Mechanical model construction method for robot bone grinding

Abstract

The invention provides a robot bone grinding mechanical model construction method which comprises the following steps: analyzing a robot bone grinding process to obtain a robot bone grinding mechanical analysis geometric model; according to the mechanical analysis geometric model, a finite element analysis model of robot bone grinding is established, and the influence rule of the main shaft rotating speed and the feeding speed of the spherical grinding head on the grinding force is obtained; according to a mechanical analysis geometric model and finite element model data, a mechanical model of robot bone grinding is established, and mathematical characterization among grinding force, the rotating speed of a main shaft and the feeding speed is obtained. According to the technical scheme provided by the invention, the construction of the mechanical model of robot bone grinding can be realized.

Description

[Technical field]

[0001] The invention relates to a mechanical model construction method for robot bone grinding, and belongs to the field of robot bone grinding processing. [Background technology]

[0002] The mathematical model based on grinding force can be used to find the optimal grinding parameters to minimize the damage to bone tissue caused by bone grinding. This mathematical model describes the mapping relationship between grinding parameters and grinding force and can be used as a constraint in the objective function optimization problem. In addition, the mathematical model based on grinding force can also be used in a model-based controller to adjust the grinding force, thus playing an important role in the robotic grinding process. It can be seen that the mathematical model of grinding force is of great significance for the optimization and control of robotic grinding parameters.

[0003] Grinding force models can be constructed through theoretical modeling and empirical analysis. These models can not only help us understand the changes in force under different grinding conditions, but also develop optimal surgical strategies and minimize tissue damage. The theoretical modeling method analyzes the micro-geometry, motion state and force conditions of the spherical drill bit to obtain a complex integral form of the grinding force. This complex form makes it difficult to intuitively see the relationship between the grinding force and grinding parameters such as feed speed and rotation speed, and it is difficult to directly apply it to actual robot control. Although the empirical analysis method can observe the influence of grinding parameters such as rotation speed and feed speed on the grinding force, it has no clear mathematical representation and is difficult to apply in robot autonomous grinding. In summary, it is of great theoretical research value to conduct a study on the construction method of a mechanical model for robot bone grinding. [Summary of the invention]

[0004] In view of this, the present invention provides a method for constructing a mechanical model of robotic bone grinding to achieve mechanical modeling of robotic bone grinding.

[0005] The present invention provides a method for constructing a mechanical model of robot bone grinding, comprising:

[0006] Analyze the process of robotic bone grinding and obtain the mechanical analysis geometric model of robotic bone grinding;

[0007] Based on the mechanical analysis geometric model, a finite element analysis model of robot bone grinding was established to obtain the influence of the spindle speed and feed speed of the spherical grinding head on the grinding force.

[0008] Based on the mechanical analysis geometric model and finite element model data, a mechanical model of robot bone grinding was established to obtain the mathematical representation of the grinding force, spindle speed and feed speed.

[0009] In the above method, a finite element analysis model of robot bone grinding is established based on the mechanical analysis geometric model to obtain the influence of the spindle speed and feed speed of the spherical grinding head on the grinding force, including:

[0010] According to the mechanical analysis geometric model of robot bone grinding, the solid geometric model of the spherical grinding head and the bone is constructed using 3D modeling software, and the generated model is imported into the finite element simulation software. In the assembly, the relative position of the bone model and the spherical grinding head is set;

[0011] According to the material essential properties of the bone model and the spherical grinding head, the material properties and constitutive model of the bone model and the spherical grinding head are constructed;

[0012] According to the geometry and stress state of the simulation model, a multi-density grid structure of the bone model and the spherical grinding head is constructed;

[0013] According to the actual bone grinding state, the grinding contact constraints of the spherical grinding head and the bone model are set respectively. The spherical grinding head is simplified into a rigid body with a reference point (RP); the bottom surface of the bone model is constrained and fixed to realize the modeling of the actual scene of robot bone grinding.

[0014] According to the above conditions, explicit dynamics is used to analyze the complex dynamic behavior of the spherical grinding head and bone. t (X-axis grinding force) and grinding force perpendicular to the feed direction F n (Y-axis grinding force). The results show that the grinding force decreases with the increase of the spindle speed of the robot spherical grinding head; the grinding force increases with the increase of the feed speed of the robot spherical grinding head.

[0015] According to the above finite element analysis model, the grinding force data are collected under different spindle speeds and different feed speeds to provide sufficient experimental data.

[0016] In the above method, a mechanical model of robot bone grinding is constructed based on the mechanical analysis geometric model and the finite element analysis model data to obtain the mathematical representation between the grinding force and the spindle speed and feed speed, including:

[0017] According to the mechanical analysis model of robot bone grinding, the X-axis grinding force F is obtained. t and Y-axis grinding force F n for:

[0018]

[0019] Where F is the X-axis grinding force F t and Y-axis grinding force F n The resultant force of θ is the resultant force F and the Y-axis grinding force F n Angle.

[0020] Based on Y-axis grinding force F n The influencing factors include three parts: tool characteristics, bone density, and instantaneous volume of material removal, which can be expressed as:

[0021]

[0022] Among them, γ n represents the correction parameter, ρ represents the bone density, V represents the instantaneous volume of bone removal, k ρ and k v Indicates the influencing factors of ρ and V; since the grinding depth is less than the radius of the spherical grinding head, A=πrh c , where h c Represents the thickness of grinding. Under the motion conditions of the spherical grinding head spindle speed n and feed speed f, the instantaneous volume of bone removed V = λVnf = λπrh c nf.

[0023] Therefore, the X-axis grinding force F t It can be expressed as:

[0024]

[0025] Therefore, the resultant force F can be expressed as:

[0026]

[0027] According to the mathematical representation of the grinding force, spindle speed, and feed speed and the finite element analysis model data, the influencing factor γ of the mechanical model affecting robot bone grinding is obtained. n , k ρ , k v , which will serve as the basis for the optimization and control of motion parameters in robotic bone grinding.

[0028] It can be seen from the above technical solutions that the present invention has the following beneficial effects:

[0029] In the technical solution of the present invention, a mechanical analysis geometric model of robot bone grinding is obtained; based on the mechanical analysis geometric model, a finite element analysis model of robot bone grinding is established to obtain the influence of the spindle speed and feed speed of the spherical grinding head on the grinding force; based on the mechanical analysis geometric model and the finite element model data, a mechanical model of robot bone grinding is established to obtain the mathematical representation between the grinding force and the spindle speed and feed speed, thereby providing a model basis for the optimization and control of the robot grinding parameters and, at the same time, providing a theoretical basis for the research of the robot bone grinding system.

Brief Description of the Drawings

[0030] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required for use in the embodiments are briefly introduced below. It is obvious that the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creativity and labor.

[0031] Figure 1 It is a schematic flow chart of a method for constructing a force model for robot bone grinding provided by an example of the present invention;

[0032] Figure 2 is a schematic diagram of a bone grinding robot system provided in an example of the present invention;

[0033] Figure 3 It is a schematic diagram of a spherical grinder provided in an example of the present invention;

[0034] Figure 4 is a schematic diagram of a mechanical analysis geometric model provided in an embodiment of the present invention;

[0035] Figure 5 Schematic diagram of finite element analysis provided in an embodiment of the present invention: (a) three-dimensional model of grinding; (b) bone model and spherical grinding head mesh; (c) interaction between bone model and spherical grinding head; (d) load constraints of bone model and spherical grinding head;

[0036] Figure 6 Schematic diagram of the time-space distribution of the finite element simulation provided in the embodiment of the present invention: (a) cut-in state; (b) stable state; (c) stable state; (d) cut-out state;

[0037] Figure 7 is a schematic diagram of X-axis grinding force varying with time at different speeds in a finite element simulation provided in an embodiment of the present invention;

[0038] Figure 8 is a schematic diagram of X-axis grinding force varying with time at different feed speeds in a finite element simulation provided in an embodiment of the present invention;

[0039] Fig. 9 It is a schematic diagram of the smoothing process of the physical experiment provided in the example of the present invention;

[0040] Fig.10 It is a schematic diagram of the X-axis grinding force changing with time at different rotation speeds in the physical experiment provided in the example of the present invention;

[0041] Fig.11 It is a schematic diagram of the X-axis grinding force changing with time at different feed speeds in the physical experiment provided in the example of the present invention;

[0042] Fig.12It is a schematic diagram of the predicted value of the grinding force model and the finite element simulation value provided in the example of the present invention;

[0043] Fig.13 It is a schematic diagram of the Sobol analysis method provided in the example of the present invention for analyzing the influence of motion parameters on grinding force;

[0044] Fig.14 It is a schematic diagram of the grinding mechanics model provided in the example of the present invention;

[0045] Fig.15 It is a contour diagram of the grinding mechanics model provided in the example of the present invention; [Specific embodiment]

[0046] In order to better understand the technical solution of the present invention, the embodiments of the present invention are described in detail below with reference to the accompanying drawings.

[0047] It should be clear that the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0048] The present invention provides a method for constructing a mechanical model of robot bone grinding. Figure 1 , which is a flow chart of the method for constructing a force model for robot bone grinding provided by the present invention, such as Figure 1 As shown, without being limited to the above, the mechanical model construction method of robot bone grinding is applicable to the field of orthopedic surgery, and provides a safe contact force output model for robot bone grinding during surgical procedures, so as to more accurately control the contact force of robot bone grinding and ensure the safety of robot autonomous bone grinding. The method includes the following steps:

[0049] Step 101, analyzing the process of robot bone grinding to obtain a mechanical analysis geometric model of robot bone grinding;

[0050] The bone grinding robot system 201 includes a robot arm 202, a six-dimensional force sensor device 213, a high-speed grinding drill 215 and a spherical grinding knife 216 device, such as Figure 2 As shown. The bone grinding robot system 201 can be arranged for autonomous grinding to improve accuracy and prevent the risk of damage to the surrounding tissue of the lesion area. The bone grinding robot system 201 provides full control of the autonomous movement of the robot arm 202, the high-speed grinding drill 215 and the ball grinding knife 216, and at the same time, the grinding force collected by the six-dimensional force sensor 213 is used as a feedback signal.

[0051] The robot arm 202 is a six-degree-of-freedom robot arm, including a base flange 203, a rotation 1 joint 204, a rotation 2 joint 205, a 1-link 206, a rotation 3 joint 207, a 2-link 208, a rotation 4 joint 209, a rotation 5 joint 210, a rotation 6 joint 211, and an end flange 212. A six-dimensional force sensor 213 is mounted and fixed on the end flange 212, a high-speed grinding drill fixing component 214 is mounted and fixed on the six-dimensional force sensor 213, a high-speed grinding drill 215 is mounted and fixed on the high-speed grinding drill fixing component 214, and a spherical grinding tool 216 is mounted and fixed on the high-speed grinding drill 215.

[0052] The spherical grinding tool 216 includes a handle 301 and a spherical grinding head 302. Figure 3 As shown, the diameter of the spherical grinding head 302 is 5 mm, the number of blades is 14, the helix angle is 35 degrees, and the diameter of the handle 301 is 3. The spherical grinding knife 216 moves in a fixed direction, and the spherical grinding head 302 contacts and grinds the bone model 303. It is worth noting that the spherical grinding knife in this example is not limited to these parameters.

[0053] Specifically, the process of robot bone grinding is analyzed, and the X-axis, Y-axis and Z-axis of the spherical grinding head are constructed, such as Figure 4 As shown in the left figure, the X-axis is the feed direction, the Y-axis is along the spherical grinding head perpendicular to the X-axis, and the Z-axis satisfies the right-hand screw rule and is perpendicular to the X-axis and the Y-axis.

[0054] According to the coordinate axes of the robot bone grinding process, the mechanical analysis geometric model of robot bone grinding is constructed, such as Figure 4 The right figure shows the grinding force F of the spherical grinding head along the X-axis direction. t , Grinding force F of spherical grinding head along Y axis n , the combined force F of the spherical grinding head along the X-axis and Y-axis, the grinding force F of the spherical grinding head along the Y-axis n The angle θ with the resultant force F, the spindle speed n of the spherical grinding head, the feed speed f of the spherical grinding head, the contact area A between the spherical grinding head and the bone, the depth h of the spherical grinding head into the bone c , the radius r of the spherical grinding head.

[0055] Step 102, establishing a finite element analysis model of robot bone grinding based on the mechanical analysis geometric model, and obtaining the influence of the spindle speed and feed speed of the spherical grinding head on the grinding force;

[0056] Specifically, according to the mechanical analysis model of robot bone grinding, the solid geometry model of 301 bone and 302 spherical grinding head was constructed using Solidworks 3D modeling software, and then imported into Abaqus finite element simulation software, such as Figure 5As shown in (a), the relative position between the bone model and the spherical grinding head is set during assembly, that is, the spherical grinding head is perpendicular to the bone model, the grinding depth is set to 0.5 mm, and a certain distance between the spherical grinding head and the bone model is ensured.

[0057] Furthermore, the material properties and constitutive model of the bone model and the spherical grinding head are set. The biomechanical properties of the bone bridge are close to those of the cortical bone, and its material properties are: density is 1640 kg / m 3 , elastic modulus is 17 GPa, Poisson's ratio is 0.35, see Table 1 for details. The material properties of the spherical grinding head are: density is 7840 kg / m 3 , the elastic modulus is 210 GPa, and the Poisson's ratio is 0.3. See Table 2 for details.

[0058] Considering the constitutive model is a key factor in finite element analysis, which establishes the stress and strain relationship in the grinding zone and can predict the stress distribution and strain accumulation in the grinding zone.

[0059] According to the Johnson-Cook material model, as shown in the following formula,

[0060]

[0061] Where, ε is the equivalent plastic strain; and is the equivalent plastic strain rate and the reference plastic strain rate; T is the temperature of the bone grinding site; T r is the melting point of the material; T m is room temperature; n is the strain hardening index; m is the thermal softening index; A, B, C are the yield strength, strain and strain sensitivity of the material. The strain parameters of the designed bone model are shown in Table 3.

[0062] According to the Johnson-Cook damage model, as shown in the following formula,

[0063]

[0064] In the formula, ε f is the strain equivalent when the material is damaged, D1, D2, and D3 are the damage coefficients related to quasi-static damage, and the D4 coefficient is related to the influence of the strain rate. The damage parameters of the designed bone model are shown in Table 4.

[0065] Furthermore, the mesh properties of the bone model and the spherical grinding head are set. Figure 5(b) The bone model was meshed using C3D8R linear eight-node hexahedral elements, with the global size set to 1 mm and the resulting mesh size being 13,000 cells. The spherical drill was meshed using C3D10M quadratic tetrahedral elements, with the global size set to 0.4 mm and the resulting mesh size being 10,167 cells. In order to improve the solution accuracy and reduce the solution time, the bone model was meshed using the multi-grid density method. In this method, the region of interest (grinding region) was meshed using high-density cells, and the local mesh design rules were set to 0.2 mm in the feed direction and 0.2 mm in the depth direction, and other regions were meshed using low-density cells.

[0066] Further, the interaction between the bone model and the spherical grinding head is set. Figure 5 As shown in (c), a reference point (RP) 401 is set on the spherical grinding head. It is worth noting that, considering that the hardness of the spherical grinding head is much higher than that of the bone material, the spherical grinding head is set as a rigid body with a reference point (RP) during the modeling process to better adapt to changes in contact conditions and apply motion to the reference point. Secondly, the contact area 402 between the bone model and the spherical grinding head is set, and the contact properties between the spherical grinding head and the bone model are set, wherein a tangential behavior is added, the friction rule is selected as a penalty, and the friction factor is set to 0.15; a normal behavior is added, and the default setting is used. Finally, the grinding contact area between the spherical grinding head and the bone model is set.

[0067] Furthermore, the loads of the bone model and the spherical grinding head are set. Figure 5 As shown in (d), in the bone grinding simulation, the bone model is fixed, and the boundary conditions of the bone model are to constrain the six degrees of freedom of the bottom surface (U1=U2=U3=UR1=UR2=UR3=0). The spherical grinding head needs to move in contact with the bone model. Different feed speeds in the negative direction of the X-axis and different spindle speeds in the Y-axis direction are applied to the reference point of the spherical grinding head to ensure that it is the same as the actual grinding physical scene.

[0068] Based on the above conditions, explicit dynamics is used to analyze the complex dynamic behavior of the spherical grinding head and bone. The entire grinding process is divided into three stages: cutting-in, steady state and cutting-out, and each stage is analyzed, such as Figure 6 As shown, the grinding force F in the feed direction is collected t (X-axis grinding force) and grinding force perpendicular to the feed direction F n (Y-axis grinding force).

[0069] It should be noted that the examples of the present invention observe and discover the characteristic change of the force in the X-axis direction of the bone cutter by changing the spindle speed of the spherical grinding head under the conditions that the feed speed of the spherical grinding head and the diameter of the spherical grinding head are constant; and observe and discover the characteristic change of the force in the X-axis direction of the bone cutter by changing the feed speed of the spherical grinding head under the conditions that the spindle speed of the spherical grinding head and the diameter of the spherical grinding head are constant, as follows:

[0070] In the first case, under the condition of keeping the spherical grinding head feed speed and spherical grinding head diameter constant, the grinding force of the X axis decreases with the increase of the spherical grinding head spindle speed, such as Figure 7 As shown;

[0071] In the second case, under the condition of keeping the spindle speed and the diameter of the spherical grinding head constant, the grinding force increases with the increase of the feed speed of the robot spherical grinding head, such as Figure 8 Show;

[0072] According to the above finite element analysis model, the grinding force data are collected under different spindle speeds and different feed speeds to provide sufficient experimental data.

[0073] In order to prove the correctness of the finite element analysis model, the present invention conducted a grinding experiment on a bone model, and after completion, observed and analyzed the force signal change trend and variance generated in the X-axis direction during the feeding process of the bone knife grinding.

[0074] Specifically, the original force signal generated in the X-axis direction during the feeding process when the bone cutter grinds the bone model is collected, and the original force signal is subjected to noise reduction processing to obtain the target force signal.

[0075] Among them, the embodiment of the present invention selects the X-direction grinding force of the feeding process as the force feature as the input, and clearly represents the grinding force numerical information of the bone model grinding.

[0076] It should be noted that the force signal fed back when the bone knife grinds the bone model is transmitted to the host computer via the six-dimensional force sensor via USB to RS485. Since the sampling frequency of the six-dimensional force is 100Hz, the original force signal transmitted via USB to RS485 may contain a lot of noise, which seriously affects the verification accuracy of the finite element analysis model. Therefore, it is very necessary to filter the original force signal.

[0077] It is understood that curve smoothing is a technique commonly used in data analysis and signal processing to reduce noise in data and highlight major trends and patterns. This example uses a window with an exposure point of 19 for smoothing and uses a second-order polynomial fitting method to achieve smoothing.

[0078] Specifically, this choice is based on the following reasons: First, the number of exposure points is 19, which means that when smoothing, each data point will refer to the 9 points before and after it and itself, for a total of 19 points. This window width selection can effectively balance noise suppression and signal fidelity. When the window width is small, although it can reflect local changes more accurately, it may not be able to fully suppress noise; and if the window width is too large, it may lead to the loss of important details. Secondly, a second-order polynomial is used for fitting, that is, the data is approximated by a quadratic curve. Compared with the first-order polynomial (linear fitting), the second-order polynomial is more flexible and can capture nonlinear trends in the data. Compared with higher-order polynomials, its computational complexity is lower and it can avoid overfitting problems.

[0079] Among them, the quadratic polynomial y = ax 2 +bx+c has the form, where the coefficients a, b, and c are determined from the data points within the window by the least squares method. This method can better describe the local changes of the curve while maintaining computational simplicity.

[0080] It can be understood that the combination of selecting 19 exposure points and 2nd-order polynomial fitting can effectively suppress noise during the smoothing process, retain the main trends and patterns of the data, and has good computational efficiency and robustness. The processing results are as follows: Fig. 9 shown.

[0081] It should be noted that the examples of the present invention observe and discover the characteristic change of the force in the X-axis direction of the bone cutter by changing the spindle speed of the spherical grinding head under the conditions that the feed speed of the spherical grinding head and the diameter of the spherical grinding head are constant; and observe and discover the characteristic change of the force in the X-axis direction of the bone cutter by changing the feed speed of the spherical grinding head under the conditions that the spindle speed of the spherical grinding head and the diameter of the spherical grinding head are constant, as follows:

[0082] In the first case, under the condition of keeping the spherical grinding head feed speed and spherical grinding head diameter constant, the grinding force of the X axis decreases with the increase of the spherical grinding head spindle speed, such as Fig.10 As shown;

[0083] In the second case, under the condition of keeping the spindle speed and the diameter of the spherical grinding head constant, the grinding force increases with the increase of the feed speed of the robot spherical grinding head, such as Fig.11 Show;

[0084] Step 103, establishing a mechanical model of robot bone grinding based on the mechanical analysis geometric model and finite element model data, and obtaining a mathematical representation between the grinding force and the spindle speed and feed speed;

[0085] According to the mechanical analysis model of robot bone grinding, the X-axis grinding force F is obtained. t and Y-axis grinding force Fn for:

[0086]

[0087] Where F is the X-axis grinding force F t and Y-axis grinding force F n The resultant force of θ is the resultant force F and the Y-axis grinding force F n Angle.

[0088] According to the fact that the depth of the spherical grinding head into the bone is less than the radius r of the spherical grinding head, the contact area A between the spherical grinding head and the bone can be expressed as:

[0089] A=πrh c

[0090] Among them, r represents the radius of the spherical grinding head, h c Represents the depth of the spherical grinding head cutting into the bone.

[0091] Therefore, the instantaneous volume V of bone material removed can be expressed as:

[0092] V=λVnf=λπrh c nf

[0093] Among them, n represents the spindle speed of the spherical grinding head, and f represents the feed speed of the spherical grinding head.

[0094] Based on Y-axis grinding force F n The influencing factors include three parts: tool characteristics, bone density, and the instantaneous volume of bone material removed. Therefore, the grinding force F in the Y axis is n It can be expressed as:

[0095]

[0096] Among them, γ n represents the correction parameter, ρ represents the bone density, V represents the instantaneous volume of bone removal, k ρ and k v represents the influence factor of ρ and V;

[0097] Therefore, the X-axis grinding force F t It can be expressed as:

[0098]

[0099] Therefore, the resultant force F can be expressed as:

[0100]

[0101] According to the mathematical representation of the grinding force, spindle speed, and feed speed and the finite element analysis model data, the influencing factor γ of the mechanical model affecting robot bone grinding is obtained. n, k ρ , k v , which will serve as the basis for the optimization and control of motion parameters in robotic bone grinding.

[0102] In order to quantify the influence of various parameters on the grinding force, the φ, k v ,k n Parameters. Considering the linearization of ball drill speed and feed speed as predictive variables, functional regression is used to realize multivariate linear regression, and the grinding force formula is adjusted:

[0103]

[0104] To linearize the formula, take the natural logarithm of both sides:

[0105] ln(F)=α+k v ln(f)+k n ln(n)

[0106] The finite element model numerical simulation data is used to determine the constants in the formula and obtain α = 7.9694, k v =0.727257, k n =-0.783481. Finally, the empirical formula is:

[0107] F = exp(7.9694)f 0.727257 n -0.783481

[0108] To further evaluate the effectiveness of the model, mean absolute error (RMSE), root mean square error (MAE), and coefficient of determination (R 2 ) and mean absolute percentage error (MAPE) to evaluate the grinding mechanics model.

[0109] For the specific mean absolute error, see the formula:

[0110]

[0111] The specific root mean square error is shown in the formula:

[0112]

[0113] For the specific coefficient of determination, see the formula:

[0114]

[0115] Specific mean absolute percentage error

[0116]

[0117] Among them, Fi is the actual value of the ith observation, is the predicted value of the ith observation, is the mean of the actual observations, and n is the total number of observations.

[0118] As shown in Table 5, the mean absolute error (RMSE), root mean square error (MAE), determination coefficient (R2), and mean absolute percentage error (MAPE) of the grinding force are shown. From the calculation criteria, it is found that the RMSE and MAE are relatively small. In addition, for the output of the model, the MAPE is relatively low. In addition, the determination coefficient is 0.978965, which is close to 1, and the prediction ability of the model is relatively good.

[0119] Further comparison of the predicted values ​​of the grinding mechanical model and the simulated values, such as Fig.12 As shown, the maximum deviation of the grinding force is 5.96%. It is worth noting that a maximum value and a minimum value are removed during the calculation process to ensure the reliability of the numerical value.

[0120] To further analyze the sensitivity of the grinding force, the Sobol analysis method was used to analyze the sensitivity of the grinding force model and verify the contribution of feed speed and spindle speed to the grinding force. Within the input variation range based on the experiment, all input parameters were changed simultaneously and their effects on the output variables were monitored simultaneously, such as Fig.13 It is shown that the feed rate is 79.9% and the spindle speed is 20.1%. It can be concluded that the grinding force is most sensitive to the feed rate. It is worth noting that the results obtained by the Sobol analysis method are related to the range of feed rate and spindle speed. The quantification of this example is based on the range of experimental parameters.

[0121] Further analysis of the safe area of ​​grinding force, such as Fig.14 and Fig.15 As shown, we can see the distribution of the relationship between grinding force, spindle speed and feed speed.

[0122] Table 1 Physical properties of bones

[0123]

[0124] Table 2 Physical properties of spherical grinding heads

[0125]

[0126] Table 3 Main parameters of John-cook material model

[0127]

[0128]

[0129] Table 4 John-cook damage model parameters

[0130]

[0131] Table 5 RMSE, MAE, MAPE and R of grinding force model 2

[0132]

Claims

1. A method for constructing a mechanical model of robot bone grinding, characterized in that: The method comprises: Analyze the process of robotic bone grinding and obtain the mechanical analysis geometric model of robotic bone grinding; Based on the mechanical analysis geometric model, a finite element analysis model of robot bone grinding was established to obtain the influence of the spindle speed and feed speed of the spherical grinding head on the grinding force. Based on the mechanical analysis geometric model and finite element model data, a mechanical model of robot bone grinding was established to obtain the mathematical representation of the grinding force, spindle speed and feed speed.

2. The method according to claim 1, characterized in that Based on the mechanical analysis geometric model, a finite element analysis model of robot bone grinding was established to obtain the influence of the spindle speed and feed speed of the spherical grinding head on the grinding force, including: The process of robot bone grinding was analyzed, and the X-axis, Y-axis and Z-axis of the spherical grinding head were constructed, with the X-axis as the feeding direction, the Y-axis along the spherical grinding head perpendicular to the X-axis, and the Z-axis satisfying the right-hand screw rule and perpendicular to the X-axis and Y-axis; According to the coordinate axis of the robot bone grinding process, the mechanical analysis geometric model of robot bone grinding is constructed. The grinding force F of the spherical grinding head along the X-axis direction is t , Grinding force F of spherical grinding head along Y axis n , the combined force F of the spherical grinding head along the X-axis and Y-axis, the grinding force F of the spherical grinding head along the Y-axis n The angle θ with the resultant force F, the spindle speed n of the spherical grinding head, the feed speed f of the spherical grinding head, the contact area A between the spherical grinding head and the bone, the depth h of the spherical grinding head into the bone c , the radius r of the spherical grinding head; According to the mechanical analysis geometric model of robot bone grinding, the solid geometric model of the spherical grinding head and the bone is constructed using 3D modeling software, and the generated model is imported into the finite element simulation software. In the assembly, the relative position of the bone model and the spherical grinding head is set; According to the material essential properties of the bone model and the spherical grinding head, the material properties and constitutive model of the bone model and the spherical grinding head are constructed; According to the geometry and stress state of the simulation model, a multi-density grid structure of the bone model and the spherical grinding head is constructed; According to the actual bone grinding state, the interaction between the bone model and the spherical grinding head is constructed, and the grinding contact constraints of the spherical grinding head and the bone model are set respectively. The spherical grinding head is simplified into a rigid body with a reference point (RP); the bottom surface of the bone model is constrained and fixed to realize the modeling of the actual scene of robot bone grinding. According to the above conditions, explicit dynamics is used to analyze the complex dynamic behavior of the spherical grinding head and bone. t (X-axis grinding force) and grinding force perpendicular to the feed direction F n (Y-axis grinding force). The results show that the grinding force decreases with the increase of the spindle speed of the robot spherical grinding head; the grinding force increases with the increase of the feed speed of the robot spherical grinding head. According to the above finite element analysis model, the grinding force data are collected under different spindle speeds and different feed speeds to provide sufficient experimental data.

3. The method according to claim 1, characterized in that Based on the mechanical analysis geometric model and finite element analysis model data, a mechanical model of robot bone grinding is constructed to obtain the mathematical representation between the grinding force and the spindle speed and feed speed, including: According to the mechanical analysis model of robot bone grinding, the X-axis grinding force F is obtained. t and Y-axis grinding force F n for: Where F is the X-axis grinding force F t and Y-axis grinding force F n The resultant force of θ is the resultant force F and the Y-axis grinding force F n Angle. Based on Y-axis grinding force F n The influencing factors include three parts: tool characteristics, bone density, and instantaneous volume of material removal, which can be expressed as: Among them, γ n represents the correction parameter, ρ represents the bone density, V represents the instantaneous volume of bone removal, k ρ and k v Indicates the influencing factors of ρ and V; since the grinding depth is less than the radius of the spherical grinding head, A=πrh c , where h c Represents the thickness of grinding. Under the motion conditions of the spherical grinding head spindle speed n and feed speed f, the instantaneous volume of bone removed V = λVnf = λπrh c nf. Therefore, the X-axis grinding force F t It can be expressed as: Therefore, the resultant force F can be expressed as: According to the mathematical representation of the grinding force, spindle speed, and feed speed and the finite element analysis model data, the influencing factor γ of the mechanical model affecting robot bone grinding is obtained. n , k ρ , k v , which will serve as the basis for the optimization and control of motion parameters in robotic bone grinding.

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