Method for calculating friction torque of planetary roller screw pair

Abstract

The application discloses a kind of calculation methods of friction torque of planetary roller screw pair, comprising: establishing roller thread load distribution model;Solving the contact characteristic index of planetary roller screw pair;Calculate the elastic hysteresis friction torque caused by elastic deformation hysteresis before and after rigid body loading and unloading;Calculate the spin slip friction torque caused by the fact that the actual rotation axis of roller is not perpendicular to the common normal of contact surface;Calculate the differential slip friction caused by the relative sliding between screw, roller and nut;Calculate the lubricant viscous friction torque caused by the surface viscous force of lubricant;Iterate the above friction torque to obtain the friction torque of the whole planetary roller screw pair.The thread load distribution law and contact characteristics of the planetary roller screw pair can effectively and accurately derive each part friction torque, which can effectively improve the transmission efficiency of the planetary roller screw pair, and has guiding significance for the parameter design of the planetary roller screw pair.

Description

Technical Field

[0001] This invention belongs to the field of planetary roller screw transmission performance, and in particular, it is a method for calculating the frictional torque of a planetary roller screw pair. Background Technology

[0002] Planetary roller screw pairs are mechanical transmission devices that can convert linear motion into rotational motion, possessing combined characteristics of threaded transmission and rolling helical transmission. Compared to ball screw drives, its rolling elements are not multiple spheres, but multiple threaded rollers, increasing the number of contact points in the transmission unit and thus increasing the load-bearing capacity of the transmission device. The frictional torque of a planetary roller screw pair refers to the resistance torque constituted by all frictional factors that hinder the movement of the rollers within the contact raceway between the screw and nut during the helical transmission process. It is a crucial technical indicator for evaluating the performance of planetary roller screw pairs, and its magnitude directly affects the energy loss of the planetary roller screw pair, thus leading to a decrease in transmission efficiency. Therefore, it is essential to develop a method for calculating the frictional torque of planetary roller screw pairs.

[0003] The frictional torque of a planetary roller screw pair is affected by many factors, including its design parameters, materials, operating conditions, and lubrication, resulting in its complexity and randomness. Therefore, only by thoroughly studying its generation mechanism and identifying its main influencing factors can its precise value be accurately calculated, providing a reference for the structural optimization design of planetary roller screws. Summary of the Invention

[0004] The purpose of this invention is to address the problem of complex and random influencing factors of friction torque in planetary roller screw pairs by proposing a method for calculating the friction torque of planetary roller screw pairs.

[0005] The technical solution to achieve the objective of this invention is: a method for calculating the frictional torque of a planetary roller screw pair, the method comprising the following steps:

[0006] Step 1: Establish a load distribution model for the roller thread teeth by analyzing the stress states of the lead screw, rollers, and nut.

[0007] Step 2: Solve the contact characteristic index of the planetary roller screw pair based on Hertzian contact theory;

[0008] Step 3: Calculate the elastic hysteresis friction torque caused by the elastic deformation hysteresis before and after rigid body loading and unloading;

[0009] Step 4: Calculate the spin sliding friction torque caused by the roller's actual rotation axis not being perpendicular to the common normal of the contact surface;

[0010] Step 5: Calculate the differential sliding friction torque caused by the relative sliding between the lead screw, rollers, and nut;

[0011] Step 6: Calculate the viscous friction torque of the lubricant caused by the surface viscosity of the lubricant;

[0012] Step 7: Iterate through the above frictional torques to obtain the frictional torque of the entire planetary roller screw pair.

[0013] Furthermore, in step 1, the roller thread tooth load distribution model on the leadscrew side is as follows:

[0014] F ai =F i cosαcosβ

[0015] F ti =F i cosαsinβ

[0016] F ri =F i sinα

[0017]

[0018]

[0019] Under external load F, F ai F ri F ti These represent the axial, radial, and tangential forces on the leadscrew side of any roller thread tooth; α is the roller thread profile angle; β is the roller thread helix angle; n is the number of rollers; p is the roller thread pitch; A s A represents the effective contact area of ​​the lead screw. n E represents the effective contact area of ​​the nut. sr C represents the equivalent elastic modulus of the lead screw and rollers. s For lead screw stiffness; C n z represents the stiffness of the nut; z represents the number of threads on the roller thread.

[0020] On the nut side, the roller thread tooth load distribution model is the same as above; simply replace the screw parameters with the nut parameters.

[0021] Furthermore, in step 2, according to Hertz contact theory, under axial load, an elliptical contact area will be formed between each pair of rollers and screw raceways, and between rollers and nut raceways, and the stress at each point in the contact area follows a semi-ellipsoidal distribution.

[0022] The first and second principal curvature radii ρ of the contact area between the lead screw and the roller side s11 ρ s12 ρ s21 ρ s22Principal curvature and ∑ρ s The first and second principal curvature radii ρ of the contact area between the nut and the roller side n11 ρ n12 ρ n21 ρ n22 Principal curvature and ∑ρ n They are respectively:

[0023]

[0024]

[0025] ∑ρ s =ρ s11 +ρ s12 +ρ s21 +ρ s22

[0026] ∑ρ n =ρ n11 +ρ n12 +ρ n21 +ρ n22

[0027] Among them, R r Let the radius be the equivalent sphere radius of the roller. l r For roller lead; l s For the lead screw; l n For nut lead; d r d is the pitch diameter of the roller; s d is the lead screw pitch diameter; n The mean diameter of the nut;

[0028] The length of the semi-ellipse of the contact area between the lead screw and the roller is a. s , length of the short semi-axis b s The semi-elliptical length a of the contact area between the nut and the roller n , length of the short semi-axis b n They are respectively:

[0029]

[0030]

[0031]

[0032]

[0033] In the formula, m as m is the eccentricity coefficient of the semi-major axis of the lead screw ellipse. bs m is the eccentricity coefficient of the minor semi-axis of the lead screw ellipse. an m is the eccentricity coefficient of the semi-major axis of the nut ellipse. bnE(k) is the eccentricity coefficient of the minor semi-axis of the nut ellipse. 2 ) represents a complete elliptic integral of the second kind; k s The elliptic eccentricity of the lead screw; k n The elliptic eccentricity of the nut; Poisson's ratio of the lead screw material; μ r Poisson's ratio for the roller material; μ n E represents the Poisson's ratio of the nut material. s E represents the elastic modulus of the lead screw material. r E represents the elastic modulus of the roller material. n The elastic modulus of the nut material;

[0034] The contact stress σ at any point in the contact area between the lead screw and the roller s (x,y), the contact stress σ at any point in the contact area between the nut and the roller. n (x, y) are respectively:

[0035]

[0036]

[0037] Furthermore, in step 3, the elastic hysteresis friction torque M is caused by the elastic deformation hysteresis before and after the rigid body loading and unloading. esi M eni for:

[0038]

[0039]

[0040] In the formula, γ is the material energy loss coefficient.

[0041] Furthermore, step 4 specifically involves:

[0042] Based on the stress distribution law at any point on the contact elliptical surface in step 2, the frictional force generated by the spin motion at that point is calculated as dF. s =f s σ(x,y)dxdy;

[0043] By integrating over a single contact area, the frictional torque M caused by spin sliding in the roller-screw and roller-nut contact areas is obtained. bsi and M bni They are respectively:

[0044]

[0045]

[0046] In the formula, f srf is the coefficient of sliding friction between the lead screw and the roller. nr The coefficient of sliding friction between the nut and the roller.

[0047] Furthermore, in step 5, the differential sliding friction torque M of the planetary roller screw is calculated according to the rolling bearing analysis method. dsi and M dni for:

[0048]

[0049]

[0050] In the formula, f s f n This is the curvature coefficient of the raceway of the lead screw and nut, which is usually taken between 0.515 and 0.54.

[0051] Furthermore, in step 6, the viscous friction torque M of the lubricant caused by the surface viscosity of the lubricant... vsi M vni for:

[0052]

[0053]

[0054] In the formula, E sr E represents the equivalent elastic modulus of the lead screw and rollers. nr ρ is the equivalent elastic modulus of the lead screw and rollers. xs ρ is the equivalent radius of curvature in the x-direction of the roller screw side. xn Equivalent radius of curvature in the x-direction of the roller nut side; ρ s The ratio of the equivalent radius of curvature on the roller screw side; ρ n The ratio of the radius of curvature of the nut and lead screw sides; G s U s W s G represents the dimensionless parameters of the roller screw side material, speed, and load. n U n W n The dimensionless parameters of material, speed, and load on the nut and screw side are calculated as follows:

[0055]

[0056]

[0057]

[0058] G s =E sr α p Gn =E nr α p ;

[0059]

[0060]

[0061]

[0062] In the formula, ρ ys Let ρ be the equivalent radius of curvature in the y-direction of the roller screw side. yn Let α be the equivalent radius of curvature in the y-direction on the side of the roller nut. p η0 is the viscosity-pressure coefficient of the lubricant; η0 is the dynamic viscosity of the lubricant; v0 t This represents the tangential velocity of the roller in the raceway.

[0063] Further, step 7 iterates through the above frictional torque to obtain the frictional torque of the entire planetary roller screw pair, specifically as follows:

[0064] Iterate through the above frictional torques to obtain the frictional torque M between the roller and the lead screw. s The frictional torque M between the roller and the nut n They are respectively:

[0065]

[0066]

[0067] The frictional torque M of the entire planetary roller screw pair is:

[0068] M = M s +M n

[0069] Compared with the prior art, the significant advantages of this invention are:

[0070] 1) Based on the uneven load distribution of the reference thread, and considering the stress conditions of the roller thread teeth, parameters such as the thread profile angle and helix angle are comprehensively considered. The axial load on each thread tooth is calculated by iterative normal force formula for each thread tooth, and the summation equals the external load. This mathematical relationship allows for a more accurate calculation of the normal force on each thread tooth, facilitating the subsequent calculation of various friction torques.

[0071] 2) Based on Hertzian contact theory, the principal curvature, major semi-axis length, and minor semi-axis length of each elliptical contact region are calculated when the lead screw, roller, and nut undergo elastic deformation under external load, which facilitates the subsequent calculation of each friction torque.

[0072] 3) The method proposed in this invention first divides the frictional torque into two parts: the frictional torque on the screw and roller sides, and the frictional torque on the nut and roller sides. Second, taking full account of the motion of the planetary roller screw pair, the two parts of frictional torque are further divided into four parts: elastic hysteresis frictional torque, spin sliding frictional torque, differential sliding frictional torque, and lubricant viscous frictional torque. Finally, based on an accurate thread load distribution model and the parameters of the Hertzian contact ellipse, the frictional torque of the planetary roller screw pair is calculated iteratively. This process comprehensively considers the force and motion of the thread teeth, and the calculation results of the frictional torque are very accurate and reliable.

[0073] The present invention will now be described in further detail with reference to the accompanying drawings. Attached Figure Description

[0074] Figure 1 This is a flowchart illustrating the calculation method for the frictional torque of a planetary roller screw pair.

[0075] Figure 2 This is a schematic diagram of the contact force between the lead screw and the roller.

[0076] Figure 3 The planetary roller screw has an elliptical contact ellipse.

[0077] Figure 4 This is a curve showing the axial loading deformation of a planetary roller screw.

[0078] Figure 5 This is a diagram showing the load distribution of the roller thread in an embodiment of the present invention. Detailed Implementation

[0079] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0080] In one embodiment, combined Figure 1 A method for calculating the frictional torque of a planetary roller screw pair is provided, the method comprising the following steps:

[0081] A load distribution model for the roller thread teeth is established by considering the force states of the lead screw, rollers, and nut; during the motion of the planetary roller lead screw, the axial force F on any roller thread tooth on the lead screw side is... ai Radial force F ri and tangential force F ti Force analysis under external load F is as follows: Figure 2 As shown:

[0082] F ai =F i cosαcosβ

[0083] F ti =F i cosαsinβ

[0084] F ri =F i sinα

[0085]

[0086]

[0087] Under external load F, F ai F ri F ti These represent the axial, radial, and tangential forces on the leadscrew side of any roller thread tooth; α is the roller thread profile angle; β is the roller thread helix angle; n is the number of rollers; p is the roller thread pitch; A s A represents the effective contact area of ​​the lead screw. n E represents the effective contact area of ​​the nut. sr C represents the equivalent elastic modulus of the lead screw and rollers. s For lead screw stiffness; C n z represents the stiffness of the nut; z represents the number of threads on the roller thread.

[0088] On the nut side, the roller thread tooth load distribution model is the same as above; simply replace the screw parameters with the nut parameters.

[0089] According to Hertzian contact theory, under axial load, a contact gap will form between each pair of rollers and screw raceways, and between rollers and nut raceways. Figure 3 The elliptical contact region is shown, and the stress at each point on the contact region follows the order as follows: Figure 4 The distribution shown is semi-ellipsoidal.

[0090] The first and second principal curvature radii ρ of the contact area between the lead screw and the roller side s11 ρ s12 ρ s21 ρ s22 Principal curvature and ∑ρ s The first and second principal curvature radii ρ of the contact area between the nut and the roller side n11 ρ n12 ρ n21 ρ n22 Principal curvature and ∑ρ n They are respectively:

[0091]

[0092]

[0093] ∑ρ s =ρs11 +ρ s12 +ρ s21 +ρ s22

[0094] ∑ρ n =ρ n11 +ρ n12 +ρ n21 +ρ n22

[0095] Among them, R r Let the radius be the equivalent sphere radius of the roller. l r For roller lead; l s For the lead screw; l n For nut lead; d r d is the pitch diameter of the roller; s d is the lead screw pitch diameter; n The mean diameter of the nut;

[0096] The length of the semi-ellipse of the contact area between the lead screw and the roller is a. s , length of the short semi-axis b s The semi-elliptical length a of the contact area between the nut and the roller n , length of the short semi-axis b n They are respectively:

[0097]

[0098]

[0099]

[0100]

[0101] In the formula, m as m is the eccentricity coefficient of the semi-major axis of the lead screw ellipse. bs m is the eccentricity coefficient of the minor semi-axis of the lead screw ellipse. an m is the eccentricity coefficient of the semi-major axis of the nut ellipse. bn E(k) is the eccentricity coefficient of the minor semi-axis of the nut ellipse. 2 ) represents a complete elliptic integral of the second kind; k s The elliptic eccentricity of the lead screw; k n The elliptic eccentricity of the nut; Poisson's ratio of the lead screw material; μ r Poisson's ratio for the roller material; μ n E represents the Poisson's ratio of the nut material. s E represents the elastic modulus of the lead screw material. r E represents the elastic modulus of the roller material. n The elastic modulus of the nut material;

[0102] The contact stress σ at any point in the contact area between the lead screw and the roller s (x,y), the contact stress σ at any point in the contact area between the nut and the roller. n (x, y) are respectively:

[0103]

[0104]

[0105] Because the roller undergoes a brief loading-unloading cycle when passing through the contact area. At the front of the contact area, the roller contacts and compresses with the raceway and begins to load and store energy. At the rear of the contact area, the roller contacts and separates from the raceway and begins to unload and release energy. However, the deformation caused by loading is actually less than that caused by unloading. Therefore, the energy of loading and compression is less than the energy of unloading and release, which causes energy loss. This is the elastic hysteresis friction that hinders the pure rolling of the roller.

[0106] Due to the relative motion of the rollers and leadscrew, the elliptical contact area constantly changes, making elastic hysteresis friction unavoidable. The frictional torque M caused by elastic hysteresis in the roller-leadscrew and roller-nut contact areas is... esi M eni They are respectively:

[0107]

[0108]

[0109] In the formula, γ is the material energy loss coefficient.

[0110] According to the theory of bearing friction torque analysis, both roller bearings and ball bearings with a contact angle greater than zero will experience spin sliding on the contact surface, resulting in a certain spin sliding torque. Based on the kinematic relationship of planetary roller screws, due to the presence of the thread profile angle and helix angle, the actual rotation axis of the roller is parallel to the screw axis and clearly not perpendicular to the common normal of the contact surface. Therefore, the roller's rotation is not pure rolling; while rolling along the screw raceway, it also spins around the common normal of the contact point, leading to spin sliding at the contact point and ultimately causing spin sliding friction greater than normal rolling friction.

[0111] Based on the stress distribution law at any point on the contact elliptical surface, the frictional force generated by the spin motion at that point is calculated as dF. s =f s σ(x,y)dxdy;

[0112] By integrating over a single contact area, the frictional torque M caused by spin sliding in the roller-screw and roller-nut contact areas is obtained. bsi and M bniThey are respectively:

[0113]

[0114]

[0115] In the formula, f sr f is the coefficient of sliding friction between the lead screw and the roller. nr The coefficient of sliding friction between the nut and the roller.

[0116] Since the rollers, nuts, and leadscrews are not perfectly rigid bodies, under the action of preload and external load, elastic contact deformation will occur when the rollers move in the threaded raceways of the nut and leadscrew, changing the contact area from point contact to surface contact. At any point in the contact area, the speeds of the rollers and leadscrews are not equal, resulting in relative sliding between them. The friction caused by this sliding is called differential sliding friction.

[0117] The friction is related to the size of the contact surface, the coefficient of friction of the contact materials, and the radius of curvature of the rollers at the contact point. The larger the contact area between the rollers and the screw thread raceway, the more pronounced the differential sliding friction. Based on the rolling bearing analysis method, the differential sliding friction torque M of the planetary roller screw is calculated. dsi and M dni for:

[0118]

[0119]

[0120] In the formula, f s f n This is the curvature coefficient of the raceway of the lead screw and nut, which is usually taken between 0.515 and 0.54.

[0121] Because planetary roller screw pairs operate under high-speed, heavy-load conditions, appropriate lubricant is required to reduce frictional resistance and wear. However, as operating time increases, temperature rise and torque gradually increase. Under external shear forces, the lubricant will experience internal frictional resistance deformation, thus forming fluid viscous forces that hinder the movement of the planetary roller screw pair and consequently affect the transmission efficiency of the entire transmission system. Therefore, the frictional torque caused by the surface viscosity of the lubricant must be considered.

[0122] This part consists of the viscous friction torque M caused by the surface viscosity of the lubricant. vsi M vni for:

[0123]

[0124]

[0125] In the formula, E sr E represents the equivalent elastic modulus of the lead screw and rollers. nr ρ is the equivalent elastic modulus of the lead screw and rollers. xs ρ is the equivalent radius of curvature in the x-direction of the roller screw side. xn Equivalent radius of curvature in the x-direction of the roller nut side; ρ s The ratio of the equivalent radius of curvature on the roller screw side; ρ n The ratio of the radius of curvature of the nut and lead screw sides; G s U s W s G represents the dimensionless parameters of the roller screw side material, speed, and load. n U n W n The dimensionless parameters of material, speed, and load on the nut and screw side are calculated as follows:

[0126]

[0127]

[0128]

[0129] G s =E sr α p G n =E nr α p ;

[0130]

[0131]

[0132]

[0133] In the formula, ρ ys Let ρ be the equivalent radius of curvature in the y-direction of the roller screw side. yn Let α be the equivalent radius of curvature in the y-direction on the side of the roller nut. p η0 is the viscosity-pressure coefficient of the lubricant; η0 is the dynamic viscosity of the lubricant; v0 t This represents the tangential velocity of the roller in the raceway.

[0134] Step 7: Iterate through the above frictional torques to obtain the frictional torque of the entire planetary roller screw pair.

[0135] Iterate through the above frictional torques to obtain the frictional torque M between the roller and the lead screw. s The frictional torque M between the roller and the nut n They are respectively:

[0136]

[0137]

[0138] The frictional torque M of the entire planetary roller screw pair is:

[0139] M = M s +M n .

[0140] In one embodiment, the invention will be further described in detail as a specific example.

[0141] The basic structural parameters of the planetary roller screw pair used in this embodiment are shown in Table 1, and other parameters used in the calculation process are shown in Table 2.

[0142] Table 1 Basic Parameters of Planetary Roller Screw Pairs

[0143] <![CDATA[Lead screw diameter d s > <![CDATA[Roller diameter d r > <![CDATA[Number of starts n of the lead screw s > Lead screw helix angle β 27mm 9mm 5 3.8° Pressure angle α Roller pitch p Number of rollers n Number of roller thread teeth z 45° 2mm 11 30

[0144] Table 2 Other parameters

[0145] <![CDATA[Equivalent elastic modulus E of ball screw rs > Poisson's ratio μ Material energy loss coefficient γ 210Gpa 0.27 0.008 coefficient of sliding friction f <![CDATA[Roller path curvature coefficient f s / f n > Load F 0.05 0.52 5800N

[0146] Based on the parameters in Tables 1 and 2, the calculation method of this invention is used to calculate the tooth load distribution of the roller thread, as follows: Figure 5 As shown in Table 3, the frictional torques of each part are as follows.

[0147] Table 3 Friction torque of each part

[0148]

[0149] In summary, the method for calculating the frictional torque of a planetary roller screw pair provided by this invention firstly determines the load distribution model of the screw, roller, and nut threads based on the stress conditions and deformation coordination of the planetary roller screw pair threads; secondly, it analyzes the stress distribution at the thread contact points and the basic parameters of the contact ellipse based on Hertzian contact theory; finally, considering the resistance encountered during the motion of the planetary roller screw pair, the frictional torque is divided into pure rolling frictional torque caused by material elastic hysteresis, spin sliding frictional torque caused by the self-rotation of the rollers around their own axis, differential sliding frictional torque caused by the elastic deformation of the contact surface, and viscous frictional torque caused by the viscous force of the lubricant surface. Among these, the viscous frictional torque fully considers various lubricant parameters, resulting in a more accurate result, and thus the overall frictional torque is more consistent with reality.

[0150] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely illustrative of the principles of the invention. Various changes and modifications can be made to the present invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the present invention as claimed.

Claims

1. A method for calculating the frictional torque of a planetary roller screw pair, characterized in that, The method includes the following steps: Step 1: Establish a load distribution model for the roller thread teeth by analyzing the stress states of the lead screw, rollers, and nut. Step 2: Solve the contact characteristic index of the planetary roller screw pair based on Hertzian contact theory; Step 3: Calculate the elastic hysteresis friction torque caused by the elastic deformation hysteresis before and after rigid body loading and unloading; Step 4: Calculate the spin sliding friction torque caused by the roller's actual rotation axis not being perpendicular to the common normal of the contact surface; Step 5: Calculate the differential sliding friction torque caused by the relative sliding between the lead screw, rollers, and nut; Step 6: Calculate the viscous friction torque of the lubricant caused by the surface viscosity of the lubricant; Step 7: Iterate through the above frictional torques to obtain the frictional torque of the entire planetary roller screw pair; In step 1, the roller thread tooth load distribution model on the leadscrew side is as follows: Under external load F, , , These represent the axial force, radial force, and tangential force on the lead screw side of any thread tooth of the roller; For roller thread tooth profile angle; The helix angle of the roller thread; The number of rollers; The pitch of the roller thread; This refers to the effective contact area of ​​the lead screw; This refers to the effective contact area of ​​the nut. This is the equivalent elastic modulus of the lead screw and rollers; For lead screw stiffness; z represents the stiffness of the nut; z represents the number of threads on the roller thread. On the nut side, the roller thread tooth load distribution model is the same as above; simply replace the screw parameters with the nut parameters. In step 2, according to Hertz contact theory, under axial load, an elliptical contact area will be formed between each pair of rollers and screw raceways, and between rollers and nut raceways, and the stress at each point in the contact area follows a semi-ellipsoidal distribution. The first and second principal curvature radii of the contact area between the lead screw and the roller side , , , Principal curvature and The first and second principal radii of curvature of the contact area between the nut and the roller side , , , Principal curvature and They are respectively: in, Let the radius be the equivalent sphere radius of the roller. ; For roller lead; For the lead screw; For the nut lead; The median diameter of the roller; The lead screw's mean diameter; The mean diameter of the nut; The length of the semi-elliptical semi-axis of the contact area between the lead screw and the roller , length of short half axis The semi-elliptical length of the contact area between the nut and the roller , length of short half axis They are respectively: In the formula, The eccentricity coefficient of the major semi-axis of the lead screw ellipse; The eccentricity coefficient of the minor semi-axis of the lead screw ellipse; The eccentricity coefficient of the major semi-axis of the nut ellipse; The eccentricity coefficient of the minor semi-axis of the nut ellipse; This is a complete elliptic integral of the second kind; The elliptic eccentricity of the lead screw; The elliptic eccentricity of the nut; Poisson's ratio of the lead screw material; Poisson's ratio for the roller material; Poisson's ratio of the nut material; The elastic modulus of the lead screw material; The elastic modulus of the roller material; The elastic modulus of the nut material; Contact stress at any point in the contact area between the lead screw and the roller The contact stress at any point in the contact area between the nut and the roller They are respectively: 。 2. The method for calculating the frictional torque of a planetary roller screw pair according to claim 1, characterized in that, In step 3, the frictional torque in the contact area between the roller-screw and the roller-nut is caused by elastic hysteresis. , They are respectively: In the formula, γ is the material energy loss coefficient.

3. The method for calculating the frictional torque of a planetary roller screw pair according to claim 2, characterized in that, Step 4 is as follows: Based on the stress distribution pattern at any point on the contact elliptical surface in step 2, the frictional force generated by the spin motion at that point is calculated as follows: ; By integrating over a single contact area, the frictional torque caused by spin sliding in the roller-screw and roller-nut contact areas is obtained. and They are respectively: In the formula, The coefficient of sliding friction between the lead screw and the roller is denoted as . The coefficient of sliding friction between the nut and the roller.

4. The method for calculating the frictional torque of a planetary roller screw pair according to claim 3, characterized in that, In step 5, the differential sliding friction torque of the planetary roller screw is calculated according to the rolling bearing analysis method. and for: In the formula, , The curvature coefficient of the raceway of the lead screw and nut is between 0.515 and 0.

54.

5. The method for calculating the frictional torque of a planetary roller screw pair according to claim 4, characterized in that, In step 6, the viscous friction torque of the lubricant is caused by the surface viscosity of the lubricant. , for: In the formula, This is the equivalent elastic modulus of the lead screw and rollers; This is the equivalent elastic modulus of the lead screw and rollers; The equivalent radius of curvature in the x-direction of the roller screw side; Equivalent radius of curvature in the x-direction on the side of the roller nut; The ratio of the equivalent radius of curvature on the roller screw side; The ratio of the radius of curvature of the nut and lead screw sides; The dimensions of the material, speed, and load on the roller screw side are provided. The dimensionless parameters of material, speed, and load on the nut and screw side are calculated as follows: In the formula, Let be the equivalent radius of curvature in the y-direction of the roller screw side. Let be the equivalent radius of curvature in the y-direction on the side of the roller nut. This refers to the viscosity-pressure coefficient of the lubricant. The dynamic viscosity of the lubricant; This represents the tangential velocity of the roller in the raceway.

6. The method for calculating the frictional torque of a planetary roller screw pair according to claim 5, characterized in that, Step 7 iterates through the above frictional torques to obtain the frictional torque of the entire planetary roller screw pair, specifically as follows: The frictional torque between the roller and the lead screw is obtained by iterating through the above frictional torque. Frictional torque between rollers and nuts They are respectively: The frictional torque of the entire planetary roller screw pair for: 。

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