Data and mechanism hybrid driven threaded connection structure pressure-bearing surface friction coefficient prediction method
By combining BP neural network and three-dimensional fractal theory, a mathematical model of the friction coefficient of the bearing surface of the threaded connection structure with the tightening torque was established, which solved the uncertainty problem of preload control, realized high-precision friction coefficient prediction, and improved the rigidity and precision of the mechanical structure.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-12-08
- Publication Date
- 2026-03-27
AI Technical Summary
Existing technologies lack unified process standards for preload control, traditional theoretical models have limited prediction accuracy, and the friction coefficient has significant uncertainty, making it difficult to guarantee the accuracy of threaded connections.
By combining the BP neural network model with three-dimensional fractal theory, a mathematical model of the friction coefficient of the bearing surface with respect to the tightening torque is established. By measuring the microstructure and calculating the fractal parameters, a prediction model is constructed using MATLAB software to improve the prediction accuracy.
It enables accurate prediction of the friction coefficient of threaded connections, improves the accuracy of preload control, and enhances the rigidity and precision of mechanical structures.
Smart Images
Figure CN121744533A_ABST
Abstract
Description
TECHNICAL FIELD
[0001] The application relates to the technical field of mechanical assembly and tribology, and particularly relates to a method for predicting a friction coefficient of a pressure surface of a threaded connection structure based on a data and mechanism hybrid driving. BACKGROUND
[0002] The threaded connection is widely applied in mechanical structures due to its compact structure, convenient disassembly and low cost. In high-end numerical control machine tools, the threaded connection performance of key components (such as a column and a bed) directly determines the rigidity, precision and stability of the whole machine. For example, the "column-bed" joint of a heavy numerical control gantry milling machine relies on multiple high-strength prestressed bolts, and the joint surface is made to generate sufficient friction force through accurate pre-tightening force, so as to resist cutting force and other loads and ensure the precision of the machine tool. Therefore, the control of the bolt pre-tightening force becomes a key technology.
[0003] At present, the pre-tightening operation is mainly performed by using a tightening torque method, but there is a lack of unified process standards, and the method mainly depends on experience. Since the pre-tightening force is affected by multiple factors such as the friction coefficient, and there is complex friction in the tightening process, the traditional theoretical model is limited in prediction accuracy due to the assumption of the contact pressure and the friction radius and other parameters. In order to overcome the theoretical limitations, scholars have studied the influence of factors such as materials and tightening speed on the pre-tightening force through experiments, and it is found that the friction coefficient has significant uncertainty.
[0004] Therefore, the application provides a method driven by data and theory, which is used for predicting the friction coefficient of the pressure surface of the threaded connection, so as to improve the accuracy of the pre-tightening force control. SUMMARY
[0005] The application aims to provide a method for predicting the friction coefficient of the pressure surface of the threaded connection structure based on data and mechanism hybrid driving in the field of mechanical assembly, so as to solve the problem of the precision requirement of the threaded connection.
[0006] The method for predicting the friction coefficient of the pressure surface of the threaded connection structure based on data and mechanism hybrid driving combines a BP neural network model and a three-dimensional fractal theory model to establish a mathematical model of the friction coefficient of the pressure surface with the tightening torque.
[0007] The method for predicting the friction coefficient of the pressure surface of the threaded connection structure based on data and mechanism hybrid driving has the following specific steps:
[0008] S10, a mapping model of the friction coefficient of the pressure surface, the fractal dimension D(T) and the scale coefficient G(T) is established based on the three-dimensional fractal theory, wherein T represents the tightening torque;
[0009] S101, a friction coefficient model is established based on the three-dimensional fractal theory and by considering the domain expansion factor and the elastic-plastic deformation of the microconvex body, and the friction coefficient is a function expression related to the fractal parameters and is shown in the following formula: Q = P tan φ (1) Qe = P tan φe (2) Qep = P tan φep (3) Pe = P cos φe (4) Pep = P cos φep (5) Pp = P cos φp (6) where φe < φep < φp, the formula can be expressed as: where φe < φp < φep, the formula can be expressed as: where φe < φp < φep, the formula can be expressed as: where φe < φp < φep, the formula can be expressed as: where D(T) and G(T) are fractal parameters, —spectrum density size parameter, —equivalent elastic modulus, —single micro-convex body theoretical contact area, —single micro-convex body elastic deformation and elastic-plastic deformation critical load area, —single micro-convex body elastic deformation and plastic deformation critical load area, —domain expansion factor, , —material properties and joint surface type parameter correlation coefficient, is the critical load area of the joint surface between the first elastic-plastic deformation and the second elastic-plastic deformation, is the critical load area of the joint surface between the second elastic-plastic deformation and plastic deformation.
[0010] S102 When the connected parts and bolt specifications are known, the material parameters are fixed values, and then the above formula is simplified to express the related function of the friction coefficient with fractal parameters D(T) and G(T) as shown in the following formula:
[0011]
[0012] S20 Measure the micro-morphology of the pressure surface under different tightening torques, and calculate the fractal parameters D(T i ) and G(T i ) by using the structure function method, where T i represents the tightening torque corresponding to different experimental groups;
[0013] S201 Apply different torques to the experimental group bolts with constant tightening speed;
[0014] S202 Use a three-dimensional topography instrument to observe the rough surface of the bolted joint interface, and obtain the micro-morphology diagram and surface morphology data of the bearing surface under different tightening torques;
[0015] S203 After measuring the morphology of the rough surface by the three-dimensional topography instrument, calculate the fractal parameters using the structure function method.
[0016] S204 Process the obtained data by Ultra to obtain the profile curve of the bolted joint interface rough surface and export the data as a TXT file;
[0017] S205 Linearly fit the exported data in MATLAB using the structure function method to obtain the fractal parameters D(T i ) and G(T i ) of the tightened bearing surface.
[0018] S30 Use MATLAB software to construct a BP neural network prediction model, with initial fractal parameters D0 and G0 and tightening torque as input, and output fractal parameters.
[0019] S301 constructs vectors and as input and output mode references to train the set BP neural network.
[0020] S302 The trained BP neural network predicts the test data and compares the predicted value with the experimental value to verify the accuracy of the neural network.
[0021] S40 Substitute the fractal parameter-torque equation into the bearing surface friction coefficient theoretical model to establish a mathematical model of its change with tightening torque.
[0022] S401 Substitute the initial fractal parameters , and the tightening torque T into the neural network model trained in S30 to obtain the corresponding predicted fractal parameters D i , G i as shown in the following formula:
[0023]
[0024] S402 Substitute the predicted fractal parameters into the friction coefficient calculation formula to obtain the predicted model of the bearing surface friction coefficient with tightening torque, as shown in the following formula:
[0025]
[0026] S403 selecting the experimental group to predict the mathematical model, and obtaining the predicted value of the pressure-bearing surface friction coefficient The pressure-bearing surface friction coefficient obtained by the experiment is compared with the predicted value to verify the accuracy of the model.
[0027] The beneficial effects of the technical solutions provided by the application are as follows: a thread connection structure pressure-bearing surface friction coefficient prediction method based on data and mechanism hybrid driving is provided, which simplifies the relatively complex friction coefficient influencing factors into a mathematical model of friction coefficient changing with tightening torque, facilitates the prediction process of the friction coefficient, and improves the prediction accuracy. BRIEF DESCRIPTION OF DRAWINGS
[0028] Figure 1 The friction coefficient changes with the tightening torque prediction model establishment method flowchart
[0029] Figure 2 The pressure-bearing surface micro-morphology under different tightening torques
[0030] Figure 3 The fractal dimension of the pressure-bearing surface under the action of different tightening torques
[0031] Figure 4 The scale coefficient of the pressure-bearing surface under the action of different tightening torques
[0032] Figure 5 The BP network training effect
[0033] Figure 6 The test value and the predicted value are compared
[0034] Figure 7 The relative error of the BP network predicted value DETAILED DESCRIPTION
[0035] The technical solutions in the embodiments of the application will be described in detail below with reference to the friction coefficient changes with the tightening torque prediction model establishment method flowchart shown in the accompanying drawings. It should be understood that the specific embodiments described herein are only used to explain the application and not to limit the application. Based on the embodiments in the application, other embodiments obtained by those skilled in the art without creative labor are within the scope of the application. Figure 1 The friction coefficient changes with the tightening torque prediction model establishment method flowchart shown in the accompanying drawings.
[0036] The friction coefficient changes with the tightening torque prediction model establishment method flowchart shown in the accompanying drawings.
[0037] S10, a pressure-bearing surface friction coefficient and fractal dimension D(T) and scale coefficient G(T) mapping model is established based on three-dimensional fractal theory, wherein T represents the tightening torque;
[0038] S101 Based on three-dimensional fractal theory, the domain expansion factor and the elastic-plastic deformation of micro-convex body are considered to establish the friction coefficient model and get the verification. The friction coefficient is a function related to the fractal parameters, and the expression is as follows: (In the formula, Q is the tangential load, P is the normal load, is the tangential load generated by the elastic deformation micro-convex body, is the tangential load generated by the elastic-plastic deformation micro-convex body, is the normal load borne by the elastic deformation micro-convex body, is the normal load borne by the elastic-plastic deformation micro-convex body, is the normal load borne by the plastic deformation micro-convex body) When , the formula can be expressed as: When , the formula can be expressed as: When , the formula can be expressed as: When , the formula can be expressed as: Where D(T) and G(T) are fractal parameters, —spectrum density size parameter, —equivalent elastic modulus, —theoretical contact area of a single micro-convex body, —critical load area of a single micro-convex body elastic deformation and elastic-plastic deformation, —critical load area of a single micro-convex body elastic deformation and plastic deformation, —domain expansion factor, , —material properties and related coefficients of joint surface fractal parameters, is the critical load area of the joint surface between the first stage of elastic-plastic deformation and the second stage of elastic-plastic deformation, is the critical load area of the joint surface between the second stage of elastic-plastic deformation and plastic deformation.
[0039] S102 When the connected parts and bolt specifications are known and the material parameters are fixed values, the above formula is simplified to get the related function of the friction coefficient represented by the fractal parameters D(T) and G(T) as follows:
[0040]
[0041] S20 Measure the micro-morphology of the pressure surface under different tightening torques, and calculate the fractal parameters D(T)i ) and G(T i ), wherein T i represents the tightening torque corresponding to different experimental groups;
[0042] S201, a constant tightening speed of 20 rpm is taken, no lubrication treatment is performed, and no gasket is used. Seven identical connected parts are selected, one connected part in each experimental group is fixed on the test device, one hole corresponds to one pre-tightening process, a pre-tightening torque of 1 Nm is applied to the first bolt, and the torque applied to each subsequent bolt is increased by 1 Nm until 12 Nm.
[0043] S202, the rough surface of the bolted joint interface in the seventh experimental group is observed by a three-dimensional morphology instrument, and the micro-morphology diagram and surface morphology data of the pressure-bearing surface under different tightening torques are obtained, as shown in Figure 2 .
[0044] 203, after the morphology of the rough surface is measured by the three-dimensional morphology instrument, the fractal parameters are calculated by using the structure function method.
[0045] S204, the obtained data is processed by Ultra to obtain the profile curve of the rough surface of the bolted joint interface, and the data is exported as a TXT file.
[0046] S205, the exported data is linearly fitted in MATLAB by using the structure function method, and then the fractal parameters D(T i ) and G(T i ) of the tightened pressure-bearing surface are obtained, as shown in Figure 3 , Figure 4 .
[0047] Step S30, a BP neural network prediction model is constructed by using MATLAB software, the initial fractal parameters D0 and G0 and the tightening torque are taken as inputs, and the fractal parameters are output.
[0048] S301, vectors and are constructed as input and output mode references to train the set BP neural network.
[0049] In the training, 12 data points are selected from the 7 groups of experimental data of S20 as sample data, and a total of 84 groups of sample data are obtained. The 84 groups of sample data are divided into two parts, 12 groups are randomly selected as a test sample set, and the remaining 72 groups are used as a training sample set.
[0050] In the training process of the BP neural network, the data is normalized to the interval [0, 1]. The network structure is set to double hidden layers (the first and second hidden layers are 20 nodes and 5 nodes respectively), the LM algorithm is used for training, the upper limit of the training times is 500, and the error tolerance is 10⁻5 , training effect see Figure 5 . Figure 5 When the number of training reaches 271 times, the error tolerance is reached, the training is stopped, and the time consumption is 4 seconds.
[0051] S302 uses the trained BP neural network to predict 12 sets of test data and compares the predicted values with the experimental values, and the comparison effect is shown in Figure 6 ;
[0052] Figure 7 The relative error curve of the predicted values of the BP network model and the experimental values is shown in Figure 7 The relative error of the 12 sets of test data is less than 10%, indicating that the calculated values of the method are similar to the experimental values.
[0053] S40 substitutes the fractal parameter-torque equation into the theoretical model of the friction coefficient of the pressure surface to establish a mathematical model of its change with the tightening torque.
[0054] S401 substitutes the initial fractal parameters , and the tightening torque T into the neural network model trained in S30 to obtain the corresponding predicted fractal parameters D i , G i , as shown in the following formula:
[0055]
[0056] S402 substitutes the predicted fractal parameters into the friction coefficient calculation formula to obtain the predicted model of the friction coefficient of the pressure surface with the tightening torque, i.e., the mathematical model of the friction coefficient of the pressure surface with the tightening torque, as shown in the following formula:
[0057]
[0058] S403 selects 5 sets of experiments, predicts through the mathematical model, the input quantity , the output quantity , the predicted value of the friction coefficient of the pressure surface , and compares with the experimental results , the relative errors are 8.62%, 7.59%, 6.47%, 7.48%, and 6.96% respectively. The errors are all within 10%, indicating that the calculated values of the method are similar to the experimental values.
Claims
1. A method for predicting the friction coefficient of the bearing surface of a threaded connection structure driven by a combination of data and mechanism, characterized in that, Includes the following steps: S10 establishes a mapping model between the friction coefficient of the bearing surface and the fractal dimension D(T) and scale coefficient G(T) based on three-dimensional fractal theory, where T represents the tightening torque; S20 was used to measure the microstructure of the bearing surface under different tightening torques, and the fractal parameter D(T) was calculated using the structure function method. i ) and G(T i ), where T i This indicates the tightening torque corresponding to different experimental groups; S30 uses MATLAB software to build a BP neural network prediction model, taking the initial fractal parameters D0 and G0 and the tightening torque as inputs, and outputting the fractal parameters D(T) and G(T); S40 substitutes the fractal parameter-torque equation into the theoretical model of the friction coefficient of the bearing surface to establish a mathematical model of its variation with tightening torque.
2. The method for predicting the friction coefficient of the bearing surface of a threaded connection structure driven by a combination of data and mechanism, as described in claim 1, is characterized in that... Step S10 includes the following steps: Based on three-dimensional fractal theory, considering the domain expansion factor and the elastoplastic deformation of micro-convex bodies, S101 establishes a friction coefficient model, where the friction coefficient is a function related to the fractal parameters, as shown in the following equation: In the formula, Q is the tangential load and P is the normal load. The tangential load is generated by the elastically deformable micro-protrusion. The tangential load generated by the elastoplastic deformation micro-protrusion. The normal load borne by the elastically deformable micro-protrusion. The normal load borne by the elastoplastic deformable micro-protrusion. The normal load borne by the plastically deformable micro-protrusion; Among them when When, the formula is expressed as: ;when When, the formula is expressed as: ;when When, the formula is expressed as: ； when When, the formula is expressed as: Where D(T) and G(T) are fractal parameters, For spectral density size parameters, For the equivalent elastic modulus, This represents the maximum contact area of the micro-protrusion. This represents the theoretical contact area of a single micro-protrusion. This represents the critical load area for elastic and elastoplastic deformation of a single micro-protrusion. This represents the critical load area for the elastic and plastic deformation of a single micro-protrusion. For the domain expansion factor, , The correlation coefficient between material properties and bonding surface parting parameters. The Poisson's ratio of the material, The boundary load area is the interface between the first and second stages of elastic-plastic deformation. The boundary load area is the interface between the two-stage elastic-plastic deformation and plastic deformation. Given the specifications of the connected parts and bolts, S102 assumes fixed material parameters. Simplifying the above equation yields a function representing the friction coefficient using fractal parameters D(T) and G(T), i.e. 。 3. The method for predicting the friction coefficient of the bearing surface of a threaded connection structure driven by a combination of data and mechanism, as described in claim 1 or 2, is characterized in that... Step S20, the bolt tightening test, and obtaining fractal parameter data, includes the following steps: S201 applies different torques to the bolts in the experimental group using a constant tightening speed; S202 used a three-dimensional morphology instrument to observe the morphology of the rough surface of the bolted joint in the experimental group, and obtained the micro morphology diagram and surface morphology data of the bearing surface under different tightening torques. After S203 measured the morphology of the rough surface using a three-dimensional profilometer, it used the structure function method to calculate the fractal parameters. S204 processes the obtained data using Ultra to obtain the rough surface profile curve of the bolted joint surface and exports the data as a TXT file; S205 uses the structure function method in MATLAB to perform linear fitting on the exported data, thereby obtaining the fractal parameter D(T) of the bearing surface after tightening. i ) and G(T i ).
4. The method for predicting the friction coefficient of the bearing surface of a threaded connection structure driven by a combination of data and mechanism, as described in claim 1, is characterized in that... Step S30 includes the following steps: S301 Construct Vector and vectors The pre-configured BP neural network is trained using these as input and output pattern references respectively. S302 uses the trained BP neural network to predict test data and compares the predicted values with the experimental values to verify the accuracy of the neural network.
5. The method for predicting the friction coefficient of the bearing surface of a threaded connection structure driven by a combination of data and mechanism, as described in claim 1, is characterized in that... Step S40 includes the following steps: S401 sets the initial fractal parameters , The tightening torque T is then substituted into the trained neural network model in S30 to obtain the corresponding predicted fractal parameters D. i G i ,Right now ； S402 substitutes the predicted fractal parameters into the friction coefficient calculation formula to obtain a predicted model of the friction coefficient of the bearing surface as a function of tightening torque, i.e. ； S403 selected the experimental group to predict the mathematical model, and obtained the predicted value of the friction coefficient of the bearing surface. Friction coefficient of the bearing surface obtained from the test The model was compared to the others to verify its accuracy.