grinding of bone is established, thereby obtaining the influence of bone density, the vibration amplitude of the cylindrical grinding drill of the ultrasonic equipment, and the feed rate on the grinding force. S3: Based on the finite element analysis model, establish a mechanical model for ultrasonic grinding of bone drills, and then obtain a mathematical representation of the relationship between grinding force, vibration amplitude, and feed rate.

2. The method for constructing a mechanical model for ultrasonic drilling and bone grinding by a robotic arm according to claim 1, characterized in that, Step S1 includes the following specific steps: Based on the machining motion of a single abrasive grain on a cylindrical grinding drill tool, the X-axis displacement X is obtained. t Y-axis displacement t and Z-axis displacement Z t ; Based on the machining motion of the cylindrical grinding drill tool, the X-axis displacement S is obtained. x and Z-axis displacement S z ; Based on X-axis displacement S x and Z-axis displacement S z The X-axis and Z-axis velocities V are obtained. x and V z That is, the ultrasonic processing motion model; Based on the ultrasonic machining motion model, the relationship between radial and axial velocities, feed rate, ultrasonic amplitude, and ultrasonic frequency is analyzed, and used as the basis for setting the motion parameters of the finite element analysis model.

3. The method for constructing a mechanical model for ultrasonic drilling and bone grinding by a robotic arm according to claim 2, characterized in that, X-axis and Z-axis speeds V x and V z Specifically as follows: In the formula, V0 is the velocity in the feed direction, and F x F is the radial amplitude of the ultrasonic drill. z ω is the axial amplitude of the ultrasonic drill, φ is the ultrasonic vibration angular frequency, φ is the phase difference between the radial and axial amplitudes, and t is time.

4. The method for constructing a mechanical model for ultrasonic drilling and bone grinding by a robotic arm according to claim 1, characterized in that, Step S2 includes the following specific steps: First, solid geometric models of the cylindrical drill and bone are constructed using 3D modeling software, and then the generated solid geometric models are imported into finite element simulation software. Based on the material parameter library of the bone model and cylindrical grinding head, parameters including density elasticity, material model and damage model are set, and values ​​are assigned to the solid geometry model by setting the cross section. Based on the relative positional relationships in a real grinding scenario, the solid geometric model is instantiated and assembled into a complete model, namely the finite element analysis model. Based on the geometric features, material properties, analysis step size, and mechanical characteristics of the finite element analysis model, the conditions for the bone model and the cylindrical grinding head are set. Based on the ultrasonic machining motion model, the load parameters of the finite element analysis model are set to simulate the ultrasonic grinding process of bone drilling. Based on the set conditions, the dynamic behavior of the bone model and the cylindrical grinding head was analyzed by explicit dynamic analysis, and the grinding force in the feed direction of multiple sets of simulation results was analyzed. Based on the finite element analysis model, data on the grinding force in the feed direction under different bone densities, ultrasonic amplitudes, and feed speeds were collected to provide data support for the mechanical model.

5. The method for constructing a mechanical model for ultrasonic grinding of bone by a robotic arm according to claim 1, characterized in that, Step S3 includes the following specific steps: Based on the finite element analysis model, a response surface analysis experiment was designed, and the data was processed according to the experimental results to plot the response surface. Based on response surface methodology experiments, sum of squares significance analysis, lack of fit analysis, and goodness-of-fit analysis were performed on models of different orders to construct a mechanical model for ultrasonic bone grinding. Based on the mechanical model, a mathematical representation of the relationship between grinding force, vibration amplitude, and feed rate is obtained, which serves as the basis for optimizing and controlling the motion parameters of ultrasonic grinding drill bone grinding in robotic arms. Based on the mechanical model, residual analysis is used to evaluate the goodness of fit and significance of the mechanical model.

6. The method for constructing a mechanical model for ultrasonic grinding of bone by a robotic arm according to claim 4, characterized in that, The calculation formulas for the material model are as follows: Where σ is the flow stress, and A, B, and C are the initial yield stress, hardening modulus, and strain rate sensitivity coefficients of the material; ε, and Here, represents the equivalent plastic strain, equivalent plastic strain rate, and reference plastic strain rate; n is the strain hardening exponent; m is the temperature softening exponent; T * For normalized temperature, Where T is the temperature of the bone grinding area; T r T is the melting point of the material. m Room temperature; The calculation formula for the damage model is as follows: Where, ε f D1 represents the failure strain; D2, D3, and D4 are coefficients related to material damage. For the normalized strain rate, σ * It is a stress triaxiality.

7. The method for constructing a mechanical model for ultrasonic drilling and bone grinding by a robotic arm according to claim 5, characterized in that, The calculation formula for the mechanical model is as follows: F=-29.83658+0.27510*ρ+0.62448*A+4.51561*v+2.80472*10 -4 *ρ*A-0.024785*ρ*v-0.026459*A*v-8.66684*10 -4 *r 2 -4.41860*10 -3 *A 2 +0.25692*v 2 Where ρ, A, and v represent the actual values ​​of bone density, ultrasonic drill amplitude, and ultrasonic drill feed rate, respectively.

8. A mechanical model construction device for ultrasonic grinding of bone by a robotic arm, characterized in that, include: The first processing unit is used to obtain the ultrasonic machining motion model of ultrasonic drilling bone grinding based on the motion process of ultrasonic drilling. The second processing unit is used to establish a finite element analysis model of ultrasonic grinding drill bone grinding based on the ultrasonic processing motion model, and then obtain the bone density, the vibration amplitude of the cylindrical grinding drill of the ultrasonic equipment, and the influence law of feed speed on grinding force. The third processing unit is used to establish a mechanical model of ultrasonic grinding of bone drill based on the finite element analysis model, and then obtain the mathematical characterization of the relationship between grinding force, vibration amplitude, and feed rate.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the steps of the mechanical model construction method for ultrasonic grinding of bone by a robotic arm according to any one of claims 1-7.

10. A computer device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the steps of the mechanical model construction method for ultrasonic grinding of bone by a robotic arm according to any one of claims 1-7.

Images