A rough interface dynamic friction coefficient calculation method based on transient finite element

Abstract

This invention discloses a method for calculating the dynamic friction coefficient of a rough interface based on transient finite element method, belonging to the field of gear meshing interface friction and wear technology. The method first determines the calculation point on the gear tooth surface, extracts parameters such as load, sliding speed, roughness, and radius of curvature from the overall meshing transient simulation, establishes a local transient finite element model containing the rough morphology, and performs simulation. It then extracts the time-domain data of normal pressure and tangential friction resistance, calculates the transient friction coefficient through programming, and obtains the effective dynamic friction coefficient by taking the root mean square value. This invention fully considers the coupling effects of transient load, motion, vibration, and deformation in gear meshing, overcomes the limitations of experimental conditions, has high calculation accuracy, and a wide range of applications, providing reliable data for gear transmission efficiency analysis, power consumption calculation, and optimization design.

Description

Technical Field

[0001] This invention relates to the field of gear meshing interface friction and wear technology, specifically to a method for calculating the dynamic friction coefficient of a rough interface based on transient finite element method. Background Technology

[0002] In gear transmission systems, the tooth surface friction coefficient is a key parameter affecting transmission efficiency, power consumption, and heat generation characteristics. Existing research indicates that during gear meshing, the meshing force is borne jointly by the oil film and the micro-protrusions caused by the tooth surface roughness. Therefore, the total tooth surface friction is composed of two friction components with distinctly different mechanisms: one is the viscous shear friction of the oil film under the elastohydrodynamic lubrication interface, and the other is the contact collision of micro-protrusions induced by the relative motion of micro-roughness peaks in the tooth surface roughness interface. Based on this core friction mechanism, the academic community has developed a series of semi-empirical prediction models for the tooth surface friction coefficient based on simplified contact tests such as double-disc and ball-disc. Among them, the determination of the contact friction coefficient component of the tooth surface roughness interface usually relies on multiple regression analysis or nonlinear fitting methods based on classical experimental data.

[0003] However, the dynamic evolution of the friction coefficient of the rough tooth surface is strongly influenced by multiple factors such as meshing motion state, load distribution characteristics, material constitutive properties, surface topology, and lubrication state. This leads to significant limitations in existing calculation methods based on classical experiments: First, it is difficult to reproduce the coupling effects of transient load fluctuations, transient motion conditions, transient vibrations, and deformations during actual gear meshing, resulting in insufficient transient adaptability of the obtained friction coefficient data to real working conditions and limited calculation accuracy. Second, the rotational speed range, load level, and lubrication condition control of the experimental device have inherent physical boundaries, and different researchers have significant differences in the design of experimental schemes such as specimen material selection, surface treatment process, and lubrication medium. This results in a lack of unified standards for the applicable boundaries and parameter ranges of the obtained models and results, making it difficult to achieve universal promotion across working conditions and scenarios.

[0004] In summary, existing methods for calculating the friction coefficient of tooth surface roughness are limited by the differences in test schemes, the simplification of test devices, the limitations of working condition coverage, and the neglect of dynamic coupling effects. Their calculation accuracy and applicability are no longer able to meet the technical requirements of modern gear transmission systems that are developing towards high speed, heavy load, precision, standardization, and long service life. Summary of the Invention

[0005] In view of this, the present invention provides a method for calculating the dynamic friction coefficient of a rough interface based on transient finite element method. It establishes a local rough interface model based on transient simulation of the overall gear meshing, and accurately obtains the dynamic friction coefficient through transient simulation and time domain data processing, which is suitable for real meshing conditions.

[0006] To achieve the above objectives, the present invention provides the following technical solution:

[0007] A method for calculating the dynamic friction coefficient of a rough interface based on transient finite element method is proposed. This method establishes a local model of gear meshing at the point to be calculated based on transient simulation results of gear meshing and performs simulation. The time-varying contact force in the simulation results is processed through software programming, ultimately obtaining the dynamic friction coefficient of the rough interface of gear meshing based on transient simulation of gear meshing. The method includes the following steps:

[0008] Step 1: Determine the location of the point where the friction coefficient of the contact interface of the gear meshing is to be calculated;

[0009] Step 2: Obtain the load conditions and morphological characteristics of the point where the friction coefficient is to be calculated;

[0010] Step 3: Establish a local transient finite element model of the contact interface at the point to be calculated and perform simulation;

[0011] Step 4: Extract the time-domain variation curves of contact forces representing normal pressure and frictional resistance from the transient simulation analysis results and export the data file;

[0012] Step 5: Based on the friction coefficient calculation formula, the time-domain data of normal pressure and tangential friction resistance are processed by programming to obtain the dynamic friction coefficient of the tooth surface rough interface.

[0013] Furthermore, in step 1, based on the existing transient simulation analysis results of gear meshing, the positions of the tooth surface units involved in meshing are locked, and the position of the friction coefficient calculation point along the tooth profile is determined.

[0014] Furthermore, in step 2, based on the transient simulation results of gear meshing, the linear load and relative sliding speed at the point where the friction coefficient is to be calculated are extracted. Combined with the surface roughness and geometric parameters of the gear teeth in the gear model, the roughness and radius of curvature of that point are obtained.

[0015] Furthermore, in step 3, based on the obtained radius of curvature, roughness, contact line load, and relative sliding speed of the point to be calculated, a local finite element model of the contact interface with rough morphology during meshing is established, and sliding simulation calculation of the surface contact interface is carried out.

[0016] Further, in step 4, the transient simulation analysis result file of the gear meshing local model is opened in the post-processing software, and the time-varying contact force curves representing tangential frictional resistance and normal pressure along the contact surface of the local model are extracted respectively, and the effective time period data in the curves are exported. The effective time period data refers to the stable stage curve data of the local model when it experiences the rough surface during the simulation process.

[0017] Furthermore, in step 5, the data file of the contact force time-domain variation curve is processed by programming to obtain the time-varying data matrix of the tangential resistance and normal pressure at the point to be calculated, thereby calculating the time-varying matrix of the transient sliding friction coefficient, and taking its root mean square value as the final effective sliding friction coefficient.

[0018] Furthermore, the formula for calculating the transient sliding friction coefficient is as follows:

[0019]

[0020] In the formula, The transient sliding friction coefficient; Transient sliding friction that hinders motion, This is the transient normal pressure.

[0021] Furthermore, the formula for calculating the root mean square value is as follows:

[0022]

[0023] In the formula, RMS root mean square value, Let be the transient friction coefficient at a certain moment, and n be the number of transient friction coefficients in the series.

[0024] The beneficial effects of this invention are as follows:

[0025] Compared to existing methods that are "limited by differences in test schemes, simplification of test equipment, limitations in working condition coverage, and neglect of dynamic coupling effects, thus affecting the accuracy and applicability of calculations," this invention is both economical and efficient. It is also applicable to various working conditions and has a wide range of practical applications. Furthermore, by comprehensively considering the instantaneous effects of gear meshing instantaneous curvature radius, roughness, relative sliding speed, linear load, and vibration deformation caused by roughness peak collisions, it effectively improves the accuracy of the dynamic friction coefficient calculation results for the roughness interface of the gear teeth.

[0026] This invention can be widely applied to gear transmission research in aerospace, transportation, and engineering machinery equipment, providing real and reliable dynamic friction coefficient data of the tooth surface roughness interface for gear elastohydrodynamic lubrication analysis, power consumption calculation, and optimization design.

[0027] Other advantages, objectives, and features of the invention will be set forth in part in the description which follows, and in part will be apparent to those skilled in the art from the following examination, or may be learned from practice of the invention. The objectives and other advantages of the invention can be realized and obtained through the following description. Attached Figure Description

[0028] To make the objectives, technical solutions, and advantages of the present invention clearer, the preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings, wherein:

[0029] Figure 1 This is a flowchart of the present invention;

[0030] Figure 2 This is a schematic diagram of a gear model;

[0031] Figure 3 This diagram illustrates the correspondence between the row numbers of the tooth profile units involved in meshing on the driving gear and the meshing points during gear meshing.

[0032] Figure 4 This is a schematic diagram of a local contact arc surface model containing a rough surface morphology;

[0033] Figure 5 This is a preliminary schematic diagram of the local finite element model (including rough morphology) of the contact interface at meshing point 5 when the gears mesh;

[0034] Figure 6 This is a complete schematic diagram of the local finite element model (including rough morphology) of the contact interface at meshing point 5 when the gears mesh;

[0035] Figure 7 A schematic diagram of load application;

[0036] Figure 8 This is a schematic diagram of the rotational speed loading.

[0037] Figure 9 This is a stress contour plot at the contact interface of the meshing point 5 when the gears mesh;

[0038] Figure 10 The time-domain curve of the contact force between the driving wheel (small square) and the driven wheel (slide rail) at meshing point 5 is shown. Detailed Implementation

[0039] The following specific examples illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and various details in this specification can be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the illustrations provided in the following embodiments are only schematic representations of the basic concept of the present invention. Unless otherwise specified, the following embodiments and features can be combined with each other.

[0040] The accompanying drawings are for illustrative purposes only and are schematic diagrams, not actual pictures. They should not be construed as limiting the invention. To better illustrate the embodiments of the invention, some parts in the drawings may be omitted, enlarged, or reduced, and do not represent the actual product dimensions. It is understandable to those skilled in the art that some well-known structures and their descriptions may be omitted in the drawings.

[0041] See Figure 1 As shown in the figure, this embodiment provides a method for calculating the dynamic friction coefficient of a rough tooth surface interface based on transient finite element method. Based on the results of transient simulation analysis of gear meshing, a local model of gear meshing at the point to be calculated is established and transient simulation is performed. The time-varying contact force in the simulation results is processed using MATLAB programming, and finally, the dynamic friction coefficient of the rough tooth surface interface based on transient finite element method is obtained. The specific steps are as follows:

[0042] Step 1:

[0043] During gear meshing, the load and relative sliding velocity at different positions on the tooth surface (along the tooth tip to the tooth root profile) change continuously in the time domain and have different peak values. The transient effects such as vibration and deformation caused by the collision of tooth surface roughness peaks are different, resulting in differences in the friction coefficient at different meshing points (along the unit column of the tooth tip to the tooth root profile). Therefore, taking a pair of gears as an example (e.g.) Figure 2 As shown), open the transient simulation analysis result file of the gear during meshing in the Pre-post software, view the gear meshing stress cloud diagram in the previous finite element simulation results, and find the tooth surface that participates in a complete meshing process. This will lock the position of the tooth surface element involved in meshing. Then, number the nodes (i.e., meshing points) at the tooth surface meshing elements in order from "tooth root" to "tooth tip" to determine the required friction coefficient calculation point location, such as... Figure 3 As shown. Figure 2 This is a schematic diagram of a pair of gears, where the pinion is the driving gear and the gear is the driven gear. Figure 3 The driving gear teeth participate in one complete meshing process during the meshing of this pair of gears. On the tooth surface of its driving meshing side, the gear mesh participating in the meshing process consists of 9 meshing points from row 10 to row 18, which are named meshing points 1-9, and are also the points to be calculated. Here, we take meshing point 5 (located at the pitch line, which is representative) as an example for the subsequent calculation of the contact interface friction coefficient, and the other meshing points are calculated in the same way.

[0044] Step 2:

[0045] Based on the transient simulation results of gear meshing, the linear load and relative sliding velocity of meshing point 5 were extracted and processed. Simultaneously, based on the determined position of meshing point 5, combined with the known roughness of the driving wheel (Ra=0.8µm) and geometric parameters, the surface roughness and radius of curvature of this point were determined. The preliminary parameters are summarized in Table 1. The linear load at meshing point 5 is 46.24 N / mm, the relative sliding velocity at this point is 2783.45 mm / s, the surface roughness Ra is 0.8µm, and the radius of curvature on the driving wheel corresponding to meshing point 5 is 5.11 mm, while the radius of curvature on the driven wheel is 11.08 mm.

[0046] Table 1. Parameters and conditions when meshing point 5 participates in meshing.

[0047] Parameter name Parameter value Linear load (N / mm) 46.24 Relative sliding speed (mm / s) 2783.45 Surface roughness Ra (µm) 0.8 Corresponding radius of curvature on the drive wheel (mm) 5.11 Radius of curvature (mm) on the driven wheel 11.08

[0048] Step 3:

[0049] Based on the determined surface roughness at engagement point 5, a local contact arc surface model of the surface roughness morphology is established in ABQUS (reference mesh size, approximately 0.5 mm in length and width; approximately 0.01 mm in thickness), as shown below. Figure 4 As shown in Table 2, due to the small size of the surface roughness peaks, the length unit used in the modeling was changed from millimeters (mm) to micrometers (µm), which is equivalent to a 1000-fold magnification. The conversion relationships between the units are shown in Table 2.

[0050] Table 2 Unit Dimension Conversion Relationships

[0051]

[0052] Subsequently, the local contact arc surface model was opened in ANSA. Combining the radius of curvature of the driven wheel corresponding to meshing point 5 and other parameter conditions, a local finite element model of the meshing contact (including rough morphology) was established. The material was assumed to be 45 steel. Figure 5 As shown in the figure, the red slider contact interface has a roughness morphology of Ra=0.8µm, representing the driving wheel; the purple arc-shaped slide rail contact interface also has a roughness morphology of Ra=0.8µm, representing the driven wheel; the yellow slide rail is a smooth interface, reserving space for the process of relative sliding speed from 0 to the rated value.

[0053] Due to the presence of ultra-high-speed phases in actual operating conditions, where the relative sliding speed is relatively high, to achieve the rated relative sliding speed using the maximum rotational speed loading rate that does not affect the contact force, the slide rail needs to rotate through a larger angle, even exceeding one revolution, during the ultra-high-speed phase. Therefore, to reduce modeling workload and improve model universality, the yellow smooth slide rail section is extended until it forms a loop, as shown in the figure. Figure 6 As shown in the blue section; simultaneously, a rigid support for the slide rail is established to ensure the accuracy of relative motion, such as... Figure 6The green section is shown in the image. Boundary conditions are then applied to establish a complete local finite element model of the meshing contact (including rough morphology) and the simulation is then performed. The red squares represent the meshing force loads applied, as shown in the image. Figure 7 As shown; the supporting rigid body applies a sliding velocity between the two, causing the slide rail to slide relative to the small cube, as... Figure 8 As shown; since only the dynamic friction coefficient under the influence of the tooth surface roughness peak is calculated, the contact interface friction coefficient is set to 0, and the global damping is set to small damping. Because the position of the small block remains unchanged, the sliding friction coefficient can be obtained from the ratio between the tangential resistance of the contact surface that hinders its relative motion and the pressure acting in the normal direction of the contact surface in the simulation results.

[0054] Step 4:

[0055] Open the transient simulation analysis result file of the gear meshing local model obtained in step 3 in the Pre-post software to obtain the Hertzian contact layer stress cloud diagram of meshing point 5, as shown below. Figure 9 As shown, the stress pattern results are normal. Then, based on the geometric dimensions of the local simulation analysis model, it was calculated that the small cube enters the rough surface interface at 0.0195s and leaves at 0.0213s. Therefore, the contact force time-domain variation curves along the normal and tangential directions of the contact surface of the local model were extracted. Combining this with the previously calculated range, the stable phase curve data (0.0199s-0.0210s, locally refined) when passing through the rough surface was selected, as shown below. Figure 10 As shown, export the data file (.csv) for that period.

[0056] Step 5:

[0057] The exported data file (.csv) is processed using MATLAB programming to obtain the time-varying data matrix of the tangential resistance and normal pressure at the point to be calculated, thereby calculating the time-varying data matrix of the transient friction coefficient. Some data are shown in Table 3.

[0058] Table 3 Partial Schematic Diagram of Transient Friction Coefficient Matrix

[0059]

[0060] The formula for calculating the transient friction coefficient is:

[0061]

[0062] In the formula, The transient sliding friction coefficient; The transient sliding friction force that hinders motion is the negative Z-axis component of the contact force acting on the small cube. This is the positive pressure at that moment, i.e., the positive component of the transient contact force along the Y-axis.

[0063] In the simulation of a local model with rough morphology, the friction coefficient calculated according to the definition of friction coefficient has strong transient characteristics due to the transient effects such as vibration and deformation caused by the contact collision between the rough peaks of the contact interface during the sliding process. Therefore, its root mean square value (RMS) is taken as the final effective sliding friction coefficient, with a specific value of 0.0317.

[0064] The formula for calculating the root mean square (RMS) value is:

[0065]

[0066] In the formula, Let be the transient friction coefficient at a certain moment, and n be the number of transient friction coefficients in the series.

[0067] The example ultimately yielded an effective value of 0.0317 for the dynamic friction coefficient of the rough interface of the tooth surface at meshing point 5. Based on experimental experience, the dynamic friction coefficient of the material used in this example—45 steel—generally ranges from 0.01 to 0.1 under lubrication conditions, verifying the accuracy of the calculation method proposed in this invention.

[0068] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A method for calculating the dynamic friction coefficient of a rough interface based on transient finite element method, characterized in that: Based on the transient simulation results of gear meshing, a local model of gear meshing at the point to be calculated is established and the simulation is carried out. The time-varying contact force in the simulation results is processed by software programming, and finally the dynamic friction coefficient of the gear meshing rough interface based on the transient simulation of gear meshing is obtained. The specific steps include: Step 1: Determine the location of the point where the friction coefficient of the contact interface of the gear meshing is to be calculated; Step 2: Obtain the load conditions and morphological characteristics of the point where the friction coefficient is to be calculated; Step 3: Establish a local transient finite element model of the contact interface at the point to be calculated and perform simulation; Step 4: Extract the time-domain variation curves of contact forces representing normal pressure and frictional resistance from the transient simulation analysis results and export the data file; Step 5: Based on the friction coefficient calculation formula, the time-domain data of normal pressure and tangential friction resistance are processed by programming to obtain the dynamic friction coefficient of the tooth surface rough interface.

2. The method for calculating the dynamic friction coefficient of a rough interface based on transient finite element method according to claim 1, characterized in that: In step 1, based on the existing transient simulation analysis results of gear meshing, the positions of the tooth surface units involved in meshing are locked, and the position of the friction coefficient calculation point along the tooth profile is determined.

3. The method for calculating the dynamic friction coefficient of a rough interface based on transient finite element method according to claim 2, characterized in that: In step 2, based on the transient simulation results of gear meshing, the linear load and relative sliding speed at the point where the friction coefficient is to be calculated are extracted. Combined with the surface roughness and geometric parameters of the gear teeth in the gear model, the roughness and radius of curvature of that point are obtained.

4. The method for calculating the dynamic friction coefficient of a rough interface based on transient finite element method according to claim 3, characterized in that: In step 3, based on the obtained radius of curvature, roughness, linear load at contact, and relative sliding speed of the point to be calculated, a local finite element model of the contact interface with rough morphology during meshing is established, and sliding simulation calculation of the surface contact interface is carried out.

5. The method for calculating the dynamic friction coefficient of a rough interface based on transient finite element method according to claim 4, characterized in that: In step 4, the transient simulation analysis result file of the local gear meshing model is opened in the post-processing software. The time-varying contact force curves representing tangential frictional resistance and normal pressure along the contact surface of the local model are extracted respectively, and the effective time period data in the curves are exported. The effective time period data refers to the stable stage curve data of the local model when it experiences a rough surface during the simulation process.

6. The method for calculating the dynamic friction coefficient of a rough interface based on transient finite element method according to claim 5, characterized in that: In step 5, the data file of the contact force time-domain variation curve is processed by programming to obtain the time-varying data matrix of the tangential resistance and normal pressure at the point to be calculated, thereby calculating the time-varying matrix of the transient sliding friction coefficient, and taking its root mean square value as the final effective sliding friction coefficient.

7. The method for calculating the dynamic friction coefficient of a rough interface based on transient finite element method according to claim 6, characterized in that, The formula for calculating the transient sliding friction coefficient is as follows: In the formula, The transient sliding friction coefficient; Transient sliding friction that hinders motion, This is the transient normal pressure.

8. The method for calculating the dynamic friction coefficient of a rough interface based on transient finite element method according to claim 6, characterized in that, The formula for calculating the root mean square value is as follows: In the formula, RMS root mean square value, Let be the transient friction coefficient at a certain moment, and n be the number of transient friction coefficients in the series.

Images