Method for calculating load distribution of planetary roller screw based on mixed lubrication interface characteristics

Abstract

The present application relates to a planetary roller screw load distribution calculation method based on mixed lubrication interface characteristics, contact parameters of each thread engagement point are calculated by obtaining machining roughness; a planetary roller screw engagement interface mixed lubrication model is established based on machining microtopography, entrainment angle and surface elastic deformation; machining roughness and contact parameters of each thread engagement point are respectively introduced into the corresponding mixed lubrication model, and the mixed lubrication results of each engagement point are obtained by parallel calculation; a nonlinear contact stiffness model under mixed lubrication is established to calculate the mixed lubrication contact stiffness of the thread engagement point; a planetary roller screw load distribution calculation model under mixed lubrication is established; the accurate planetary roller screw load distribution result is obtained through the iterative solution of the mixed lubrication model and the load distribution model. Through the consideration of the interaction between the mixed lubrication of the planetary roller screw engagement interface and the load distribution, more accurate load distribution calculation is realized than the traditional method.

Description

Technical Field

[0001] The present invention belongs to the technical field of planetary roller screw load distribution calculation, and in particular relates to a planetary roller screw load distribution calculation method based on mixed lubrication interface characteristics. Background Art

[0002] Planetary roller screws are high-precision linear drive components that transmit motion and power through multi-point meshing of the screw, rollers, and nut threads. They offer high load capacity, long life, compact size, and high transmission accuracy, making them widely used in aerospace electromechanical actuation systems, CNC machine tool feed systems, and humanoid robot joints. Planetary roller screws often operate under heavy loads and frequent starts and stops, with significant relative slip between the screw and roller meshing surfaces. Lubricants are often used to reduce friction and wear at these interfaces.

[0003] Due to the machining roughness of the thread surface, the meshing interface often operates in a mixed lubrication state. Furthermore, the coordinated interaction between various deformations caused by thread load leads to uneven load distribution on the thread teeth. The lubrication characteristics of the planetary roller screw meshing interface affect the contact stiffness, which in turn affects the load distribution. Conversely, the load distribution affects the interface lubrication behavior. It can be seen that there is an inherent interaction between the interface lubrication and load distribution of the planetary roller screw. Therefore, considering the mixed lubrication interface characteristics and their interaction with load distribution is of great significance for accurately calculating the load distribution of the planetary roller screw.

[0004] However, current calculations of planetary roller screw load distribution are typically based on the dry contact assumption. This load distribution calculation method, which uses a simplified Hertzian contact theory, ignores the influence of meshing interface lubrication, leading to large calculation errors. In addition, direct contact of roughness peaks and elastohydrodynamic lubrication coexist in the mixed lubrication domain of the meshing interface, and the roughness peak contact ratio varies with the contact load, causing nonlinear changes in the mixed lubrication contact stiffness. However, this nonlinear change in mixed lubrication contact stiffness has not been taken into account in current planetary roller screw load distribution calculation methods. Therefore, developing a load distribution calculation method based on the characteristics of the mixed lubrication interface is of great significance for improving the accuracy of planetary roller screw load distribution prediction.

[0005] The present invention intends to provide a planetary roller screw load distribution calculation method based on the mixed lubrication interface characteristics. Based on the calculation of the nonlinear contact stiffness of the planetary roller screw under mixed lubrication, and with the contact stiffness as the link, the coupled modeling and calculation of mixed lubrication and load distribution are realized. By considering the mixed lubrication of the planetary roller screw meshing interface and its interaction with load distribution, a more accurate load distribution calculation is achieved than the traditional method. Summary of the Invention

[0006] The purpose of the present invention is to provide a planetary roller screw load distribution calculation method based on the mixed lubrication interface characteristics, which is used to calculate the nonlinear contact stiffness of the planetary roller screw under mixed lubrication, and use the contact stiffness as a link to realize the coupled modeling and calculation of mixed lubrication and load distribution. By considering the mixed lubrication of the planetary roller screw meshing interface and its interaction with load distribution, a more accurate load distribution calculation is achieved than the traditional method.

[0007] In order to solve the above technical problems, the technical solutions adopted by the present invention are as follows:

[0008] A planetary roller screw load distribution calculation method based on mixed lubrication interface characteristics includes the following steps:

[0009] S1: Measure the machining micromorphology of the thread surface, obtain the machining roughness, and calculate the contact parameters of each thread engagement point;

[0010] S2: A mixed lubrication model for the planetary roller screw meshing interface is established based on the machining microstructure, entrainment angle, and surface elastic deformation.

[0011] S3: The machining roughness and the contact parameters of each thread meshing point are respectively imported into the corresponding mixed lubrication model, and the mixed lubrication results of each thread meshing point are obtained by parallel calculation;

[0012] S4: Based on the mixed lubrication interface characteristics, a nonlinear contact stiffness model under mixed lubrication is established, and the mixed lubrication contact stiffness of all thread meshing points is calculated based on the mixed lubrication results of each meshing point;

[0013] S5: Based on the deformation coordination relationship between the roller and the contact sides of the screw and nut, as well as the load balance relationship, a load distribution calculation model for the planetary roller screw under mixed lubrication is established;

[0014] S6: Iteratively execute steps S2-S5 to form a coupled iterative cycle. During the iteration process, the mixed lubrication model provides the load distribution model with the mixed lubrication results required for calculating the contact stiffness, and the load distribution model provides the mixed lubrication model with a new load distribution result. The Newton iteration method is used to solve the above load distribution model, and the relative error of the load distribution between adjacent iterative steps is used as the convergence criterion. Finally, the accurate planetary roller screw load distribution result is calculated.

[0015] Preferably, the specific process of step S1 is as follows:

[0016] An optical profilometer is used to measure the machined microtopography of the thread surface and convert it into a machined roughness matrix. Based on the structural parameters, operating parameters, and material properties of the planetary roller screw, the contact geometry, speed, and load parameters of each thread engagement point are calculated.

[0017] Preferably, the Reynolds equation of the mixed lubrication model of the planetary roller screw meshing interface in step S2 is expressed as follows:

[0018] ;

[0019] in, h and p represents the mixed lubrication film thickness and pressure distribution, r and or Indicates lubricant density and viscosity, t Indicates time, u e and v e Indicates lubricant along x and y Directional component of velocity;

[0020] Film thickness h The formula is as follows:

[0021] ;

[0022] in, h 0 is the normal approximation of the two surfaces, R x and R y is the equivalent radius of curvature of the two contact surfaces, s 1 and s 2 is the machining roughness of the two contact surfaces, v is the elastic deformation, and its calculation formula is as follows:

[0023] ;

[0024] in, E ' represents the equivalent Young's modulus, p represents the mixed lubrication pressure distribution, x and g Indicates the integral point x and y Axis coordinate values.

[0025] Preferably, in step S4, based on the mixed lubrication interface characteristics, the formula for establishing the nonlinear contact stiffness model under mixed lubrication is as follows:

[0026] ;

[0027] in, F represents the axial contact load, h 0 is the normal phase approximation of the two surfaces, obtained from the mixed lubrication model of the planetary roller screw meshing interface, ψr and β Indicates the lead angle and flank angle of the roller thread.

[0028] Preferably, the formula for the planetary roller screw load distribution calculation model under mixed lubrication established in step S5 is as follows:

[0029] ;

[0030] Among them, K 2n×2n represents a matrix consisting of the stiffness of the screw, roller and nut shaft segments, thread stiffness, contact stiffness, 0 and 1, where the contact stiffness varies with the axial load and its value is calculated by the nonlinear contact stiffness model under lubrication. 2n×1 It represents the axial load distribution matrix of roller, screw and nut side, matrix f 2n×1 middle P r 、 P s and P n Indicates the thread pitch of rollers, screws and nuts, F 0 represents the external load of the planetary roller screw, z Indicates the number of rollers in a planetary roller screw.

[0031] The beneficial effects of the present invention include:

[0032] The present invention provides a planetary roller screw load distribution calculation method based on mixed lubrication interface characteristics, comprising the following steps: obtaining machining roughness and calculating the contact parameters of each thread meshing point; establishing a planetary roller screw meshing interface mixed lubrication model based on machining micromorphology, entrainment angle, and surface elastic deformation; importing the machining roughness and the contact parameters of each thread meshing point into the corresponding mixed lubrication model, and using parallel calculation to obtain the mixed lubrication results of each meshing point; establishing a nonlinear contact stiffness model under mixed lubrication based on the mixed lubrication interface characteristics, and calculating the mixed lubrication contact stiffness of the thread meshing point; establishing a planetary roller screw load distribution calculation model under mixed lubrication; and calculating an accurate planetary roller screw load distribution result by iteratively solving the mixed lubrication model and the load distribution model. By considering the mixed lubrication of the planetary roller screw meshing interface and its interaction with load distribution, a more accurate load distribution calculation is achieved than traditional methods.

[0033] First, the planetary roller screw load distribution calculation method proposed in the present invention considers in detail the mixed lubrication characteristics of each thread meshing interface. Compared with the traditional dry contact load distribution calculation method, it can more accurately calculate the load distribution of the planetary roller screw.

[0034] Secondly, the load distribution calculation model proposed in this invention not only takes into account the mixed lubrication of the planetary roller screw meshing interface, but also takes into account the interaction between mixed lubrication and load distribution, which is closer to actual engineering.

[0035] Thirdly, the present invention uses parallel computing to calculate the mixed lubrication of all thread engagement points of the planetary roller screw, which can significantly improve the computing efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 It is a flow chart of the planetary roller screw load distribution calculation method based on the mixed lubrication interface characteristics of the present invention.

[0037] Figure 2 This is a comparison chart of the results of the planetary roller screw load distribution calculation method based on the mixed lubrication interface characteristics of the present invention and the traditional method. DETAILED DESCRIPTION

[0038] The following is combined with Figure 1~Figure 2 The present invention is described in further detail:

[0039] Example 1

[0040] See attached Figure 1 As shown, the planetary roller screw load distribution calculation method based on the mixed lubrication interface characteristics includes the following steps:

[0041] S1: Measure the machining micromorphology of the thread surface, obtain the machining roughness, and calculate the contact parameters of each thread engagement point;

[0042] S2: A mixed lubrication model for the planetary roller screw meshing interface is established based on the machining microstructure, entrainment angle, and surface elastic deformation.

[0043] S3: The machining roughness and the contact parameters of each thread meshing point are respectively imported into the corresponding mixed lubrication model, and the mixed lubrication results of each thread meshing point are obtained by parallel calculation;

[0044] S4: Based on the mixed lubrication interface characteristics, a nonlinear contact stiffness model under mixed lubrication is established, and the mixed lubrication contact stiffness of all thread meshing points is calculated based on the mixed lubrication results of each meshing point;

[0045] S5: Based on the deformation coordination relationship between the roller and the contact sides of the screw and nut, as well as the load balance relationship, a load distribution calculation model for the planetary roller screw under mixed lubrication is established;

[0046] S6: Iteratively execute steps S2-S5 to form a coupled iterative cycle. During the iteration process, the mixed lubrication model provides the load distribution model with the mixed lubrication results required for calculating the contact stiffness, and the load distribution model provides the mixed lubrication model with a new load distribution result. The Newton iteration method is used to solve the above load distribution model, and the relative error of the load distribution between adjacent iterative steps is used as the convergence criterion. Finally, the accurate planetary roller screw load distribution result is calculated.

[0047] In this embodiment, the specific process of step S1 is as follows:

[0048] An optical profilometer is used to measure the machined microtopography of the thread surface and convert it into a machined roughness matrix. Based on the structural parameters, operating parameters, and material properties of the planetary roller screw, the contact geometry, speed, and load parameters of each thread engagement point are calculated.

[0049] Optical profilometers are based on the principle of white-light interferometry, which analyzes interference fringes to obtain surface height information. They non-contactly scan the thread surface, collecting 3D coordinate point cloud data covering microscopic fluctuations in areas such as the thread profile, groove bottom, and flanks. By securing the threaded specimen, the profilometer's scanning parameters, including measurement range and resolution, must be set to cover the effective engagement length of the thread and to match the resolution required for roughness analysis.

[0050] The collected point cloud data is filtered to remove noise, including abnormal points introduced by environmental vibration and optical interference during scanning, and a single thread profile or effective analysis area is cropped. The scan is started, and the instrument collects surface height data point by point / line by line to generate a three-dimensional point cloud containing the micro-morphology. The three-dimensional point cloud is projected onto a two-dimensional plane, which can be set to the axial-circumferential plane of the thread. The grid is divided into equal intervals. The grid size is determined by the roughness characteristics and is usually much smaller than the basic thread profile size. The surface height value of each grid node is calculated to form a roughness matrix. The matrix elements correspond to the node height, reflecting the fluctuations in the micro-morphology.

[0051] Measure the structural parameters and material properties of rollers, screws, and nuts. Structural parameters include thread angle, pitch, nominal diameter, etc. Material properties include elastic modulus and Poisson's ratio.

[0052] Based on the structural parameters of the planetary roller screw, the thread profile equations for the screw, roller, and nut are established. The thread meshing satisfies the conjugate meshing condition, meaning that the unit normal vectors of the contact points of the two meshing thread surfaces are in opposite directions. This allows the coordinates of the meshing point to be determined. Based on the obtained meshing point coordinates, the contact geometry parameters of the meshing point are calculated.

[0053] Based on the operating parameters of a planetary roller screw, assuming a fixed cage, the screw, rollers, and nut rotate relative to the cage plane. Motion is transmitted between the rollers and nut via gears. Ideally, the ratio of the roller and nut rotational speeds is inversely proportional to their nominal diameters. Furthermore, based on the motion principle of a planetary roller screw, the velocity at the meshing point of the planetary roller screw can be calculated.

[0054] According to the material properties of the planetary roller screw, the contact load of each meshing point of the planetary roller screw is obtained by using the Hertz contact theory and Newton iteration method, based on the deformation coordination relationship between the shaft deformation on the contact side of the screw-roller and roller-nut, the deformation of the thread teeth and the deformation of the thread contact, as well as the load balance relationship between the contact load at the meshing point and the external load.

[0055] Example 2

[0056] Based on Example 1, the Reynolds equation of the mixed lubrication model of the planetary roller screw meshing interface in step S2 is expressed as follows:

[0057] ;

[0058] in, h and p represents the mixed lubrication film thickness and pressure distribution, r and or Indicates lubricant density and viscosity, t Indicates time, u e and v e Indicates lubricant along x and y Directional component of velocity;

[0059] Film thickness h The formula is as follows:

[0060] ;

[0061] in, h 0 is the normal approximation of the two surfaces, R x and R y is the equivalent radius of curvature of the two contact surfaces, s 1 and s 2 is the machining roughness of the two contact surfaces, v is the elastic deformation, and its calculation formula is as follows:

[0062] ;

[0063] in, E ' represents the equivalent Young's modulus,p represents the mixed lubrication pressure distribution, x and g Indicates the integral point x and y Axis coordinate values.

[0064] Example 3

[0065] On the basis of Example 1 or Example 2, in step S4, based on the mixed lubrication interface characteristics, the formula for establishing the nonlinear contact stiffness model under mixed lubrication is as follows:

[0066] ;

[0067] in, F represents the axial contact load, h 0 is the normal phase approximation of the two surfaces, obtained from the mixed lubrication model of the planetary roller screw meshing interface, ψ r and β Indicates the lead angle and flank angle of the roller thread.

[0068] The formula for the planetary roller screw load distribution calculation model under mixed lubrication established in step S5 is as follows:

[0069] ;

[0070] Among them, K 2n×2n represents a matrix consisting of the stiffness of the screw, roller and nut shaft segments, thread stiffness, contact stiffness, 0 and 1, where the contact stiffness varies with the axial load and its value is calculated by the nonlinear contact stiffness model under lubrication. 2n×1 It represents the axial load distribution matrix of roller, screw and nut side, matrix f 2n×1 middle P r 、 P s and P n Indicates the thread pitch of rollers, screws and nuts, F 0 represents the external load of the planetary roller screw, z Indicates the number of rollers in a planetary roller screw.

[0071] Example 4

[0072] Iterative execution of steps S2-S5 forms a coupled iterative cycle. During the iteration process, the mixed lubrication model provides the load distribution model with the mixed lubrication results required for calculating the contact stiffness, and the load distribution model provides the mixed lubrication model with a new load distribution result.

[0073] The Newton iteration method is used to solve the load distribution model. The relative error of the load distribution between adjacent iteration steps is used as the convergence criterion, and the accurate load distribution result of the planetary roller screw is finally calculated.

[0074] The load distribution results obtained by the method proposed in the embodiment of the present invention and the traditional dry contact or Hertz load distribution calculation method are as follows: Figure 2 As shown in the figure, it can be seen that there is a large gap between the calculation results of the proposed method and the traditional method, which shows the effectiveness and accuracy of the method proposed in the present invention.

[0075] In summary, the planetary roller screw load distribution calculation method based on the mixed lubrication interface characteristics provided by the present invention includes the following steps: obtaining machining roughness and calculating the contact parameters of each thread meshing point; establishing a planetary roller screw meshing interface mixed lubrication model based on machining micromorphology, entrainment angle and surface elastic deformation; importing the machining roughness and the contact parameters of each thread meshing point into the corresponding mixed lubrication model respectively, and using parallel calculation to obtain the mixed lubrication results of each meshing point; establishing a nonlinear contact stiffness model under mixed lubrication based on the mixed lubrication interface characteristics, and calculating the mixed lubrication contact stiffness of the thread meshing point; establishing a planetary roller screw load distribution calculation model under mixed lubrication; and calculating an accurate planetary roller screw load distribution result by iteratively solving the mixed lubrication model and the load distribution model. The present invention realizes the calculation of the nonlinear contact stiffness of the planetary roller screw under mixed lubrication, and uses the contact stiffness as a link to realize the coupled modeling and calculation of mixed lubrication and load distribution. This invention achieves more accurate load distribution calculation than traditional methods by considering the mixed lubrication of the planetary roller screw meshing interface and its interaction with load distribution.

Claims

1. A planetary roller screw load distribution calculation method based on mixed lubrication interface characteristics is characterized by: The following steps are involved: S1: Measure the machining micromorphology of the thread surface, obtain the machining roughness, and calculate the contact parameters of each thread engagement point; S2: A mixed lubrication model for the planetary roller screw meshing interface is established based on the machining microstructure, entrainment angle, and surface elastic deformation. S3: The machining roughness and the contact parameters of each thread meshing point are respectively imported into the corresponding mixed lubrication model, and the mixed lubrication results of each thread meshing point are obtained by parallel calculation; S4: Based on the mixed lubrication interface characteristics, a nonlinear contact stiffness model under mixed lubrication is established, and the mixed lubrication contact stiffness of all thread meshing points is calculated based on the mixed lubrication results of each meshing point; S5: Based on the deformation coordination relationship between the roller and the contact sides of the screw and nut, as well as the load balance relationship, a load distribution calculation model for the planetary roller screw under mixed lubrication is established; S6: Iteratively execute steps S2-S5 to form a coupled iterative cycle. During the iteration process, the mixed lubrication model provides the load distribution model with the mixed lubrication results required for calculating the contact stiffness, and the load distribution model provides the mixed lubrication model with a new load distribution result. The Newton iteration method is used to solve the above load distribution model. The relative error of the load distribution between adjacent iterative steps is used as the convergence criterion. Finally, an accurate load distribution result of the planetary roller screw is calculated. In step S4, based on the mixed lubrication interface characteristics, the formula for establishing the nonlinear contact stiffness model under mixed lubrication is as follows: ； in, F represents the axial contact load, h 0 is the normal approximation of the two surfaces, which is obtained from the mixed lubrication model of the planetary roller screw meshing interface. ψ r and β Indicates the lead angle and flank angle of the roller thread.

2. The planetary roller screw load distribution calculation method based on mixed lubrication interface characteristics according to claim 1 is characterized in that: The specific process of step S1 is as follows: An optical profilometer is used to measure the machining microtopography of the thread surface and convert it into a machining roughness matrix. Based on the structural parameters, operating parameters and material properties of the planetary roller screw, the contact geometry, speed and load parameters of each thread engagement point are calculated.

3. The planetary roller screw load distribution calculation method based on mixed lubrication interface characteristics according to claim 1, characterized in that: The Reynolds equation of the mixed lubrication model of the planetary roller screw meshing interface in step S2 is expressed as follows: ； in, h and p represents the mixed lubrication film thickness and pressure distribution, ρ and η Indicates lubricant density and viscosity, t Indicates time, u e and v e Indicates lubricant along x and y Directional component of velocity; Film thickness h The formula is as follows: ； in, h 0 is the normal approximation of the two surfaces, R x and R y is the equivalent radius of curvature of the two contact surfaces, s 1 and s 2 is the machining roughness of the two contact surfaces, v is the elastic deformation, and its calculation formula is as follows: ； in, E ' represents the equivalent Young's modulus, p represents the mixed lubrication pressure distribution, ξ and ζ Indicates the integral point x and y Axis coordinate values.

4. The planetary roller screw load distribution calculation method based on mixed lubrication interface characteristics according to claim 1, characterized in that: The formula for the planetary roller screw load distribution calculation model under mixed lubrication established in step S5 is as follows: ； Among them, K 2n×2n represents a matrix consisting of the stiffness of the screw, roller and nut shaft segments, thread stiffness, contact stiffness, 0 and 1, where the contact stiffness varies with the axial load and its value is calculated by the nonlinear contact stiffness model under lubrication. 2n×1 It represents the axial load distribution matrix of roller, screw and nut side, matrix f 2n×1 Medium P r 、P s and P n Indicates the thread pitch of the roller, screw and nut, F0 represents the external load of the planetary roller screw, z Indicates the number of rollers in a planetary roller screw.

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