CN115438438A - Method for calculating friction moment of planetary roller screw pair - Google Patents
Method for calculating friction moment of planetary roller screw pair Download PDFInfo
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Abstract
The invention discloses a method for calculating the friction moment of a planetary roller screw pair, which comprises the following steps: establishing a roller thread tooth load distribution model; solving the contact characteristic index of the planetary roller screw pair; calculating elastic hysteresis friction torque caused by elastic deformation hysteresis before and after rigid body loading and unloading; calculating the self-rotating sliding friction moment caused by the fact that the actual rotating axis of the roller is not perpendicular to the common normal line of the contact surface; calculating differential sliding friction due to relative sliding between the screw, the roller and the nut; calculating a lubricant viscous friction torque due to a surface viscous force of the lubricant; and iterating the friction torque to obtain the friction torque of the whole planetary roller screw pair. According to the invention, the friction torque of each part can be effectively and accurately deduced through the thread load distribution rule and the contact characteristic of the planetary roller screw pair, the transmission efficiency of the planetary roller screw pair can be effectively improved, and the method has guiding significance on parameter design of the planetary roller screw pair.
Description
Technical Field
The invention belongs to the field of transmission performance of a planetary roller screw pair, and particularly relates to a method for calculating friction moment of the planetary roller screw pair.
Background
The planetary roller screw pair is a mechanical transmission device capable of mutually converting linear motion and rotary motion, and has the comprehensive characteristics of screw transmission and rolling screw transmission. Compared with ball screw transmission, the rolling bodies of the ball screw transmission device are not a plurality of spheres but a plurality of rolling cylinders with threads, so that the number of contact points of the transmission unit is increased, and the bearing capacity of the transmission device is further increased. The friction torque of the planetary roller screw pair is resistance torque formed by all friction factors which hinder rollers from moving in a contact raceway of a screw and a nut in the process of screw transmission of the planetary roller screw pair, is an important technical index for evaluating the performance of the planetary roller screw pair, and directly influences the energy loss of the planetary roller screw pair by the size of the friction torque, so that the transmission efficiency of the planetary roller screw pair is reduced. Therefore, it is necessary to develop a method for calculating the friction torque of the planetary roller screw pair.
The friction torque of the planetary roller screw pair is influenced by a plurality of factors such as design parameters, materials, operating conditions, lubrication and the like, so that the planetary roller screw pair has complexity and randomness. Therefore, only by deeply researching the generation mechanism and finding out the main influence factors, the accurate numerical value can be accurately analyzed and calculated to analyze the main influence factors, and reference can be provided for the structure optimization design of the planetary roller screw.
Disclosure of Invention
The invention aims to provide a method for calculating the friction moment of a planetary roller screw pair, aiming at the problem that the influence factors of the friction moment of the planetary roller screw pair are complex and random.
The technical solution for realizing the purpose of the invention is as follows: a method of calculating the friction torque of a planetary roller screw pair, the method comprising the steps of:
step 1, establishing a roller thread tooth load distribution model through the stress states of a screw rod, a roller and a nut;
step 2, solving the contact characteristic index of the planetary roller screw pair based on the Hertz contact theory;
step 3, calculating elastic hysteresis friction torque caused by elastic deformation hysteresis before and after rigid body loading and unloading;
step 4, calculating the self-rotating sliding friction torque caused by the fact that the actual rotation axis of the roller is not perpendicular to the common normal line of the contact surface;
step 6, calculating the viscous friction torque of the lubricant caused by the surface viscous force of the lubricant;
and 7, iterating the friction torque to obtain the friction torque of the whole planetary roller screw pair.
Further, on the screw side in step 1, the roller thread load distribution model is as follows:
F ai ＝F i cosαcosβ
F ti ＝F i cosαsinβ
F ri ＝F i sinα
wherein, under an external load F, F ai 、F ri 、F ti Axial force, radial force and tangential force of any thread tooth of the roller at the side of the screw rod are respectively; alpha is a roller thread profile angle; beta is the screw lead angle of the roller thread; n is the number of the rollers; p is the thread pitch of the roller; a. The s Is the effective contact area of the lead screw; a. The n Is the effective contact area of the nut; e sr Equivalent modulus of elasticity for the screw and the roller; c s Is the screw stiffness; c n Is a nutA stiffness; z is the number of the thread teeth of the roller;
and on the nut side, replacing the screw parameters with the nut parameters by using the roller thread tooth load distribution model.
Further, according to the Hertz contact theory in the step 2, under the action of an axial load, an elliptical contact area is formed between the roller and the screw rod raceway as well as between the roller and the nut raceway, and the stress of each point on the contact area follows semi-ellipsoidal distribution;
first and second main curvature radiuses rho of contact area of lead screw and roller side s11 、ρ s12 、ρ s21 、ρ s22 Principal curvature and Σ ρ s First and second principal radii of curvature ρ of the nut in the contact region with the roller side n11 、ρ n12 、ρ n21 、ρ n22 Principal curvature and Σ ρ n Respectively is as follows:
∑ρ s ＝ρ s11 +ρ s12 +ρ s21 +ρ s22
∑ρ n ＝ρ n11 +ρ n12 +ρ n21 +ρ n22
wherein R is r Is the equivalent spherical radius of the roller,
l r is a roller lead; l s Is a lead screw lead; l n Is a nut lead; d r The pitch diameter of the roller; d s The middle diameter of the lead screw; d is a radical of n The pitch diameter of the nut;
the contact area of the screw rod and the roller has an elliptical long semi-axis length a s Minor semi-axis length b s The length of the semi-axis of the ellipse of the contact area between the nut and the roller n Minor semi-axis length b n Respectively is as follows:
in the formula, m as The eccentricity coefficient of the elliptic major axis and the elliptic minor axis of the lead screw; m is bs The eccentricity coefficient of the elliptic short semi-axis of the lead screw is obtained; m is an The eccentricity coefficient of the elliptic major semi-axis of the nut is shown; m is a unit of bn The eccentricity coefficient of the elliptic minor semi-axis of the nut is obtained; e (k) 2 ) Is a second type of complete elliptic integral; k is a radical of s The elliptical eccentricity of the lead screw; k is a radical of n Is the elliptical eccentricity of the nut;
the screw rod material Poisson's ratio; mu.s r Is the Poisson's ratio of the roller material; mu.s n The Poisson's ratio of the nut material; e s The elastic modulus of the lead screw material; e r The elastic modulus of the roller material; e n The elastic modulus of the nut material;
contact stress sigma corresponding to any point of contact area of screw and roller s (x, y) contact stress σ corresponding to any point of the contact area between the nut and the roller n (x, y) are respectively:
further, in step 3, elastic hysteresis friction torque M caused by elastic deformation hysteresis before and after rigid body loading and unloading esi 、M eni Comprises the following steps:
wherein γ is a material energy loss coefficient.
Further, step 4 specifically includes:
according to the stress distribution rule of any point of the contact ellipsoid in the step 2, the frictional force dF generated by the self-spinning motion of the point is obtained s ＝f s σ(x,y)dxdy；
By integrating over a single contact area, the friction torque M caused by the spin-slip in the contact area of roller-screw and roller-nut is determined bsi And M bni Respectively as follows:
in the formula, f sr Is the coefficient of sliding friction between the screw and the roller, f nr Is the coefficient of sliding friction between the nut and the roller.
Further, in step 5, the planetary roller screw differential sliding friction torque M is calculated according to the rolling bearing analysis method dsi And M dni Comprises the following steps:
in the formula (f) s 、f n The curvature coefficient of the screw rod and the nut raceway is usually between 0.515 and 0.54.
Further, in step 6, the lubricant viscous frictional torque M due to the surface viscous force of the lubricant vsi 、M vni Comprises the following steps:
in the formula, E sr Equivalent modulus of elasticity for the screw and the roller; e nr Equivalent modulus of elasticity for the screw and the roller; rho xs The equivalent curvature radius of the roller screw in the x direction is shown; ρ is a unit of a gradient xn The roller nut side x-direction equivalent curvature radius; rho s The equivalent curvature radius ratio of the roller screw side is obtained; rho n The equal idle curvature radius ratio of the nut and the screw rod side; g s 、U s 、W s Is the parameters of the material, speed and load on the side of the roller screw, G n 、U n 、W n The calculation method is that the parameters of the material, the speed and the load on the screw side of the nut are dimensionless, and comprises the following steps:
G s ＝E sr α p ；G n ＝E nr α p ；
in the formula, ρ ys Is the equivalent curvature radius, rho, of the roller screw side in the y direction yn Is the equivalent curvature radius, alpha, of the roller nut side in the y direction p Is the viscosity pressure coefficient of the lubricant; eta 0 Is the dynamic viscosity of the lubricant; v. of t Is the tangential velocity of the roller in the raceway.
Further, step 7 iterates the friction torque to obtain the friction torque of the whole planetary roller screw pair, specifically:
iterating the friction torque to obtain the friction torque M between the roller and the screw rod s Friction torque M between roller and nut n Respectively as follows:
the friction torque M of the whole planetary roller screw pair is:
M＝M s +M n
compared with the prior art, the invention has the remarkable advantages that:
1) According to the load distribution unevenness rule of the screw thread, parameters such as a thread profile angle and a helix angle are comprehensively considered according to the stress condition of the roller thread, the axial load borne by each thread is calculated through the iterative normal force formula of each thread, the mathematical relation of equal external load is accumulated, the normal force borne by each thread is more accurately calculated, and subsequent friction torque calculation is facilitated.
2) According to the Hertz contact theory, the principal curvature, the long semi-axis length and the short semi-axis length of each elliptical contact area are calculated when the screw rod, the roller and the nut are elastically deformed under the action of an external load, so that each subsequent friction torque can be conveniently calculated.
3) The method provided by the invention comprises the following steps of firstly, dividing friction torque into a screw rod and a roller side friction torque, and a nut and a roller side friction torque; secondly, the motion condition of the planetary roller screw pair is fully considered, and the two parts of friction torque are divided into four parts of elastic hysteresis friction torque, spinning sliding friction torque, differential sliding friction torque and lubricant viscous friction torque; and finally, on the basis of the accurate thread load distribution model and various parameters of the Hertz contact ellipse, the friction torque of the planetary roller screw pair is obtained through iterative calculation, the stress condition and the motion condition of the threads are comprehensively considered in the process, and the calculation result of the friction torque is very accurate and reliable.
The present invention is described in further detail below with reference to the attached drawing figures.
Drawings
FIG. 1 is a flow chart of a method for calculating the friction torque of a planetary roller screw pair.
FIG. 2 is a schematic view of the contact force of the screw and the roller.
Fig. 3 is a planetary roller screw contact ellipse.
FIG. 4 is a graph of axial loading deformation of a planetary roller screw.
FIG. 5 is a roller thread load profile for an embodiment of the present invention.
Detailed Description
The present application will be described in further detail below with reference to the accompanying drawings and embodiments in order to make the objects, technical solutions and advantages of the present application more apparent. It should be understood that the specific embodiments described herein are merely illustrative of and not restrictive on the broad application.
In one embodiment, in conjunction with fig. 1, there is provided a method of calculating a friction torque of a planetary roller screw pair, the method comprising the steps of:
establishing a roller thread tooth load distribution model through the stress states of the screw rod, the roller and the nut; in the motion process of the planetary roller screw, the axial force F of any thread tooth of the roller on the screw side ai Radial force F ri And tangential force F ti The force analysis under external load F is shown in fig. 2:
F ai ＝F i cosαcosβ
F ti ＝F i cosαsinβ
F ri ＝F i sinα
wherein, under an external load F, F ai 、F ri 、F ti Axial force, radial force and tangential force of any thread tooth of the roller at the screw rod side are respectively; alpha is a roller thread form angle; beta is the helix angle of the roller thread; n is the number of the rollers; p is the thread pitch of the roller; a. The s Is the effective contact area of the lead screw; a. The n Is the effective contact area of the nut; e sr Equivalent elastic modulus of the screw and the roller; c s Is the screw stiffness; c n Is the nut stiffness; z is the number of the screw threads of the roller;
and on the nut side, replacing the screw parameters with the nut parameters by using the roller thread tooth load distribution model.
According to the Hertz contact theory, under the action of axial load, an elliptical contact area is formed between the roller and the screw raceway and between the roller and the nut raceway, as shown in figure 3, and the stress of each point on the contact area is distributed in a semi-elliptical shape as shown in figure 4.
First and second main curvature radiuses rho of contact area of lead screw and roller side s11 、ρ s12 、ρ s21 、ρ s22 Principal curvature and Σ ρ s First and second principal radii of curvature ρ of the nut in the contact region with the roller side n11 、ρ n12 、ρ n21 、ρ n22 Principal curvature and Σ ρ n Respectively as follows:
∑ρ s ＝ρ s11 +ρ s12 +ρ s21 +ρ s22
∑ρ n ＝ρ n11 +ρ n12 +ρ n21 +ρ n22
wherein R is r Is the equivalent spherical radius of the roller,
l r is a roller lead; l s Is a lead screw lead; l n Is a nut lead; d is a radical of r The pitch diameter of the roller; d s The middle diameter of the lead screw; d n The pitch diameter of the nut;
the contact area of the screw rod and the roller has an elliptical long semi-axis length a s Minor semi-axis length b s The length a of the ellipse major and semiaxis of the contact area between the nut and the roller n Short semi-axis length b n Respectively is as follows:
in the formula, m as The eccentricity coefficient of the elliptic major axis and the elliptic minor axis of the lead screw; m is bs The eccentricity coefficient of the elliptic short semi-axis of the lead screw is obtained; m is an The eccentricity coefficient of the elliptic major semi-axis of the nut is set; m is bn The eccentricity coefficient of the elliptic minor semi-axis of the nut is obtained; e (k) 2 ) Is a second class of complete elliptic integral; k is a radical of s The elliptical eccentricity of the lead screw; k is a radical of formula n Is the elliptical eccentricity of the nut;
the screw rod material Poisson's ratio; mu.s r Is the Poisson's ratio of the roller material; mu.s n The Poisson's ratio of the nut material; e s The elastic modulus of the lead screw material; e r The elastic modulus of the roller material; e n The elastic modulus of the nut material;
contact stress sigma corresponding to any point of contact area of screw and roller s (x, y) contact stress σ corresponding to any point of the contact area between the nut and the roller n (x, y) are respectively:
as the rollers undergo a short load-to-unload cycle as they pass through the contact zone. The roller and the raceway contact and compress and start to be loaded with energy to store on the front side of the contact area, and the roller and the raceway contact and separate and start to be unloaded and release energy on the rear side of the contact area.
Due to the relative movement of the rollers and the screw, the elliptical contact area changes constantly and elastic hysteresis friction is unavoidable. Friction moment M caused by elastic hysteresis in the contact zone between roller-screw and roller-nut esi 、M eni Respectively as follows:
wherein γ is a material energy loss coefficient.
According to the bearing friction torque analysis theory, the roller bearing and the ball bearing with the contact angle larger than zero can generate self-spinning sliding on the contact surface, and further generate certain self-spinning sliding torque. According to the motion relation of the planetary roller screw, due to the existence of the thread form angle and the helix angle, the actual rotation axis of the roller is parallel to the axis of the screw and obviously not perpendicular to the common normal line of the contact surface, so that the roller does not roll purely in the rotation process, and the roller also spins around the common normal line of the contact point while rolling along the roller path of the screw, so that the roller slides in a spinning mode at the contact point, and finally, the spinning sliding friction is larger than the normal rolling friction.
According to the stress distribution rule of any point of the contact ellipsoid, the frictional force dF generated by the self-spinning motion of the point is obtained s ＝f s σ(x,y)dxdy；
The friction torque M caused by the spin slip in the roller-screw and roller-nut contact area is determined by integration over a single contact area bsi And M bni Respectively as follows:
in the formula (f) sr Is the coefficient of sliding friction between the screw and the roller, f nr Is the coefficient of sliding friction between the nut and the roller.
Because the roller, the nut and the screw rod are not completely rigid bodies, under the action of pretightening force and external load, when the roller moves in the threaded raceways of the nut and the screw rod, elastic contact deformation can occur, so that the contact area is changed from point contact to surface contact. At any point in the contact area, the speeds of the roller and the screw are not equal to each other, relative sliding is formed between the roller and the screw, and friction caused by the sliding becomes differential sliding friction.
The friction is related to the size of the contact surface, the friction coefficient of the contact material, the radius of curvature of the roller at the contact point, and the like, and the differential sliding friction is more obvious when the contact area of the roller and the screw thread raceway is larger. Calculating the differential sliding friction moment M of the planetary roller screw according to the analysis method of the rolling bearing dsi And M dni Comprises the following steps:
in the formula (f) s 、f n The curvature coefficient of the screw rod and the nut raceway is usually between 0.515 and 0.54.
Because the planetary roller screw pair moves under the working conditions of high speed and heavy load, a lubricant needs to be properly added to reduce the friction resistance and reduce the abrasion. However, as the working time goes deeper, the temperature rise and the torque are gradually increased, and the lubricant can generate internal friction to resist deformation under the action of external shearing force, so that viscous force of fluid is formed, the motion of the planetary roller screw pair is blocked, and the transmission efficiency of the whole transmission system is further influenced. The friction torque due to the surface viscosity of the lubricant has to be taken into account.
This part is the lubricant viscous friction torque M caused by the surface viscous force of the lubricant vsi 、M vni Comprises the following steps:
in the formula, E sr Equivalent elastic modulus of the screw and the roller; e nr Equivalent modulus of elasticity for the screw and the roller; rho xs The equivalent curvature radius of the roller screw in the x direction is shown; ρ is a unit of a gradient xn The roller nut side x-direction equivalent curvature radius; rho s Is the equivalent curvature radius ratio of the roller screw side; rho n The equal idle curvature radius ratio of the nut and the screw rod side; g s 、U s 、W s Is the parameters of the material, speed and load on the side of the roller screw, G n 、U n 、W n The calculation method is that the parameters of the material, the speed and the load on the screw side of the nut are dimensionless, and comprises the following steps:
G s ＝E sr α p ；G n ＝E nr α p ；
in the formula, ρ ys Is the equivalent curvature radius rho of the roller screw side in the y direction yn Is the equivalent curvature radius, alpha, of the roller nut side in the y direction p Is the viscosity pressure coefficient of the lubricant; eta 0 Is the dynamic viscosity of the lubricant; v. of t Is the tangential velocity of the roller in the raceway.
And 7, iterating the friction torque to obtain the friction torque of the whole planetary roller screw pair.
Iterating the friction torque to obtain the friction torque M between the roller and the screw rod s Friction torque M between roller and nut n Respectively as follows:
the friction torque M of the whole planetary roller screw pair is:
M＝M s +M n 。
in one embodiment, the invention is described in further detail as a specific example.
The basic structural parameters of the planetary roller screw pair used in the present embodiment are shown in table 1, and other parameters used in the calculation process are shown in table 2.
TABLE 1 basic parameters of planetary roller screw assembly
| Diameter d of the screw s | Diameter d of roller r | Number n of lead screw heads s | Lead screw lead angle |
| 27mm | 9mm | ||
| 5 | 3.8° | ||
| Pressure angle alpha | Pitch p of roller | Number of rollers n | Number z of roller threads |
| 45° | 2mm | 11 | 30 |
TABLE 2 other parameters
| Equivalent modulus of elasticity E of roller screw rs | Poisson ratio mu | Coefficient of energy loss of material gamma |
| 210Gpa | 0.27 | 0.008 |
| Coefficient of sliding friction f | Coefficient of curvature f of raceway s /f n | Load F |
| 0.05 | 0.52 | 5800N |
From the parameters of tables 1 and 2, the load distribution of the roller thread ridge is calculated by the calculation method of the present invention, as shown in fig. 5, and the friction torque of each portion is shown in table 3.
TABLE 3 Friction Torque of each part
In summary, according to the method for calculating the friction torque of the planetary roller screw pair provided by the invention, firstly, a screw thread load distribution model of a screw, a roller and a nut is determined according to the stress condition and the deformation coordination relationship of the screw thread of the planetary roller screw pair; secondly, analyzing according to a Hertz contact theory to obtain the stress distribution condition of a contact point of a thread tooth and basic parameters of a contact ellipse; finally, the resistance force applied in the motion process of the planetary roller screw pair is comprehensively considered, the friction torque is divided into pure rolling friction torque caused by material elastic lag, spinning sliding friction torque caused by self transmission of the roller around the axis of the roller, differential sliding friction torque caused by elastic deformation of a contact surface and viscous friction torque caused by surface viscous force of the lubricant, wherein the viscous friction torque fully considers various parameters of the lubricant, the result is more accurate, and the overall friction torque is more practical.
The foregoing illustrates and describes the principles, general features, and advantages of the present invention. It will be understood by those skilled in the art that the present invention is not limited to the embodiments described above, which are described in the specification and illustrated only to illustrate the principle of the present invention, but that various changes and modifications may be made therein without departing from the spirit and scope of the present invention, which fall within the scope of the invention as claimed.
Claims (8)
1. A method of calculating a friction torque of a planetary roller screw pair, the method comprising the steps of:
step 1, establishing a roller thread tooth load distribution model through the stress states of a screw rod, a roller and a nut;
step 2, solving the contact characteristic index of the planetary roller screw pair based on the Hertz contact theory;
step 3, calculating elastic hysteresis friction torque caused by elastic deformation hysteresis before and after rigid body loading and unloading;
step 4, calculating the self-rotating sliding friction torque caused by the fact that the actual rotation axis of the roller is not perpendicular to the common normal of the contact surface;
step 5, calculating differential sliding friction torque caused by relative sliding among the screw rod, the roller and the nut;
step 6, calculating the viscous friction torque of the lubricant caused by the surface viscous force of the lubricant;
and 7, iterating the friction torque to obtain the friction torque of the whole planetary roller screw pair.
2. A method of calculating the friction torque of a planetary roller screw pair according to claim 1, wherein in step 1, on the screw side, the roller thread load distribution model is:
F ai ＝F i cosαcosβ
F ti ＝F i cosαsinβ
F ri ＝F i sinα
wherein, under an external load F, F ai 、F ri 、F ti Axial force, radial force and tangential force of any thread tooth of the roller at the side of the screw rod are respectively; alpha is a roller thread form angle; beta is the helix angle of the roller thread; n is the number of the rollers; p is the thread pitch of the roller; a. The s Is the effective contact area of the lead screw; a. The n Is the effective contact area of the nut; e sr Equivalent elastic modulus of the screw and the roller; c s Is the screw stiffness; c n Is the nut stiffness; z is the number of the thread teeth of the roller;
and on the nut side, replacing the screw parameters with the nut parameters by using the roller thread tooth load distribution model.
3. The method for calculating the friction moment of the planetary roller screw pair according to claim 2, wherein in the step 2, according to the Hertz contact theory, under the action of an axial load, an elliptical contact area is formed between the roller and the screw raceway as well as between the roller and the nut raceway, and the stress of each point on the contact area follows semi-ellipsoidal distribution;
first and second main curvature radiuses rho of contact area of lead screw and roller side s11 、ρ s12 、ρ s21 、ρ s22 Principal curvature, and Σ ρ s First and second principal radii of curvature ρ of the nut in the contact region with the roller side n11 、ρ n12 、ρ n21 、ρ n22 Principal curvature, and Σ ρ n Respectively is as follows:
∑ρ s ＝ρ s11 +ρ s12 +ρ s21 +ρ s22
∑ρ n ＝ρ n11 +ρ n12 +ρ n21 +ρ n22
wherein R is r Is the equivalent spherical radius of the roller,
l r is a roller lead; l s Is a lead screw lead; l n Is a nut lead; d r The pitch diameter of the roller; d s The middle diameter of the lead screw; d n The pitch diameter of the nut;
the contact area of the screw rod and the roller has an elliptical long semi-axis length a s Minor semi-axis length b s The length of the semi-axis of the ellipse of the contact area between the nut and the roller n Minor semi-axis length b n Respectively is as follows:
in the formula, m as The eccentricity coefficient of the elliptic major axis and the elliptic minor axis of the lead screw; m is a unit of bs Is the eccentricity coefficient of the elliptical short semi-axis of the screw rod; m is a unit of an The eccentricity coefficient of the elliptic major semi-axis of the nut is shown; m is bn Is the eccentricity coefficient of the elliptical minor semi-axis of the nut; e (k) 2 ) Is a second type of complete elliptic integral; k is a radical of formula s Is the elliptical eccentricity of the screw rod; k is a radical of formula n Is the elliptical eccentricity of the nut;
the Poisson's ratio of the screw rod material; mu.s r Is the Poisson's ratio of the roller material; mu.s n The Poisson's ratio of the nut material; e s The elastic modulus of the lead screw material; e r The elastic modulus of the roller material; e n The elastic modulus of the nut material;
contact stress sigma corresponding to any point of contact area of screw and roller s (x, y) contact stress σ corresponding to any point of the contact area between the nut and the roller n (x, y) are respectively:
4. a method of calculating the friction torque of a planetary roller screw pair as claimed in claim 3, wherein the friction torque M in step 3 caused by elastic hysteresis in the roller-screw and roller-nut contact areas esi 、M eni Respectively as follows:
wherein γ is a material energy loss coefficient.
5. The method for calculating the friction torque of a planetary roller screw pair according to claim 4, wherein the step 4 is specifically:
according to the stress distribution rule of any point of the contact ellipsoid in the step 2, the friction force dF generated by the self-rotation motion of the point is obtained s ＝f s σ(x,y)dxdy；
The friction torque M caused by the spin slip in the roller-screw and roller-nut contact area is determined by integration over a single contact area bsi And M bni Respectively as follows:
in the formula, f sr Is the coefficient of sliding friction between the screw and the roller, f nr Is the coefficient of sliding friction between the nut and the roller.
6. A method for calculating the friction torque of a planetary roller screw pair according to claim 5, wherein in step 5, the differential sliding friction torque M of the planetary roller screw is calculated based on the rolling bearing analysis method dsi And M dni Comprises the following steps:
in the formula (f) s 、f n The curvature coefficient of the screw rod and the nut raceway is usually between 0.515 and 0.54.
7. A method of calculating a friction torque of a planetary roller screw pair according to claim 6, wherein in step 6, a viscous friction torque M of the lubricant due to a surface viscous force of the lubricant vsi 、M vni Comprises the following steps:
in the formula, E sr Equivalent elastic modulus of the screw and the roller; e nr Equivalent elastic modulus of the screw and the roller; rho xs The equivalent curvature radius of the roller screw in the x direction is shown; rho xn The roller nut side x-direction equivalent curvature radius; rho s Is the equivalent curvature radius ratio of the roller screw side; rho n The equal idle curvature radius ratio of the nut and the screw rod side; g s 、U s 、W s Is the parameters of the material, speed and load on the side of the roller screw, G n 、U n 、W n The calculation method is that the parameters of the material, the speed and the load on the screw side of the nut are dimensionless, and comprises the following steps:
G s ＝E sr α p ；G n ＝E nr α p ；
in the formula, ρ ys Is the equivalent curvature radius rho of the roller screw side in the y direction yn Is the equivalent curvature radius, alpha, of the roller nut side in the y direction p Is the viscosity pressure coefficient of the lubricant; eta 0 Is the dynamic viscosity of the lubricant; v. of t Is the tangential velocity of the roller in the raceway.
8. The method for calculating the friction torque of the planetary roller screw pair according to claim 7, wherein the step 7 of iterating the friction torque to obtain the friction torque of the whole planetary roller screw pair specifically comprises:
iterating the friction torque to obtain the friction torque M between the roller and the screw rod s Friction torque M between roller and nut n Respectively as follows:
the friction torque M of the whole planetary roller screw pair is:
M＝M s +M n 。
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