A planetary roller screw low friction design method

Abstract

The application relates to a low-friction design method of a planetary roller screw, and belongs to the technical field of mechanical design. Step 1, a contact point position solving model and a kinematics model of the planetary roller screw are established, and the sliding speed and the entrainment speed of a screw-roller and a roller-nut contact pair at a contact point are solved; step 2, according to the definition of a slide-roller ratio, a slide-roller ratio calculation model of the screw-roller and the roller-nut contact pair of the planetary roller screw is established; step 3, according to the correct movement and meshing requirements of the planetary roller screw, a structure constraint condition is established; step 4, taking the minimization of the slide-roller ratio of the screw-roller and the roller-nut contact pair as an optimization target, and combining the structure constraint condition, a low-friction design model of the planetary roller screw is established; step 5, a multi-objective evolutionary algorithm is adopted to calculate the low-friction design model of the planetary roller screw, and optimal solutions and corresponding structure design parameters are obtained.

Description

Technical Field

[0001] This invention belongs to the field of mechanical design technology, and specifically relates to a low-friction design method for planetary roller screws. Background Technology

[0002] Planetary roller screws are a new generation of high-performance linear transmission mechanisms developed after traditional trapezoidal screws and ball screws. Through the simultaneous meshing of multiple rollers, planetary roller screws offer higher load-bearing capacity, longer service life, and superior motion accuracy and stability. Furthermore, this mechanism maintains excellent transmission performance and reliability even under high-speed, high-frequency reciprocating conditions. In recent years, planetary roller screws have been widely used in key linear actuators in fields such as artificial intelligence, precision CNC machine tools, new energy vehicles, and semiconductor processing equipment.

[0003] Planetary roller screws transmit power between the screw, rollers, and nut through the planetary motion of the rollers. Due to their structural characteristics, relative slippage is unavoidable at the threaded meshing interface. Higher slippage speeds increase frictional power consumption and accelerate surface wear, leading to decreased transmission efficiency and premature wear failure; conversely, higher entrainment speeds help form a fluid lubrication film, thereby reducing friction and wear. The slip-roll ratio, defined as the ratio of slippage speed to entrainment speed, is a key tribological parameter characterizing the relative motion state of the contact pair. A smaller slip-roll ratio implies superior tribological performance. Therefore, reducing the slip-roll ratio at the meshing interface is a core optimization direction for improving the transmission efficiency and service life of planetary roller screws.

[0004] However, existing planetary roller screw design methods mostly focus on improving load-bearing capacity, significantly lacking specific design methods for low-friction performance. Furthermore, the mapping law of various structural parameters and their coupling effects on the tribological performance of planetary roller screws is still unclear, resulting in a lack of effective low-friction design criteria and theoretical guidance in the industry. Therefore, developing a low-friction design method for planetary roller screws can not only improve their tribological performance from the source but also provide a scientific basis for high-performance structural design, possessing significant engineering application value and theoretical significance.

[0005] Based on the above background, this invention proposes a low-friction design method for planetary roller screws. This method aims to minimize the slip-roll ratio of the threaded meshing pair. Under the condition of satisfying structural constraints, it uses a multi-objective evolutionary algorithm to perform global optimization design on the key structural parameters of the planetary roller screw, thereby obtaining optimal structural parameters with excellent tribological performance. This invention enables the low-friction design of planetary roller screws, thereby significantly improving their transmission efficiency and service life. Summary of the Invention

[0006] This invention provides a low-friction design method for planetary roller screws, which addresses the technical problem of the lack of tribological performance quantification methods and optimization paths in existing design technologies.

[0007] To achieve the above objectives, the present invention is implemented through the following technical solution: A low-friction design method for planetary roller screws includes the following steps: Step 1: Establish the solution model and kinematic model for the contact point of the planetary roller screw, and solve for the sliding speed and entrainment speed of the screw-roller and roller-nut contact pairs at the contact point; Step 2: Based on the definition of slip ratio, establish a calculation model for the slip ratio of the screw-roller and roller-nut contact pairs of the planetary roller screw; Step 3: Establish structural constraints based on the requirements for correct movement and meshing of the planetary roller screw; Step 4: Taking the minimization of the slip ratio of the screw-roller and roller-nut contact pairs as the optimization objective, and combining the structural constraints, establish a low-friction design model for the planetary roller screw. Step 5: Use a multi-objective evolutionary algorithm to calculate the low-friction design model of the planetary roller screw, and obtain the optimal solution and the corresponding structural design parameters.

[0008] Furthermore, in step 1, the contact point coordinates are solved by the equation of the equality of the normal vectors of the contact pairs of the screw-roller and roller-nut contact pairs and the geometric relationship equation. The contact point coordinates are then substituted into the kinematic model to obtain the relative surface velocity, and thus the sliding velocity and the suction velocity are obtained.

[0009] Furthermore, the structural constraints described in step 3 include no relative axial motion constraints between the roller and the nut, concentric constraints between the threaded pair and the gear pair, and meshing constraints where the contact point is located between the major and minor diameters of the thread and a preset clearance is provided.

[0010] Furthermore, the structural design parameters to be optimized in step 4 include the screw thread flank angle, roller thread flank angle, nut thread flank angle, thread pitch, screw nominal radius, and screw thread number.

[0011] Furthermore, the optimal solution mentioned in step 5 is the solution corresponding to the minimum slip ratio of both the lead screw-roller and roller-nut contact pairs, or the solution that is closest to the origin of the coordinate system among the non-dominated solutions.

[0012] Furthermore, the optimal solution has a roller-nut side slip ratio approaching zero, and a screw-roller side slip ratio significantly reduced relative to the design reference point.

[0013] Furthermore, the sliding-rolling ratio is the ratio of sliding speed to suction speed, used to quantify the tribological properties of the planetary roller screw.

[0014] This invention provides a low-friction design method for planetary roller screws, with the following advantages: by reducing the slip ratio of the planetary roller screw thread pair, optimal tribological design is achieved, improving transmission efficiency and extending service life; by globally designing the multi-dimensional structural parameters of the planetary roller screw, the coupling optimization of the slip ratio of the screw-roller and roller-nut contact pairs is realized, ensuring optimal overall performance; by using the slip ratio to quantify tribological performance, the frictional performance of the thread pair is accurately characterized, avoiding complex nonlinear friction calculations, and combining representativeness with high design efficiency. Attached Figure Description

[0015] 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.

[0016] Figure 1 A schematic flowchart illustrating a low-friction design method for a planetary roller screw provided in an embodiment of the present invention; Figure 2 This is a schematic diagram of the non-dominated solution, optimal solution, and design reference point roll ratio obtained from the calculations provided in the embodiments of the present invention. Detailed Implementation

[0017] The embodiments of this application will now be described in detail with reference to the accompanying drawings.

[0018] Example: This embodiment provides a low-friction design method for planetary roller screws, including the following steps: establishing a solution model and kinematic model for the contact point position of the planetary roller screw, and solving for the sliding velocity and entrainment velocity of the screw-roller and roller-nut contact pairs at the contact points; establishing a calculation model for the sliding-roller ratio of the screw-roller and roller-nut contact pairs of the planetary roller screw based on the definition of the sliding-roller ratio; establishing structural constraints based on the requirements for correct movement and meshing of the planetary roller screw; establishing a low-friction design model for the planetary roller screw with the minimization of the sliding-roller ratio of the screw-roller and roller-nut contact pairs as the optimization objective, combined with the structural constraints; and using a multi-objective evolutionary algorithm to calculate the low-friction design model of the planetary roller screw, obtaining the optimal solution and the corresponding structural design parameters.

[0019] In this embodiment, the specific design process steps are as follows: Step S1: Establish the solution model and kinematic model for the contact point of the planetary roller screw, and solve for the sliding speed and coiling speed of the screw-roller and roller-nut contact pairs at the contact point. Step S2: Calculate the slip ratio of the screw-roller and roller-nut contact pairs of the planetary roller screw according to the definition of slip ratio; Step S3: Establish structural constraints based on the requirements for correct movement and meshing of the planetary roller screw; Step S4: With minimizing the slip-roll ratio as the optimization objective, and in conjunction with structural constraints, establish a low-friction design model for the planetary roller screw. Step S5: Use a multi-objective evolutionary algorithm to solve the low-friction design model of the planetary roller screw, and obtain the optimal solution and the corresponding structural design parameters.

[0020] Furthermore, by solving the geometric relationship equation that the normal vectors of the screw-roller and roller-nut contact pairs are equal to the surface normal vectors, the coordinates of the contact point position are obtained. Substituting the coordinates of the contact point position into the kinematic model, the relative surface velocity is obtained, and then the sliding velocity and the suction velocity are obtained.

[0021] In this embodiment, the coordinates of the contact point are obtained by solving the equations relating the equality of the normal vectors of the contact pair surfaces and the geometric relationship. The coordinates are then substituted into the kinematic model to obtain the relative surface velocity, and finally the sliding velocity and the entrainment velocity are calculated.

[0022] Furthermore, the structural constraints include no relative axial motion constraint between the roller and the nut, concentric constraint between the threaded pair and the gear pair, and meshing constraint where the contact point is located between the major and minor diameters of the thread and a preset clearance is provided.

[0023] In this embodiment, structural constraints are used to ensure the correct movement and meshing of the planetary roller screw, ensuring that there is no relative axial movement between the roller and the nut, that the threaded pair and the gear pair are concentric, and that the contact point is located in the effective meshing area of ​​the thread.

[0024] Furthermore, the structural design parameters to be optimized include the lead screw thread flank angle, roller thread flank angle, nut thread flank angle, thread pitch, lead screw nominal radius, and number of lead screw thread starts.

[0025] In this embodiment, the above-mentioned structural parameters are selected as the parameters to be optimized, and the optimization design is carried out with the goal of minimizing the roll-slip ratio.

[0026] Furthermore, the optimal solution is the solution corresponding to the minimum slip ratio of both the lead screw-roller and roller-nut contact pairs, or the solution that is closest to the origin of the coordinate system among the non-dominated solutions.

[0027] Furthermore, the optimal solution approaches zero on the roller-nut side slip ratio, and the screw-roller side slip ratio is significantly reduced relative to the design reference point.

[0028] In this embodiment, the design reference point is the midpoint of the design variable range.

[0029] Furthermore, the sliding-rolling ratio is the ratio of sliding speed to suction speed, used to quantify the tribological properties of the planetary roller screw.

[0030] In this embodiment, the tribological performance is quantified by the slip-roll ratio, with a smaller slip-roll ratio representing better tribological performance.

[0031] The implementation process of the above-mentioned low-friction design method for planetary roller screws is as follows: Figure 1 As shown, firstly, a solution model and kinematic model for the contact point position of the planetary roller screw are established to solve for the sliding velocity and entrainment velocity of the screw-roller and roller-nut contact pairs at the contact points. Next, based on the definition of the slip-roll ratio, a calculation model for the slip-roll ratio of the screw-roller and roller-nut contact pairs of the planetary roller screw is established. Then, based on the requirements for correct movement and meshing of the planetary roller screw, structural constraints are established. Then, with minimizing the slip-roll ratio as the optimization objective, combined with the structural constraints, a low-friction design model for the planetary roller screw is established. Finally, a multi-objective evolutionary algorithm is used to calculate the low-friction design model of the planetary roller screw, obtaining the optimal solution and the corresponding structural design parameters, thereby improving the tribological performance of the planetary roller screw. The specific implementation steps of the low-friction design method for planetary roller screws are as follows: Step 1: Establish the solution model and kinematic model for the contact point of the planetary roller screw, and solve for the sliding speed and coiling speed of the screw-roller and roller-nut contact pairs at the contact point.

[0032] The model for determining the contact point location of a planetary roller screw is expressed as follows: At the contact point, the normal vectors of the thread surfaces of the screw-roller and roller-nut contact pairs are equal and satisfy the following geometric relationship, as shown below: ; ; In the formula , , and These represent the surface normal vectors of the lead screw, roller lead screw side, roller nut side, and nut thread, respectively. rc S , θc S ), ( rc RS , θc RS ), ( rc RN , θc RN ) and( rc N , θc NThe coordinates of the contact points on the lead screw, roller lead screw side, roller nut side, and nut side are respectively represented. d This represents the distance between the center of the leadscrew and the roller shaft. Solving the equation will yield the coordinates of the contact point.

[0033] Based on the principle of planetary roller screw transmission, a kinematic model of the planetary roller screw is established. Substituting the obtained contact point coordinates into the following kinematic expression, the relative surface velocities of the screw-roller and roller-nut at the contact point are obtained, expressed as: ; In the formula , and These represent the contact points respectively. I The relative speeds of the lead screw relative to the cage, the rollers relative to the cage, and the cage relative to the nut. and These represent the contact points respectively. J The relative speeds of the rollers relative to the cage and the nuts relative to the cage. This indicates the relative velocity of the nut with respect to a fixed reference frame. ω S / H , ω R / H , ω N / H These represent the rotational speeds of the lead screw, rollers, and nut relative to the cage, respectively. ω S / N This indicates the input speed of the leadscrew. L S Indicates the lead of the leadscrew. Superscript I and J These represent the contact points of the lead screw-roller and the roller-nut, respectively.

[0034] The sliding speed and coiling speed of the lead screw-roller and roller-nut contact pairs at the contact point are further obtained, and are expressed as follows: ; ; In the formula and These represent the lead screw-roller contact points, respectively. I roller-nut contact point J The sliding speed at that point. and These represent the lead screw-roller contact points, respectively. I roller-nut contact point J The suction speed at that location.

[0035] Step 2: Based on the definition of slip ratio, calculate the slip ratio of the screw-roller and roller-nut contact pairs of the planetary roller screw, expressed as: ; In the formula γ SR and γ NR This indicates the slip ratio of the lead screw-roller and roller-nut contact pairs.

[0036] Step 3: Establish structural constraints based on the requirements for correct movement and meshing of the planetary roller screw.

[0037] To ensure that there is no relative axial movement between the roller and the nut, the constraint equations must be satisfied. fc 1 and fc 2. To ensure the concentricity of the threaded pair and the gear pair, the constraint equations must be satisfied. fc 3, represented as ; In the formula n S and n N This indicates the number of thread turns in the lead screw and nut. r S0 , r R0 and r N0 Indicates the nominal radius of the thread of the lead screw, roller, and nut.

[0038] Furthermore, to ensure proper meshing of the planetary roller screw's screw-roller and roller-nut threaded pairs, the contact point should be located between the major and minor diameters of the thread, with a pre-set clearance, denoted as... ; In the formula fc 4 and fc 5 represents the constraint equation for the screw engagement point located within the minor and major diameter regions of the screw. fc 6 and fc 7 represents the constraint equation for the side meshing point of the roller screw located within the minor and major diameter regions of the roller. fc 8 and fc 9 represents the constraint equation for the roller nut side engagement point located within the minor and major diameter regions of the roller. fc 10 and fc 11 The constraint equations represent the nut engagement points located within the minor and major diameter regions of the nut. r S1 , r R1 and rN1 This indicates the minor diameter of the threads in lead screws, rollers, and nuts. r S2 , r R2 and r N2 Indicates the major diameter of the thread in lead screws, rollers, and nuts. rc S , rc N , rc RS and rc RN This indicates the contact radius of the lead screw, nut, roller lead screw contact side, and nut contact side. δ This indicates that a gap has been reserved, and δ =0.25 mm.

[0039] Step 4: With minimizing the slip-roll ratio as the optimization objective, and in conjunction with structural constraints, establish a low-friction design model for the planetary roller screw.

[0040] The main structural parameter set x of the planetary roller screw is selected as the structural parameter to be optimized, including the screw thread flank angle. β S Roller thread side angle β R nut thread side angle β N Thread pitch P Nominal radius of the lead screw r S0 and the number of threads on the lead screw n S With minimizing the slip ratio of the screw-roller and roller-nut contact pairs as the optimization objective, and based on structural constraints, a low-friction design model for the planetary roller screw is established, expressed as follows: ; In the formula and This indicates the slip ratio of the lead screw-roller and roller-nut contact pairs under structural parameter x.

[0041] Step 5: Use a multi-objective evolutionary algorithm to solve the low-friction design model of the planetary roller screw, and obtain the optimal solution and the corresponding structural design parameters.

[0042] The above steps achieve a low-friction design for the planetary roller screw. The non-dominated solution calculated by the low-friction design method proposed in this invention is as follows: Figure 2 As shown. The solution or non-dominated solution that is closest to the origin of the coordinate system when the slip ratio of both the lead screw-roller and roller-nut contact pairs is simultaneously minimized is taken as the optimal solution for low friction design. The structural parameters corresponding to the optimal solution are the optimal structural design parameters.

[0043] To verify the advancement of the method of this invention, the midpoint of the range of design variable values ​​was selected as the design reference point for comparative analysis. The results show that the optimal solution obtained by the low-friction planetary roller screw design method proposed in this invention, and the slip ratio relative to the design reference point, both approach zero on the roller-nut side. On the screw-roller side, the slip ratio is significantly reduced by 47.52% relative to the design reference point. This demonstrates that the low-friction planetary roller screw design method proposed in this invention can significantly reduce the slip ratio of the planetary roller screw thread contact pair, improving the tribological performance of the transmission system from a structural perspective, and has significant engineering value for improving transmission efficiency and extending service life.

[0044] In summary, this invention achieves precise quantification of tribological performance by establishing a contact point location solution model, a kinematic model, and a slip-roll ratio calculation model; it achieves global optimization of multi-dimensional structural parameters by establishing structural constraints and a low-friction design model; it achieves simultaneous optimal design of the slip-roll ratio of the dual contact pairs by solving for the optimal solution through a multi-objective evolutionary algorithm; and it improves tribological performance from the structural source by minimizing the slip-roll ratio, ultimately enhancing the transmission efficiency and service life of the planetary roller screw.

Claims

1. A low-friction design method for planetary roller screws, characterized in that, Includes the following steps: Step 1: Establish the solution model and kinematic model for the contact point of the planetary roller screw, and solve for the sliding speed and entrainment speed of the screw-roller and roller-nut contact pairs at the contact point; Step 2: Based on the definition of slip ratio, establish a calculation model for the slip ratio of the screw-roller and roller-nut contact pairs of the planetary roller screw; Step 3: Establish structural constraints based on the requirements for correct movement and meshing of the planetary roller screw; Step 4: Taking the minimization of the slip ratio of the screw-roller and roller-nut contact pairs as the optimization objective, and combining the structural constraints, establish a low-friction design model for the planetary roller screw. Step 5: Use a multi-objective evolutionary algorithm to calculate the low-friction design model of the planetary roller screw, and obtain the optimal solution and the corresponding structural design parameters.

2. The low-friction design method for planetary roller screws according to claim 1, characterized in that, In step 1, the contact point coordinates are solved by the equation of the equality of the normal vectors of the contact pairs of the screw-roller and the roller-nut and the geometric relationship. The contact point coordinates are then substituted into the kinematic model to obtain the relative surface velocity, and then the sliding velocity and the suction velocity are obtained.

3. The low-friction design method for planetary roller screws according to claim 1, characterized in that, The structural constraints described in step 3 include no relative axial motion constraints between the roller and the nut, concentric constraints between the threaded pair and the gear pair, and meshing constraints where the contact point is located between the major and minor diameters of the thread and a preset clearance is provided.

4. The low-friction design method for planetary roller screws according to claim 1, characterized in that, In step 4, the structural design parameters corresponding to minimizing the slip ratio of the screw-roller and roller-nut contact pairs as the optimization objective include the screw thread flank angle, roller thread flank angle, nut thread flank angle, thread pitch, screw nominal radius, and screw thread number.

5. The low-friction design method for planetary roller screws according to claim 1, characterized in that, The optimal solution mentioned in step 5 is the solution corresponding to the minimum slip ratio of both the lead screw-roller and roller-nut contact pairs, or the solution that is closest to the origin of the coordinate system among the non-dominated solutions.

6. The low-friction design method for planetary roller screws according to claim 5, characterized in that, The slip-roll ratio is the ratio of the sliding speed to the suction speed, and is used to quantify the tribological properties of the planetary roller screw.

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