A Multi-Performance Coordination Design Method for Planetary Roller Screws

Abstract

This invention relates to a multi-performance coordinated design method for planetary roller screws, belonging to the field of planetary roller screw technology. It includes the following steps: Step 1, establishing a calculation model for the thread engagement point slip ratio and maximum von Mises stress based on the kinematics and load distribution model of the planetary roller screw; Step 2, establishing equal and unequal structural constraints based on the correct meshing, non-interference, and contact boundary conditions of the planetary roller screw; Step 3, establishing a multi-performance optimization design model for the planetary roller screw based on the optimization objective and constraints; Step 4, using a multi-objective genetic algorithm to solve the multi-performance design model of the planetary roller screw, obtaining the Pareto front and corresponding structural design parameters; Step 5, obtaining the Pareto front range that satisfies the given limit trade-off cost. Based on the Euclidean norm and minimizing the dimensionless distance, the optimal trade-off solution and corresponding structural design parameters are obtained.

Description

Technical Field

[0001] This invention belongs to the field of planetary roller screw technology, and specifically relates to a multi-performance coordination design method for planetary roller screws. Background Technology

[0002] Planetary roller screws are a new generation of high-end linear drive mechanisms. They achieve high power density, high reliability, and high precision conversion between rotary and linear motion through a large number of meshing threads and the planetary motion of multiple rollers. The rapid development of electrification technology is accelerating the replacement of traditional hydraulic systems with efficient and environmentally friendly electromechanical servo systems. Against this backdrop, planetary roller screws are finding increasingly widespread application in electromechanical servo systems for aircraft wing surface control, feed systems for CNC machine tools, and linear joints for humanoid robots.

[0003] Planetary roller screws transmit motion and power through threads. The interface between the screw and the roller threads exhibits significant sliding velocity, accelerating surface wear and substantially reducing transmission efficiency. Furthermore, the complex deformation coordination between adjacent meshing threads leads to significantly uneven load distribution among the contact threads, reducing their load-bearing capacity. Frictional performance and load-bearing capacity are key evaluation indicators for planetary roller screws, and the comprehensive improvement of these two properties plays a decisive role in achieving high efficiency, low wear, small size, and long service life. Since there is a one-to-one mapping relationship between the structural parameters of planetary roller screws and their load-bearing and frictional performance, conducting structural optimization design is of great significance for improving their overall performance.

[0004] However, existing planetary roller screw design methods mostly focus on load-bearing performance design, lacking a design method that considers friction performance, especially its coupling with load-bearing performance. Furthermore, there is an undisclosed constraint between friction performance and load-bearing performance, and an effective design method to coordinate these two properties is lacking. Therefore, developing a multi-performance coordination design method for planetary roller screws has significant practical application value for achieving a comprehensive improvement in both friction and load-bearing performance.

[0005] Based on the above background, this invention proposes a multi-performance coordinated design method for planetary roller screws. This method uses the slip-roll ratio and maximum von Mises stress as quantitative characterization indicators of friction performance and load-bearing performance, respectively. With minimizing the slip-roll ratio and maximum von Mises stress of the planetary roller screw as the optimization objective, and using equality and inequality structural constraints as constraints, a multi-objective genetic algorithm and optimal trade-off solution calculation method are employed to obtain the optimal friction and load-bearing performance and the corresponding structural design parameters. This invention enables the coordinated design of multiple performance characteristics of planetary roller screws, thereby significantly improving their overall performance. Summary of the Invention

[0006] This invention provides a multi-performance coordinated design method for planetary roller screws, which solves the technical problem of the limitation of current planetary roller screws that take a single performance as the design goal.

[0007] To achieve the above objectives, the present invention is implemented through the following technical solution:

[0008] A multi-performance coordinated design method for planetary roller screws includes the following steps: Step 1: Based on the kinematic model and load distribution model of the planetary roller screw, establish a calculation model for the slip-roll ratio and the maximum von Mises stress at the thread meshing point. The slip-roll ratio is a quantitative characterization index of friction performance, and the maximum von Mises stress is a quantitative characterization index of load-bearing performance; Step 2: Based on the correct meshing, structural non-interference, and contact boundary conditions of the planetary roller screw, establish equal and unequal structural constraint conditions; Step 3: Minimize the slip-roll ratio and the maximum von Mises stress as the design parameters. The optimization objective, combined with equal and unequal structural constraints, establishes a multi-performance optimization design model for the planetary roller screw; Step 4: Use a multi-objective genetic algorithm to solve the multi-performance optimization design model, obtaining the Pareto front for friction performance and load-bearing performance and the corresponding planetary roller screw structural design parameters; Step 5: Determine the range of the Pareto front that satisfies the given limit trade-off cost, and based on the Euclidean norm and minimizing the dimensionless distance, solve for the optimal trade-off solution for friction performance and load-bearing performance and the corresponding planetary roller screw structural design parameters.

[0009] Furthermore, when establishing the slip-roll ratio calculation model, the cage of the planetary roller screw is assumed to be stationary. At this time, the screw, rollers and nut only rotate relative to the cage, and the side angles of the rollers and nut are set to be equal. Sliding only occurs on the contact side of the screw and rollers. By calculating the sliding velocity vector and absolute velocity vector at the screw-roller contact point, the slip-roll ratio calculation formula at the thread engagement point is derived.

[0010] Furthermore, when establishing the load distribution model, the load distribution matrix equation is constructed based on the deformation coordination and force balance relationship between threads. The Newton iteration method is used to solve the load distribution matrix equation to obtain the load distribution matrix of the thread contact point. Then, combined with the contact load distribution and contact geometry, the von Mises stress at the thread meshing point is calculated, and then the maximum von Mises stress of all thread meshing points is extracted.

[0011] Furthermore, the equal structural constraints include no relative axial displacement between the roller and the nut, the rotation centers of the roller thread pair and the gear pair coincide, and adjacent rollers do not interfere with each other and have maximum load-bearing capacity; the unequal structural constraints include no geometric interference between the roller and nut helices, and the contact points on the screw-roller and roller-nut sides remain within the thread boundary with clearance allowance.

[0012] Furthermore, when performing dimensionless processing on the Pareto front, considering that friction performance and load-bearing performance are equally important, the Pareto front value corresponding to a lead screw side angle of approximately 45° is used as a dimensionless parameter, and all data points of the Pareto front are transformed into dimensionless values.

[0013] Furthermore, an 8th-order Gaussian function is used to fit the dimensionless Pareto front data points, and the derivative of the fitted curve is calculated. Based on a given limit, a cost trade-off is made. c ( c <0) yields the lower bound of the boundary slope of the dimensionless Pareto front. and upper limit Then, based on the boundary slope, determine the dimensional Pareto front range that satisfies the limit trade-off cost.

[0014] Furthermore, the Pareto front that satisfies the limit trade-off cost is re-dimensionless using the max-min method, and then a dimensionless distance calculation model is constructed based on the Euclidean norm. The optimal trade-off solution and the corresponding structural design parameters are obtained by minimizing the dimensionless distance.

[0015] Furthermore, the structural design parameters of the planetary roller screw include the thread flank angle of the screw, rollers and nut, the nominal radius of the screw thread, the number of thread starts of the screw and nut, the thread pitch, and the number of roller threads.

[0016] This invention provides a multi-performance coordinated design method for planetary roller screws, with the following advantages: By using the slip-roll ratio and maximum von Mises stress as quantitative characterization indicators of friction and load-bearing performance and establishing corresponding calculation models, and combining a multi-objective genetic algorithm to solve the Pareto front, the coupled optimization design of the friction and load-bearing performance of the planetary roller screw is realized, thereby improving the overall performance of the screw; by adopting the optimal trade-off solution calculation method that minimizes the dimensionless distance using the Euclidean norm, the optimal trade-off design between the two conflicting performances of friction and load-bearing is achieved; by constructing a multi-performance optimization design model based on equality and inequality structural constraints, the design performance and optimization parameters have good scalability, realizing the design requirement of adjusting the design performance and the number of optimization parameters as needed; and through a clear step-by-step design process and quantitative calculation and optimization methods, the standardization and precision of the multi-performance coordinated design of planetary roller screws are achieved. Attached Figure Description

[0017] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0018] Figure 1 A flowchart of a multi-performance coordinated design method for planetary roller screws provided in an embodiment of the present invention;

[0019] Figure 2 The Pareto front, design reference point performance, and optimal trade-off solution performance for frictional performance and load-bearing performance are calculated by the method proposed in the embodiments of the present invention.

[0020] Figure 3 The lead screw and roller side angles corresponding to the Pareto front and optimal trade-off solution provided in the embodiments of the present invention; Detailed Implementation

[0021] The embodiments of this application will now be described in detail with reference to the accompanying drawings.

[0022] Example:

[0023] like Figures 1 to 3 As shown, this embodiment provides a multi-performance coordinated design method for planetary roller screws, including the following steps: Step 1: Based on the kinematic model and load distribution model of the planetary roller screw, establish a calculation model for the slip-roll ratio at the thread meshing point and a calculation model for the maximum von Mises stress. The slip-roll ratio is a quantitative characterization index of friction performance, and the maximum von Mises stress is a quantitative characterization index of load-bearing performance; Step 2: Based on the correct meshing, structural non-interference, and contact boundary conditions of the planetary roller screw, establish equal and unequal structural constraint conditions; Step 3: Using the slip-roll ratio and the maximum von Mises stress... Minimization is the optimization objective. Combining equality and inequality structural constraints, a multi-performance optimization design model for planetary roller screws is established. Step 4: A multi-objective genetic algorithm is used to solve the multi-performance optimization design model to obtain the Pareto front for friction performance and load-bearing performance, as well as the corresponding planetary roller screw structural design parameters. Step 5: Based on the given limit trade-off cost, the range of the Pareto front that satisfies the limit trade-off cost is determined. Based on the Euclidean norm and minimizing the dimensionless distance, the optimal trade-off solution for friction performance and load-bearing performance, as well as the corresponding planetary roller screw structural design parameters, are obtained.

[0024] In this embodiment, step 1: Based on the kinematics and load distribution model of the planetary roller screw, establish a calculation model for the thread engagement point slip ratio and the maximum von Mises stress.

[0025] Based on the motion principle of planetary roller screws, a kinematic model of the planetary roller screw is established. It is represented as follows: when the side angles of the roller and nut are equal, the sliding velocity at the contact point between the roller and nut is zero, i.e., there is no sliding friction. Therefore, the side angles of the roller and nut are set to be equal; at this time, sliding only occurs on the contact side between the screw and the roller. Assuming the planetary roller screw cage is stationary, the screw (s), roller (r), and nut (n) only rotate relative to the cage (H). The surface relative velocity vector at the contact point of the screw, roller, and nut is expressed as:

[0026] ;

[0027] In the formula ( rc s , θc s )and( rc rs , θc rs ) represent the polar coordinates of the contact point of the lead screw and roller in their respective coordinate systems. ω s / n , ω n / H , ω r / H These represent the rotational speeds of the lead screw relative to the nut, the nut relative to the cage, and the roller relative to the cage, respectively. and This represents the relative velocity vector between the lead screw and the rollers relative to the cage at the point of contact. This represents the relative velocity vector of the cage with respect to the nut at the point of contact. This represents the relative velocity vector of the nut at the point of contact with respect to the fixed coordinate system. l s This represents the lead of the leadscrew. Further calculations yield the sliding velocity vector at the leadcrew-roller contact point.

[0028] ;

[0029] In the formula ζ = ω n / H / ω s / n , ς = ω r / H / ω s / n The absolute velocity vector at the lead screw-roller contact point is expressed as:

[0030] ;

[0031] Therefore, based on the kinematic model of the planetary roller screw, the slip-roll ratio calculation model at the contact point of the planetary roller screw can be obtained, as shown below.

[0032] ;

[0033] Based on the deformation compatibility and force balance relationship between the threads, a load distribution model for the planetary roller screw is established. The planetary roller screw load distribution model is expressed as:

[0034] ;

[0035] In the formula n Indicates the number of roller threads. P n , P r and P s This indicates the thread pitch of nuts, rollers, and lead screws. F 0 indicates the load size. z The matrix represents the number of rollers. B represents a matrix consisting of contact stiffness, thread stiffness, shaft compressive / tensile stiffness, and coefficients 0 and 1. D represents a matrix consisting of pitch, load magnitude, and the number of rollers. F represents the load distribution matrix at the thread contact points, obtained by solving the load distribution model using Newton's iteration method. The solution process of Newton's iteration method is a standard technique and will not be elaborated upon.

[0036] The calculation model for the maximum von Mises stress is expressed as follows: Based on the contact load distribution and contact geometry, the von Mises stress at the contact point of the planetary roller screw is calculated and expressed as:

[0037]

[0038] In the formula σ ij The elastic stress components are represented by the following formula:

[0039] ;

[0040] In the formula p ( ζ , ξ ) represents a point on the contact domain Ω. ζ , ξ Hertzian contact pressure at ) g ij This represents the influence coefficient of the elastic stress component.

[0041] Therefore, the maximum von Mises stress at all thread engagement points is expressed as:

[0042] ;

[0043] In the formulaM , N and L They represent along x axis, y shaft and z The number of discrete grid points on the axis. n Indicates the number of roller threads.

[0044] Step 2: Based on the correct meshing of the planetary roller screw, non-interference of the structure, and contact boundary conditions, establish the equal and inequal structural constraint conditions.

[0045] The constraints of the equation structure include: 1) No relative axial displacement is allowed between the roller and the nut, i.e., condition h 1 and h 2;2) The rotation centers of the roller thread pair and the gear pair must coincide, i.e., condition h 3;3) Adjacent rollers must not interfere with each other and must have maximum load-bearing capacity, i.e., condition h 4.

[0046] ;

[0047] In the formula n s and n n This indicates the number of thread turns in the lead screw and nut. r so , r ro and r no Indicates the nominal radius of the lead screw, roller, and nut. z Indicates the number of rollers. r r2 Indicates the major diameter of the roller.

[0048] The inequality constraints include: 1) The roller and nut helices cannot interfere geometrically, i.e., the condition... g 1; 2) The contact points on the lead screw-roller and roller-nut sides must be kept within the thread boundary and have sufficient clearance allowance, i.e., condition g 2- g 9.

[0049] ;

[0050] In the formula rc s , rc rs , rc rn and rc n These represent the contact radii of the respective contact points on the lead screw-roller and roller-nut sides.r s1 and r s2 This indicates the minor and major diameters of the leadscrew. r r1 and r r2 This indicates the minor and major diameters of the roller. Δ b Indicates clearance margin. r n1 and r n2 This indicates the minor and major diameters of the nut. χ 1 and χ 2 is represented as:

[0051] ;

[0052] Step 3: Based on the optimization objectives and constraints, establish a multi-performance optimization design model for the planetary roller screw.

[0053] The frictional and load-bearing performance of planetary roller screws are quantitatively characterized by the slip-roll ratio at the thread engagement point and the maximum von Mises stress, respectively, and used as multi-performance optimization design objectives. Combining the equality and inequality structural constraints of planetary roller screws, a multi-performance optimization design model for planetary roller screws is established, expressed as:

[0054] ;

[0055] Step 4: A multi-objective genetic algorithm is used. This algorithm is selected from existing technologies and will not be elaborated upon. The multi-performance optimization design model of the planetary roller screw is solved to obtain the Pareto front and the corresponding structural design parameters.

[0056] Step 5: Based on the given limit trade-off cost, obtain the Pareto front range that satisfies the limit trade-off cost. Based on the Euclidean norm and minimizing the dimensionless distance, obtain the optimal trade-off solution and the corresponding structural design parameters.

[0057] Assuming that friction performance and load-bearing performance are equally important, the Pareto front value corresponding to a lead screw side angle of approximately 45° is used as a dimensionless parameter. The Pareto front is then dimensionless and expressed as follows:

[0058] ;

[0059] An 8th-order Gaussian function is used to fit a curve to the dimensionless Pareto front data points, and the derivative of the fitted curve is expressed as:

[0060] ;

[0061] The value of c is defined as the ultimate trade-off cost, and in this embodiment, c = -2, meaning that for every unit increase in friction performance, the maximum allowable sacrifice in load-bearing performance is no more than 2 units; conversely, for every unit increase in load-bearing performance, the maximum allowable sacrifice in friction performance is also no more than 2 units.

[0062] Based on a given limit trade-off cost c ( c <0), thus obtaining the boundary slope of the dimensionless Pareto front, i.e. and The dimensional Pareto front range satisfying the limit trade-off cost is obtained based on the boundary slope. Then, the Pareto front satisfying the limit trade-off cost is re-dimensionized using the max-min method. Based on the Euclidean norm and minimizing the dimensionless distance, the optimal trade-off solution is obtained. The dimensionless distance calculation model is expressed as:

[0063] ;

[0064] In the formula This represents the dimensionless Pareto front. i This represents the total number of solutions contained in the Pareto front. j This represents the total number of performance metrics.

[0065] The above steps achieve a multi-performance coordinated design for the planetary roller screw. The Pareto front, design reference point performance, and optimal trade-off solution performance for friction and load-bearing performance calculated by the method proposed in this invention are as follows: Figure 2 As shown. The Pareto front and the optimal trade-off solution correspond to the screw and roller side angles, as shown. Figure 3 As shown, the Pareto front obtained by the multi-performance design method for planetary roller screws proposed in this invention is significantly lower than that of the design reference point in terms of both the slip-roll ratio and the maximum von Mises stress. Furthermore, the optimal trade-off solution for the frictional and load-bearing performance of the planetary roller screw reduces the slip-roll ratio and maximum von Mises stress by 61% and 35% respectively compared to the design reference point, and the optimal trade-off solution has the smallest dimensionless comprehensive error compared to the ideal design point. The design angles of the screw and nut side angles corresponding to the optimal trade-off solution are (43.6807°, 44.0046°). The comparative analysis with the design reference point shows that the method proposed in this invention can accurately solve for the optimal trade-off solution for multiple performance aspects, achieving a significant improvement in the overall performance of the planetary roller screw.

[0066] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope described in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A multi-performance coordination design method for planetary roller screws, characterized in that, Includes the following steps: Step 1: Based on the kinematic model and load distribution model of the planetary roller screw, establish a calculation model for the slip-roll ratio at the thread meshing point and a calculation model for the maximum von Mises stress. The slip-roll ratio is a quantitative characterization index of friction performance, and the maximum von Mises stress is a quantitative characterization index of load-bearing performance. Step 2: Based on the correct meshing, structural non-interference, and contact boundary conditions of the planetary roller screw, establish equal and unequal structural constraint conditions. Step 3: Taking the minimization of the slip-roll ratio and the maximum von Mises stress as the optimization objectives, and combining the equal and unequal structural constraints, establish a multi-performance optimization design model for the planetary roller screw. Step 4: Use a multi-objective genetic algorithm to solve the multi-performance optimization design model to obtain the Pareto front for friction performance and load-bearing performance and the corresponding planetary roller screw structure design parameters; Step 5: Determine the Pareto front range that satisfies the given limit trade-off cost. Based on the Euclidean norm and minimizing the dimensionless distance, solve for the optimal trade-off solution for friction performance and load-bearing performance, as well as the corresponding planetary roller screw structure design parameters.

2. The multi-performance coordination design method for planetary roller screws according to claim 1, characterized in that, In step 1, when establishing the slip-roll ratio calculation model, the cage of the planetary roller screw is assumed to be stationary. At this time, the screw, roller, and nut only rotate relative to the cage, and the side angles of the roller and nut are set to be equal. Sliding only occurs on the contact side of the screw and roller. By calculating the sliding velocity vector and absolute velocity vector at the screw-roller contact point, the slip-roll ratio calculation formula at the thread engagement point is derived.

3. The multi-performance coordination design method for planetary roller screws according to claim 2, characterized in that, In step 1, when establishing the load distribution model, the load distribution matrix equation is constructed based on the deformation coordination and force balance relationship between threads. The load distribution matrix equation is solved using the Newton iteration method to obtain the load distribution matrix of the thread contact point. Then, combined with the contact load distribution and contact geometry, the von Mises stress at the thread meshing point is calculated, and the maximum von Mises stress at all thread meshing points is extracted.

4. The multi-performance coordination design method for planetary roller screws according to claim 1, characterized in that, The equality constraints in step 2 include no relative axial displacement between the roller and the nut, the rotation centers of the roller thread pair and the gear pair coincide, and adjacent rollers do not interfere with each other and have maximum load-bearing capacity; the inequality constraints include no geometric interference between the roller and nut helices, and the contact points on the screw-roller and roller-nut sides remain within the thread boundary with clearance allowance.

5. The multi-performance coordination design method for planetary roller screws according to claim 1, characterized in that, In step 5, when performing dimensionless processing on the Pareto front, considering friction performance and load-bearing performance as equally important, the Pareto front value corresponding to a lead screw side angle of approximately 45° is used as a dimensionless parameter, and all data points of the Pareto front are transformed into dimensionless values.

6. The multi-performance coordination design method for planetary roller screws according to claim 5, characterized in that, In step 5, an 8th-order Gaussian function is used to fit the dimensionless Pareto front data points to a curve, and the derivative of the fitted curve is calculated. Based on the given limiting trade-off cost c, where c < 0, the lower limit of the boundary slope of the dimensionless Pareto front is obtained. and upper limit Then, based on the boundary slope, determine the dimensional Pareto front range that satisfies the limit trade-off cost.

7. The multi-performance coordination design method for planetary roller screws according to claim 6, characterized in that, In step 5, the Pareto front that satisfies the limit trade-off cost is re-dimensionized using the max-min method, and then a dimensionless distance calculation model is constructed based on the Euclidean norm. The optimal trade-off solution and the corresponding structural design parameters are obtained by minimizing the dimensionless distance.

8. The multi-performance coordination design method for planetary roller screws according to claim 1, characterized in that, The structural design parameters of the planetary roller screw include the thread flank angle of the screw, rollers and nut, the nominal radius of the screw thread, the number of thread starts of the screw and nut, the thread pitch, and the number of roller threads.

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