Method for analyzing machining precision of machine tool by considering bolt performance degradation of hole position error

Abstract

The invention discloses a method for analyzing the machining precision of a machine tool by bolt performance degradation in consideration of hole position errors, which considers the influence of manufacturing hole position errors on the rigidity of a bolted part for the first time. The method comprises the following steps: firstly, extracting normal and tangential contact rigidities of a joint surface under the conditions of different hole position errors, fractal parameters and pre-tightening forces by utilizing an abaqus finite element method to obtain a data set; and then, taking the hole position error, the fractal parameter and the pre-tightening force as input vectors, taking the joint surface rigidity as an output vector, and training data by utilizing a BP neural network to complete rigidity prediction. And finally, establishing a dynamic model of the gantry machine tool based on a multi-body system transfer matrix method so as to explore the influence of performance degradation of the bolts on the machining precision of the machine tool, and providing technical guidance for optimization of the bolt joint surfaces in engineering.

Description

Technical Field

[0001] This invention relates to the fields of bolt connection surface performance analysis and machine tool dynamics research, specifically to a research method for considering the impact of bolt performance degradation on machine tool machining accuracy based on hole position errors. Background Technology

[0002] Machine tools contain numerous bolted connections. Due to their discontinuous structural characteristics and susceptibility to degradation caused by creep, fretting wear, and other factors, these connections inevitably become weak points in the overall machine. Furthermore, according to relevant literature, the stiffness of bolted joint surfaces accounts for 60% of the total stiffness of a machine tool, indicating that the performance of these surfaces significantly impacts the machine's dynamic response and even machining accuracy. Therefore, investigating the performance degradation of various bolted joint surfaces and their influence on tool tip vibration and overall machine accuracy is crucial for improving bolt arrangement and assembly processes to enhance the machine tool's accuracy retention.

[0003] Currently, to address issues such as bolt performance degradation, domestic and international scholars have explored the influence of factors such as surface morphology and preload magnitude on bolt joint surface performance using the bolt joint surface stiffness index. However, they often overlook the factor of manufacturing hole position deviation. If there is a certain error in the bolt hole center distance, it may lead to uneven preload or local gaps during assembly, changing the contact pressure distribution of the joint surface, thereby reducing the effective contact area and weakening the stiffness. Therefore, this invention proposes an improvement. First, bolt connection examples with different parameters are established and finite element analysis is performed to extract bolt stiffness. Then, a BP neural network is used to analyze the hole distance error σ, fractal dimension D, fractal roughness G, and preload magnitude F. n A predictive model for the stiffness of bolted joint surfaces was constructed based on factors such as these. Finally, a dynamic model of the gantry milling machine was established using the multibody system transfer matrix method to explore the influence of bolt performance degradation at each joint surface on the machine tool's dynamic response and machining accuracy. Summary of the Invention

[0004] The purpose of this invention is to propose a research method for studying the impact of bolt performance degradation considering hole position errors on machine tool machining accuracy. A bolt joint surface stiffness model considering bolt hole position errors based on finite element method and BP neural network, and a gantry milling machine dynamic model including joint surface contact stiffness based on multibody system transfer matrix method, are established to explore the impact of bolt performance degradation at various joint surfaces on machine tool machining accuracy, providing technical guidance for bolt joint surface optimization in engineering.

[0005] The specific solution adopted in this invention is as follows:

[0006] Step 1: Use SolidWorks to randomly generate the hole spacing error σ, fractal dimension D, fractal roughness G, and bolt preload F for the same friction coefficient, bolt specifications, and number of bolts. n A solid model of a multi-bolted connection was created, and finite element static analysis was performed using Abaqus to extract the normal stiffness Kn and tangential stiffness Kt.

[0007] Step 2: Using fractal dimension D, fractal roughness G, hole spacing error σ, and bolt preload F... n The input vector is the normal contact stiffness Kn and the tangential contact stiffness Kt calculated by finite element analysis. The data is divided into training and test sample sets. The data of the training sample set is used to train the BP neural network and adjust its network parameters. After training, the training and test data are used to verify the accuracy of the BP neural network.

[0008] Step 3: Use the multibody system transfer matrix method to perform dynamic modeling of the gantry milling machine, calculate the expression between the stiffness of each bolted joint surface and the dynamic response of the tool tip; investigate the influence of each input factor in the neural network in the previous step on the displacement and acceleration response of the tool tip.

[0009] Step one specifically involves:

[0010] Based on the structure of each bolted part of the gantry milling machine, a three-dimensional model of it is constructed (with multiple hole spacing errors set for one hole). The topographic point cloud map under the given D and G parameters is generated using MATLAB and applied to the two contact surfaces in the three-dimensional model.

[0011] Import a 3D model into Abaqus, establish a static analysis step, and enable nodal forces and nodal displacements in the field output.

[0012] In the Interaction module, set the contact relationships between each contact surface, setting normal contact as hard contact and tangential contact as a penalty function calculation method.

[0013] In the Load module, apply bolt preload F to all bolts. n Submit your assignment and solve it.

[0014] Extract all nodal forces and displacements of all nodes on the contact surface from the results file, and calculate the normal and tangential stiffness of the joint surface using equation (1):

[0015]

[0016] Repeat the above steps to calculate the hole spacing error σ, fractal dimension D, fractal roughness G, and bolt preload F for different hole spacings. n The normal contact stiffness Kn and tangential contact stiffness Kt under the given conditions.

[0017] Step two specifically involves:

[0018] Construct a BP neural network, selecting hole spacing error σ, fractal dimension D, fractal roughness G, and bolt preload F as the parameters. n The normal stiffness Kn and tangential stiffness Kt of the bolted joint surface are set as input variables, while the output variables are set as output variables.

[0019] The structural parameters of the BP neural network were determined, and an appropriate number of hidden layers and neurons per layer were selected. After actual debugging, a network architecture with one hidden layer and 15 nodes was adopted.

[0020] The logarithmic sigmoid function is chosen as the activation function from the input layer to the hidden layer, and the Purelin function is chosen as the activation function from the hidden layer to the output layer.

[0021] The sample set from step one is divided into a training sample set and a test sample set. The network is then used to iterate the weight vector and threshold using the training sample set. After training, the relationship between the predicted and true values ​​in the training set and the predicted and true values ​​in the test set is verified. The prediction accuracy is evaluated by comparing the test results in the two sets.

[0022] Step three specifically involves:

[0023] Based on the overall shape of the gantry milling machine, construct a simplified diagram and topology of the gantry milling machine system dynamics model.

[0024] Based on the shapes of the components of the gantry milling machine and the criteria for determining the types of multibody system transfer matrix, each component is assigned as an EB beam, a concentrated mass block, and a spring (bolted joint).

[0025] Determine the required dimensional parameters for each component, including material parameters, dimensional parameters for each EB beam and concentrated mass block, and the anisotropic stiffness of the springs.

[0026] Based on the transfer matrix method for multibody systems, each parameter is substituted into a transfer matrix according to the transfer matrices of various components.

[0027] Based on the dynamic topology diagram of the gantry milling machine, its transfer equations are derived and transformed into equilibrium equations as shown in equation (2):

[0028] U all Z all =0 (2)

[0029] The determinant value of the total transfer matrix U all =0, and the multi-order natural frequencies and their state vectors (i.e. mode shapes) of the system can be obtained by using the stepwise search method and the bisection method.

[0030] The volume dynamics equation corresponding to the main spindle component is shown in equation (3):

[0031]

[0032] In the formula, M i C i ,K i The mass, damping, and stiffness matrix of the i-th individual element, f i It is the external force vector corresponding to the i-th individual element, which is the cutting force for the spindle. i This is the dynamic response of the i-th component. For the EB beam, v i =x i ,y i ,z i ,θ xi ] T For a lumped mass block, v i =x i ,y i ,z i ,θ xi ,θ yi ,θ zi ] T .

[0033] The typical machining process of a gantry milling machine was simulated using the Abaqus dynamics module, and the three-dimensional cutting force of the cutting process was extracted as the external force vector of the spindle element.

[0034] Solving equation (3) yields the displacement and acceleration responses at the tool tip, as shown in equations (4) and (5):

[0035]

[0036] In the formula, ω d,p It is the p-th order damped natural frequency of the entire machine. f p (τ) is the modal external force, f p (τ)= <f,V p >

[0037] By applying operations such as loosening the bolt preload and increasing the hole position error to various bolt joints in a gantry milling machine, the influence of bolt performance degradation at different mating surfaces on the machine tool tip response and machining accuracy was investigated. Weak mating surfaces were identified and optimized accordingly. Attached Figure Description

[0038] The specific embodiments of the present invention will be further described in detail below with reference to the accompanying drawings, wherein:

[0039] Figure 1 This is a flowchart of the technical solution of the present invention.

[0040] Figure 2 a and Figure 2 b represents a rough surface model created using point clouds imported from MATLAB, and a bolt joint model containing a rough surface.

[0041] Figure 3 It is a diagram of all nodal forces and nodal displacements on the mating surface extracted by Abaqus.

[0042] Figure 4 This is a schematic diagram of the BP neural network model construction.

[0043] Figure 5 This is the relative error result of the predicted normal stiffness value from the BP neural network.

[0044] Figure 6 A is a diagram of the dynamic model of a gantry milling machine based on the multibody system transfer matrix method; b is a simplified diagram of the dynamic model of the gantry milling machine based on the multibody system transfer matrix method.

[0045] Figure 7 This is an Abaqus simulation diagram of a typical machining process for a gantry milling machine.

[0046] Figure 8 The diagram shows the effect of the relaxation of the preload at the bed-column joint surface on the tool tip response and machining accuracy. Detailed Implementation

[0047] The present invention will be described in detail below with reference to the accompanying drawings and embodiments:

[0048] A finite element method for calculating the dynamic characteristics of machine tools based on parametric modeling of bolted joint surfaces, the specific implementation of which includes the following steps:

[0049] Step 1: Use SolidWorks to randomly generate the hole spacing error σ, fractal dimension D, fractal roughness G, and bolt preload F for the same friction coefficient, bolt specifications, and number of bolts. n A solid model of a multi-bolted connection was created, and finite element static analysis was performed using Abaqus to extract the normal stiffness Kn and tangential stiffness Kt.

[0050] Step 2: Using fractal dimension D, fractal roughness G, hole spacing error σ, and bolt preload F... n The input vector is the normal contact stiffness Kn and the tangential contact stiffness Kt calculated by finite element analysis. The data is divided into training and test sample sets. The data of the training sample set is used to train the BP neural network and adjust its network parameters. After training, the training and test data are used to verify the accuracy of the BP neural network.

[0051] Step 3: Model the gantry milling machine using the multibody system transfer matrix method, and calculate the expression between the stiffness of each bolted joint surface and the dynamic response of the tool tip; investigate the influence of each input factor in the neural network on the displacement and acceleration response of the tool tip.

[0052] The specific process is as follows: Figure 1 As shown.

[0053] Step one specifically includes the following steps:

[0054] Based on the structure of each bolted part of the gantry milling machine, construct its three-dimensional model (with multiple hole spacing errors set for one hole), such as Figure 2 The extracted data in b shows the bed-column bolted joint structure. This was generated using MATLAB. Figure 2 The topographic point cloud diagram shown in figure a, given the D and G parameters, is applied to the two contact surfaces in the 3D model.

[0055] Import a 3D model into Abaqus, establish a static analysis step, and enable nodal forces and nodal displacements in the field output.

[0056] In the Interaction module, set the contact relationships between each contact surface, setting normal contact as hard contact and tangential contact as a penalty function calculation method.

[0057] In the Load module, apply bolt preload F to all bolts. n Submit your assignment and solve it.

[0058] like Figure 3 As shown, the displacements and forces of the nodes on the contact surface can be extracted using the query command and saved to the results file. The nodal forces and displacements of all nodes on the contact surface are extracted from the results file, and the normal and tangential stiffness of the mating surface are calculated using equation (1):

[0059]

[0060] Repeat the above steps to calculate the hole spacing error σ, fractal dimension D, fractal roughness G, and bolt preload F for different hole spacings. n The normal contact stiffness Kn and tangential contact stiffness Kt under the given conditions.

[0061] Step two specifically includes the following steps:

[0062] Construct a BP neural network, selecting hole spacing error σ, fractal dimension D, fractal roughness G, and bolt preload F as the parameters. n The input variables are defined as the normal and tangential stiffness of the bolted joint surface, while the output variables are defined as the normal and tangential stiffness of the bolted joint surface. The diagram showing the construction of the bolted joint surface contact stiffness prediction model based on a BP neural network is shown below. Figure 4 As shown.

[0063] The structural parameters of the BP neural network were determined, and an appropriate number of hidden layers and neurons per layer were selected. After actual debugging, a network architecture with one hidden layer and 10 nodes was adopted.

[0064] The logarithmic sigmoid function is chosen as the activation function from the input layer to the hidden layer, and the Purelin function is chosen as the activation function from the hidden layer to the output layer.

[0065] The sample set from step one is divided into a training sample set and a test sample set. The training sample set is used to iterate the weight vector and threshold values. After training, the relationship between the predicted values ​​and the true values ​​on the test set is verified, and the prediction accuracy is evaluated by comparing the test results from the two sets. The comparison results of the normal stiffness test set are as follows: Figure 5 As shown in the figure, the results indicate that the maximum relative error in predicting the contact stiffness of the bolted joint surface is only 2.4%, verifying the accuracy of the model.

[0066] Step three includes the following steps:

[0067] Based on the overall shape of the gantry milling machine, the simplified diagram and topology of the gantry milling machine's mechanical system dynamics model are constructed as follows: Figure 6 As shown in a and b.

[0068] Based on the shapes of the components of the gantry milling machine and the criteria for determining the type of multi-body system transfer matrix, each component is assigned the following designations: EB beam, concentrated mass block, and spring (bolted joint). The assigned numbers and transfer matrix types for each component are shown in Table 1.

[0069] Table 1. Correspondence between component number, name, and transfer matrix type

[0070] Component No. 2 5 7 9 Remaining No. Component Name Connecting beam Main shaft Slide Cross beam Bolted joint Transfer matrix type E-B beam E-B beam Lumped mass Lumped mass Spring Component No. 11,17 13,19 15,21 23 Component Name Column Slide Bed Foundation Transfer matrix type Lumped mass Lumped mass E-B beam Lumped mass

[0071] Determine the required dimensional parameters for each component, including material parameters, dimensional parameters for each EB beam and concentrated mass block, and the anisotropic stiffness of the springs.

[0072] Based on the transfer matrix method for multibody systems, the transfer matrices of various components are used to input each parameter into a transfer matrix. The transfer matrix representing the springs of each bolted joint is shown in equation (2):

[0073]

[0074] In the formula,

[0075] In K i In the matrix, K i,x ,K i,y ,K i,zThe linear stiffness of the hinge in each direction is obtained from the normal and tangential stiffness established in steps one and two, while K... 1,x ',K 1,y ',K 1,z 'The torsional stiffness of the hinge in each direction can be calculated from the linear stiffness, according to the literature.'

[0076]

[0077] The transfer matrices for other types of components can be found in relevant literature.

[0078] Based on the dynamic topology diagram of the gantry milling machine, the transfer matrices are multiplied to derive its transfer equations and transform them into equilibrium equations as shown in equation (4):

[0079] U all Z all =0 (4)

[0080] In the formula, Z all This represents the state vectors of elements 1, 4, 5, and 24, while the system's total transfer matrix U... all The transfer matrix containing all components can be represented as:

[0081]

[0082] The determinant value of the total transfer matrix U all =0, and the multi-order natural frequencies and their state vectors (i.e. mode shapes) of the system can be obtained by using the stepwise search method and the bisection method.

[0083] The volume dynamics equation corresponding to the main spindle component is shown in equation (6):

[0084]

[0085] In the formula, M i C i ,K i The mass, damping, and stiffness matrix of the i-th individual element, f i It is the external force vector corresponding to the i-th individual element, which is the cutting force for the spindle. i This is the dynamic response of the i-th component. For the EB beam, v i =x i ,y i ,z i ,θ xi ] T For a lumped mass block, v i =x i ,y i ,z i ,θ xi ,θyi ,θ zi ] T .

[0086] The typical machining process of a gantry milling machine was simulated using the Abaqus dynamics module, and the three-dimensional cutting forces during the cutting process were extracted as the external force vectors of the spindle components. A schematic diagram of the Abaqus cutting simulation analysis is shown below. Figure 7 As shown.

[0087] Solving equation (4) yields the displacement and acceleration responses at the tool tip, as shown in equations (7) and (8):

[0088]

[0089] In the formula, ω d,p It is the p-th order damped natural frequency of the entire machine. f p (τ) is the modal external force, f p (τ)= <f,V p >

[0090] To verify the effectiveness of the MSTMM method, a 1:1000 scale model of a gantry milling machine was built in the laboratory, and MSTMM, finite element, and modal tests were conducted on it. After processing the test data, a natural frequency comparison table was obtained, as shown in Table 2. The overall natural frequency error is less than 5% and is better than that of the finite element method, which proves its calculation accuracy.

[0091] Table 2 Comparison of Natural Frequencies of Scaled Models (Error 1 is MSTMM and experimental error, Error 2 is FEM and experimental error)

[0092] Method 1st 2nd 3rd 4th 5th 6th 8th Multi-body system transfer matrix method 190.24 236.37 390.58 570.22 919.67 1070.3 1224.8 Finite element 195.64 240.85 393.73 528.16 916.6 1029.1 1211 Modal test 188.5 231.58 378.61 559.79 931.34 1062.2 1235.7 Error 1 (%) 0.92 2.06 3.16 1.86 1.25 0.76 0.88 Error 2 (%) 3.79 4.00 3.99 5.65 1.58 3.19 1.99

[0093] Finally, by applying operations such as loosening the bolt preload and increasing the hole position error to each bolted part in the gantry milling machine, the influence of bolt performance degradation at different mating surfaces on the machine tool tip response and machining accuracy can be investigated, thereby identifying weak mating surfaces and optimizing them. Figure 8 To set the displacement response curve when the preload of the bolts at the bed-column joint surface is relaxed by 10%-30%.

Claims

1. A method for analyzing the machining accuracy of a machine tool considering the degradation of bolt performance due to hole position error, characterized by, Comprise: The solidworks different hole distance error σ, fractal dimension D, fractal roughness G, and bolt pre-tightening force F n The multi-bolt connection entity model is analyzed by using the finite element statics analysis to extract the normal stiffness Kn and the tangential stiffness Kt. With the fractal dimension D, the fractal roughness G, the hole distance error σ and the bolt pre-tightening force F n The normal contact stiffness Kn and the tangential contact stiffness Kt are taken as the output vectors; the BP neural network is trained and the accuracy is verified. The dynamics model of gantry machine tool is established by using the transfer matrix method of multi-body system, and the expression between the stiffness of each bolted joint and the dynamics response of the tool tip is calculated.

2. The method according to claim 1, characterized in that, The solidworks different hole pitch error σ, fractal dimension D, fractal roughness G, bolt pre-tightening force F n The multi-bolt connection entity model is analyzed by using Abaqus for finite element statics to extract the normal stiffness Kn and the tangential stiffness Kt, including: According to the structure of each bolted part of the gantry machine tool, a three-dimensional model is constructed, and multiple hole distance errors are set for one hole. The point cloud graph under given D and G parameters is generated by Matlab and assigned to the two contact surfaces of the three-dimensional model; Abaqus imports the three-dimensional model, establishes a static analysis step, and opens the node force and node displacement in the field output; In the Interaction module, set the contact relationship between each contact surface, set the normal contact as hard contact, and the tangential contact as penalty function calculation method; Applying bolt pretension force F to all bolts in Load module n Submit job for solution; In the result file, extract all node forces and node displacements of the nodes on the contact surface, and calculate the normal and tangential stiffness of the joint surface by formula (1): The error σ, the fractal dimension D, the fractal roughness G and the bolt pre-tightening force F of different hole pitches are calculated repeatedly n The normal contact stiffness Kn and the tangential contact stiffness Kt in the case of 3. The method for analyzing the machining precision of a machine tool considering the performance degradation of bolts due to hole position errors according to claim 1, characterized in that, With the fractal dimension D, the fractal roughness G, the hole distance error σ and the bolt pre-tightening force F n The normal contact stiffness Kn and the tangential contact stiffness Kt are output vectors. Based on BP neural network, the accuracy is verified, including: The BP neural network is constructed, and the hole distance error σ, the fractal dimension D, the fractal roughness G and the bolt pre-tightening force F are selected n The normal stiffness Kn and the tangential stiffness Kt of the bolted joint surface are set as the output variables. Determine the structure parameters of BP neural network, select the appropriate number of hidden layers and the number of neurons in each layer; After actual debugging, a hidden layer network architecture is adopted, and the number of hidden layer nodes is determined as 15; Select the logarithmic Sigmoid function as the activation function from the input layer to the hidden layer, and select the Purelin function as the activation function from the hidden layer to the output layer; Divide the sample set into training sample set and test sample set, and use the training sample set to iterate the weight vector and threshold value. After training, verify the relationship between the predicted value and the true value of the training set and the predicted value and the true value of the test set, and evaluate the prediction accuracy by comparing the test results in the two sets.

4. The method for analyzing the machining precision of a machine tool considering the performance degradation of bolts due to hole position errors according to claim 1, characterized in that, The dynamics model of gantry machine tool is established by using the transfer matrix method of multi-body system, and the expression between the stiffness of each bolted joint and the dynamics response of the tool tip is calculated; Explore the influence of various factors on the displacement and acceleration response of the tool tip, including: According to the overall shape of the gantry machine tool, construct the system dynamics model diagram and topology diagram of the gantry machine tool; According to the shape of each component of the gantry machine tool and the type determination criterion of the transfer matrix method of multi-body system, each component is assigned as E-B beam, concentrated mass block and spring; Determine the size parameters required by each component, including material parameters, size parameters of each E-B beam, concentrated mass block and stiffness of spring in each direction; According to the transfer matrix of each type of element of the multi-body system transfer matrix method, bring each parameter into the transfer matrix; According to the dynamics topology diagram of the gantry machine tool, derive its transfer equation and change it into the equilibrium equation as shown in formula (2): U all Z all = 0 (2) The total transfer matrix determinant value U all = 0, the multi-order natural frequency and its state vector of the system, i.e. the modal vibration mode, are solved by using the step-by-step search method and the dichotomy method. The body dynamics equation corresponding to the spindle element is constructed as shown in formula (3): where M i i i is the mass of the i-th element, and K i i is the i-th element's corresponding external force vector, which is the cutting force for the spindle; v i i i i xi T i i i i xi yi zi T is the i-th element's dynamic response, which is​​​​​​​​​​​​​​​​ Use Abaqus display dynamics module to simulate the typical machining process of gantry machine tool, and extract the three-dimensional cutting force in the cutting process as the external force vector of the spindle element; Solving equation (3), the displacement response and acceleration response of the tool tip point can be obtained as shown in equations (4) and (5): In the formula, ω d,p is the pth order damped natural frequency of the whole machine, f p (τ) is the modal external force, f p (τ) = <f, V p >.

Images