CN114139294A - Method for calculating transmission efficiency of planetary roller screw pair - Google Patents
Method for calculating transmission efficiency of planetary roller screw pair Download PDFInfo
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Abstract
The invention discloses a method for calculating the transmission efficiency of a planetary roller screw pair, which can calculate the transmission efficiency of the planetary roller screw pair and the influence rule of each influence factor on the transmission efficiency more accurately by fully considering the influence of the factors of uneven thread load distribution and relative sliding between a roller and a screw on the transmission efficiency of the planetary roller screw pair on the basis of solving the roller load distribution rule and the accurate position of a contact point, and has wide application prospect in the technical field of mechanical transmission mechanisms.
Description
Technical Field
The invention belongs to the technical field of mechanical transmission mechanisms, and relates to a method for calculating transmission efficiency of a planetary roller screw pair.
Background
The planetary roller screw has the outstanding advantages of high precision, high bearing capacity, long service life and the like, but the development of the roller screw is always restricted by the deficiency of the transmission efficiency. In recent years, more and more scholars recognize the urgency of improving the transmission efficiency, and research on theories related to improving the transmission efficiency is also gradually conducted. However, the transmission efficiency is one of the important factors considered in practical production applications, and its influence factors are numerous.
At present, the solving method for the transmission efficiency of the planetary roller screw can be divided into two categories: solving efficiency based on stress balance analysis and solving efficiency based on friction loss. [ kinetics and Efficiency Analysis of the planar Roller cutter Mechanism, Journal of Mechanical Design, 2009, 131 (1): 011016, decomposing the normal force of the screw pair at the contact point by introducing a three-dimensional Frenet coordinate system to obtain the magnitude of the output axial force, and providing a calculation formula of the transmission efficiency based on force balance analysis; the theory and experimental research of contact, friction and working characteristics of a planetary roller screw pair refer to a ball screw pair efficiency solving method, the roller equivalently moves along a spiral line to move in a slope, a slope inclination angle is introduced on the basis of the ball screw pair, and a transmission efficiency model of the roller screw under the conditions of no pretightening force and pretightening force is respectively established; the method comprises the following steps of (1) calculating the relative motion displacement of a screw rod, a nut and a roller through motion analysis, and then introducing a coulomb friction coefficient to represent the relation between friction force and normal force so as to solve friction loss, and providing a transmission efficiency model based on friction loss; the friction resistance torque in the planetary roller screw pair is researched, friction torque caused by elastic hysteresis, self-spinning sliding friction torque of the roller and viscous resistance torque of a lubricating medium are respectively solved, output torque is expressed as driving torque under the condition of neglecting friction, and then an efficiency calculation method of the roller screw pair is provided.
In summary, the existing methods for calculating the transmission efficiency of the planetary roller screw pair mainly include two types: solving efficiency based on stress balance analysis and solving efficiency based on friction loss. The calculation method based on the stress balance analysis only considers the influence of the structural parameters of the roller screw pair on the efficiency, neglects the influence of the roller load distribution condition and the load size on the transmission efficiency of the screw pair, ignores the difference of the contact states of the screw side and the nut side, does not consider the friction loss of the screw side caused by the difference of the speeds of the roller and the screw at the contact point, and enables the calculation result to have larger deviation.
Disclosure of Invention
The invention aims to overcome the defects and provides a method for calculating the transmission efficiency of a planetary roller screw pair, which comprises the steps of firstly solving the accurate position basis of a contact point based on a thread surface equation of each part, obtaining a roller load distribution rule based on a thread deformation coordination relation, and calculating the rolling friction loss power P at the roller screw side caused by elastic hysteresis in the running process of the roller screw pair on the basis of solving the roller load distribution rule and the accurate position of the contact pointfsRolling friction loss power P with roller nut sidefnSelf-rotating sliding friction loss power P at roller screw sideksAnd the spin sliding friction loss power P of the roller nut sideknAnd sliding friction loss P caused by contact deviation on roller screw sidesAnd finally, obtaining the transmission efficiency of the roller screw pair according to the friction loss calculation result. The invention fully considers the influence of uneven thread load distribution and relative sliding factors between the roller and the screw on the transmission efficiency of the planetary roller screw pair, and can more accurately calculateThe transmission efficiency of the planetary roller screw pair and the influence rule of each influencing factor on the transmission efficiency have wide application prospect in the technical field of mechanical transmission mechanisms.
In order to achieve the above purpose, the invention provides the following technical scheme:
a method for calculating transmission efficiency of a planetary roller screw pair comprises the following steps:
(1) establishing a thread surface equation of the screw rod, the roller and the nut, and solving the position of a side contact of the roller screw rod according to the thread surface equation;
(2) determining the contact load distribution of the screw thread of the roller based on the deformation coordination relationship of the screw, the roller and the nut;
(3) calculating friction loss P in the running process of the planetary roller screw pair according to the position of the side contact of the roller screw obtained in the step (1) and the contact load distribution of the roller thread obtained in the step (2)f(ii) a The friction loss includes a rolling friction loss power P on the roller screw side caused by elastic hysteresisfsRolling friction loss power P with roller nut sidefnSelf-rotating sliding friction loss power P at roller screw sideksAnd the spin sliding friction loss power P of the roller nut sideknAnd sliding friction loss P caused by contact deviation on roller screw sides；
(4) And (4) calculating the output power of the roller screw pair, and obtaining the transmission efficiency of the roller screw pair according to the output power and the friction loss obtained in the step (3).
Further, a part coordinate system oxiyiziIn the middle, the equation of the thread curved surface of the lead screw is as follows:
zs＝ξs[tanβs(rps-rs)+pscosλs/4]/cosλs+θpsls/2π；
the equation of the thread curved surface of the roller is as follows:
the equation of the thread curved surface of the nut is as follows:
zn＝ξn[tanβn(rn-rpn)+pncosλn/4]/cosλn+θpnln/2π；
wherein the part coordinate system oxiyiziUsing the intersection point of the axis of the part and the cross section of the end where the starting point of the thread is as the origin, ziThe axis being the axis of the respective part, xiThe shaft passes through a thread starting point corresponding to the small diameter of the screw rod, a thread starting point corresponding to the small diameter of the roller and a thread starting point corresponding to the large diameter of the nut, xiThe positive direction is from the origin to the starting point of the thread, yiThe axis conforms to the right hand rule;
ξi＝±1，ξiwhen it is-1, it means the upper surface of the thread, xii1 denotes the lower thread surface, βiAnd λiNormal section profile half angle and helix angle, p, for each partiAnd liThe pitch and lead of the thread of each part, riIs the nominal radius of each part, rTIs the profile radius of the inner roller of the normal section, rpiIs an arbitrary point on the spiral curved surface at xioyiDistance on the plane to the origin o, thetapiIs any point on the spiral curved surface and xiThe included angle of the axes is set by the angle,
the parts include a screw, a roller and a nut, i ═ s, r, n, which respectively denote the screw, the roller and the nut.
It is also understood that (r)pi,θpi,zi) For each part parameter equation coordinate system orpiθpiziSpace coordinates of any point on the lower spiral curved surface, parameter equation coordinate system of each part and coordinate system ox of each partiyiziThe conversion relationship is as follows:
the end section of the parameter equation coordinate system is positioned by the axis of the part and the starting point of the spiral lineThe intersection of the planes being the origin, ziThe axis being the axis of the respective part, rpiThe axis is a spiral curved surface and any point is on xioyiDistance on the plane to the origin o, thetapiIs any point on the spiral curved surface and xiThe included angle of the axes;
further, in the step (1), according to a thread surface equation, a constraint equation set is established by utilizing a unit normal vector collinear reversal condition at a contact point, so that the position of a side contact of the roller screw is obtained.
Further, in the step (2), the thread deformation coordination relationship of each part is a deformation coordination relationship between axial tension-compression deformation of the roller and Hertz contact deformation at a contact point;
the contact load distribution formula of the roller thread ridge is as follows:
in the formula, FkIs the contact load on the kth thread ridge of the roller; faThe axial load of the roller thread ridge is the load; p is a radical ofrIs the pitch of the thread of the roller, betarIs a roller method section tooth type half angle; lambda [ alpha ]rThe helix angle of the roller; n is the number of the rollers; tau is the number of threads of a single roller; a. thesAnd AnThe effective areas of the screw rod and the nut when in contact with the roller are respectively; csAnd CnThe contact rigidity of the screw rod and the nut when the screw rod and the nut are in contact with the roller respectively, and E is the elastic modulus of the roller material.
Further, in the step (3), the rolling friction loss power P of the roller screw side due to elastic hysteresis isfsRolling friction loss power P with roller nut sidefnThe calculation method comprises the following steps:
obtaining the roller on the side of the roller screw rod caused by elastic hysteresis according to the contact load distribution of the roller thread ridge obtained in the step (2)Moment of kinetic friction MfsRolling friction moment M with roller nut sidefn：
Wherein N is the number of the rollers; tau is the number of threads of a single roller; gamma is the energy loss coefficient; b issAnd BnParameters related to the curvature of the contact surface are taken as the side of the roller screw and the side of the roller nut; m isbsAnd mbnThe minor axis coefficients of the roller screw side and roller nut side Hertz contact ellipses; e'sAnd E'nThe equivalent elastic modulus of the screw rod and the nut; sigma rhosSum Σ ρnThe curvature sum of the parts at the contact points of the side of the roller screw and the side of the roller nut is taken as the curvature sum; fkThe contact load on the kth thread of the roller is shown, and k is more than or equal to 1 and less than or equal to tau;
then according to the rolling friction moment M of the roller screw sidefsRolling friction moment M with roller nut sidefnObtaining rolling friction loss power P of roller screw sidefsRolling friction loss power P with roller nut sidefn：
Wherein the content of the first and second substances,
and
roller screw side and roller nut side respectivelyThe tangential component of the angular velocity of rotation of the roller.
Further, in the step (3), the spin-induced spin sliding friction loss power P on the roller screw side is generated by spinksAnd the spin sliding friction loss power P of the roller nut sideknThe calculation method comprises the following steps:
calculating the sliding friction moment M of the roller screw rod side caused by spin according to the contact load distribution of the roller thread ridge obtained in the step (2)ksAnd sliding friction moment M of the roller nut sidekn：
Wherein N is the number of the rollers; f is the sliding friction coefficient; tau is the number of threads of a single roller; a isskAnd bskThe length of a long semi-axis and the length of a short semi-axis of a Hertz contact ellipse on the kth thread tooth on the side of the roller screw; a isnkAnd bnkThe length of a long semi-axis and the length of a short semi-axis of a Hertz contact ellipse on a kth thread tooth on the roller nut side; fkThe contact load on the kth thread of the roller is shown, and k is more than or equal to 1 and less than or equal to tau; (X, Y) is the coordinate of each point in the Hertz contact ellipse with the center of the ellipse as the origin, the minor axis direction as the Y axis and the major axis direction as the X axis;
then according to the sliding friction moment M of the roller screw sideksAnd sliding friction moment M of the roller nut sideknObtaining the self-rotating sliding friction loss power P of the roller screw sideksAnd the spin sliding friction loss power P of the roller nut sidekn：
Wherein the content of the first and second substances,
and
the normal components of the roller rotational angular velocity of the roller screw side and the roller nut side, respectively.
Further, in the step (3), the contact point offset is the contact point offset of the screw and the roller; the method for calculating the sliding friction loss caused by the contact point deviation comprises the following steps:
calculating the relative sliding velocity v of the roller and the screw at the contact pointrs：
Wherein v isrIs the speed of the roller at the contact point; v. ofsIs the speed of the lead screw at the contact point;
according to the contact load distribution of the thread ridges of the roller and the relative sliding speed v of the roller and the screw rod at the contact point obtained in the step (2)rsCalculating the sliding friction loss caused by the contact point deviation:
wherein F is the sliding friction coefficient, tau is the number of threads of a single roller, FkThe contact load on the kth thread of the roller is shown, and k is more than or equal to 1 and less than or equal to tau.
Further, in the step (3), the speed v of the roller at the contact pointrThe calculation method comprises the following steps:
wherein v isR，vPAnd vLThe rotation speed, revolution speed and linear speed of the roller at the contact point are respectively:
vR＝ωr·rcr；vp＝ωp·rcs；vL＝n·ls；
wherein, ω isrThe rotational angular velocity of the roller; omegaPIs the revolution angular velocity of the roller, omegaP＝Kζ·ωsK is a speed ratio coefficient, K is more than or equal to 0 and less than or equal to 1, and zeta is a theoretical speed ratio omega of angular speed of the retainer and angular speed of the lead screw when relative sliding caused by contact point deviation is not consideredsIn order to determine the angular velocity of the screw,
rsis the nominal radius of the screw, a is the distance between the roller and the axis of the screw; n is the rotating speed of the lead screw; lsIs a lead screw lead; r iscrAnd rcsAnd (3) respectively obtaining the distances from the position of the roller screw side contact point to the roller axis and the distance from the position of the roller screw side contact point to the screw axis based on the position of the roller screw side contact point obtained in the step (1).
Further, in the step (4), the output power P of the roller screw pairo＝Fa·vLWherein v isLIs the linear velocity of the roller, FaIs a load;
transmission efficiency of roller screw pair
Further, in the step (3), the friction loss further includes friction loss between the retainer and the roller caused by the inconsistency between the direction of the contact force between the roller and the screw rod and the nut and the direction of the angular velocity of the roller, and viscous friction loss caused by the lubricant in the nut.
Compared with the prior art, the invention has the following beneficial effects:
(1) in the method for calculating the transmission efficiency of the planetary roller screw pair, the accurate position basis of the contact point is solved based on the thread curved surface equation of each part, the roller load distribution rule is obtained based on the thread deformation coordination relationship, and the influence of uneven thread load distribution of each part on the transmission efficiency of the planetary roller screw pair is fully considered;
(2) according to the method for calculating the transmission efficiency of the planetary roller screw pair, analysis is carried out according to the operation characteristics of the planetary roller screw pair, and the friction loss is summarized into rolling friction loss caused by elastic hysteresis, sliding friction loss caused by spinning, relative sliding friction loss caused by contact point offset, friction loss between a roller and a retainer, viscous friction loss caused by lubrication, other losses and the like, so that the friction loss of the planetary roller screw pair is closer to the friction loss of the planetary roller screw pair under the real condition;
(3) according to the method for calculating the transmission efficiency of the planetary roller screw pair, the friction loss caused by relative sliding factors between the roller and the screw is calculated based on the motion relation between the screw and the roller and based on the roller load distribution rule and the accurate position innovativeness of a contact point;
(4) the invention can more accurately calculate the transmission efficiency of the planetary roller screw pair and the influence rule of each influence factor on the transmission efficiency, and has wide application prospect in the technical field of mechanical transmission mechanisms.
Drawings
FIG. 1 is a schematic diagram of a basic coordinate system and a parametric equation coordinate system of a part according to the present invention;
FIG. 2 is a schematic view of a Hertz contact ellipse at a contact location in accordance with the present invention;
FIG. 3 is a classification chart of sources of friction loss according to the present invention;
FIG. 4 is a schematic diagram of the planetary roller screw motion of the present invention;
FIG. 5 is an exploded view of the angular velocity of the rollers of the planetary roller screw assembly of the present invention;
FIG. 6 is a schematic view of the speed direction at the contact point of the roller screw side of the present invention;
fig. 7 is a roller load distribution diagram of example 1 of the present invention.
Detailed Description
The features and advantages of the present invention will become more apparent and appreciated from the following detailed description of the invention.
The word "exemplary" is used exclusively herein to mean "serving as an example, embodiment, or illustration. Any embodiment described herein as "exemplary" is not necessarily to be construed as preferred or advantageous over other embodiments. While the various aspects of the embodiments are presented in drawings, the drawings are not necessarily drawn to scale unless specifically indicated.
The invention discloses a method for calculating the transmission efficiency of a planetary roller screw pair, which comprises the following solving steps:
(1) establishing a thread curved surface equation of the screw rod, the roller and the nut, and accurately solving the position of a contact on the side of the roller screw rod;
(2) determining a load distribution rule of the thread teeth of the roller based on the thread tooth deformation coordination relation of each part (a screw rod, the roller and a nut);
(3) researching a friction mechanism in the operation process of the planetary roller screw pair, and determining that the main sources of friction loss are rolling friction, spin sliding friction and sliding friction caused by contact point offset, which are caused by elastic hysteresis, as shown in fig. 3;
calculating rolling friction loss, spinning sliding friction loss and sliding friction loss caused by contact point offset in the running process of the planetary roller screw pair according to the position of the side contact of the roller screw obtained in the step (1) and the contact load distribution of the roller thread obtained in the step (2);
specifically, rolling friction loss and spinning sliding friction loss caused by elastic hysteresis in the running process of the planetary roller screw pair are calculated according to the contact load distribution of the roller thread teeth obtained in the step (2); analyzing the motion relation between the screw and the roller, and calculating the relative motion speed of the screw and the roller at the contact point according to the position of the side contact point of the roller screw obtained in the step (1) and the contact load distribution of the thread teeth of the roller obtained in the step (2), so as to obtain the sliding friction loss caused by the deviation of the contact point;
(4) and (4) obtaining the transmission efficiency of the roller screw pair according to the output power and the friction loss obtained in the step (3) to solve the transmission efficiency of the whole roller screw pair.
Basic coordinate system ox of partsiyiziRespectively taking the intersection point of the axial lines of the screw rod, the roller and the nut and the cross section of the end where the starting point of the thread is positioned as the origin, and taking the axial line of each part as ziAxis, xiThe shaft passes through a thread starting point corresponding to the small diameter of the screw rod, a thread starting point corresponding to the small diameter of the roller and a thread starting point corresponding to the large diameter of the nut, xiThe positive direction is from the origin to the starting point of the thread, yiAxis in accordance with right hand rule, parameter equation coordinate system orpiθpiziWith the basic coordinate system oxiyiziThe space coordinate of any point on the helical curved surface under the coordinate system of the parameter equation can be expressed as (r)pi,θpi,zi) The subscript i ═ s, r, n respectively indicates a screw, a roller, and a nut, and satisfies the relationship:
according to the normal section of the thread curved surface of each part, the equation of the spiral curved surface of the screw rod, the roller and the nut can be determined as follows:
zs＝ξs[tanβs(rps-rs)+pscosλs/4]/cosλs+θpsls/2π
zn＝ξn[tanβn(rn-rpn)+pncosλn/4]/cosλn+θpnln/2π
wherein ξiFor each part curved surface, coefficient, xiiWhen it is-1, it means the upper surface of the thread, xiiThe lower surface of the thread is denoted by 1, and the thread ridge is generally considered to be an upper surface in the upper half part and a lower surface in the lower half part along the positive direction of the axis. Beta is aiAnd λiAre respectively zeroNormal section profile half angle and helix angle of the part, piAnd liRespectively, pitch and lead, riIs the nominal radius of each part, rTIs the contour radius of the inner roller of the normal section.
Based on the helical surface equation of the screw rod, the roller and the nut, a constraint equation set is established by utilizing the collinear reverse condition of the unit normal vector at the contact point, so that the accurate position r of the contact point on the side of the roller screw rod can be obtainedcsAnd rcrRespectively representing the distance, theta, of the contact point position from the axis of the screw and the rollercs、θcrRepresenting the angle of the position of the contact point, respectively, at which the perpendicular to the axis of the screw and roller, respectively, deviates from the line connecting the centres of the screw and roller, so that the contact point can also be brought to contact with a radius rcs、rcrAnd contact declination angle thetacs、θcrAnd (4) showing.
Based on the deformation coordination relationship between the axial tension-compression deformation of the roller and the Hertz contact deformation at the contact point, the condition that the load distribution of the thread ridge of the roller meets is obtained:
in the formula, prIs the pitch of a thread, betarIs a roller tooth type half angle; lambda [ alpha ]rThe helix angle of the roller; n is the number of the rollers; tau is the number of threads of a single roller; fkIs the contact load on the kth thread ridge of the roller; a. thesAnd AnThe effective areas of the screw rod and the nut when in contact with the roller are respectively; csAnd CnThe contact rigidity of the screw rod and the nut when the screw rod and the nut are in contact with the roller respectively; e is the modulus of elasticity of the roller material; faIs an axial load, i.e. a load.
During the working process of the planetary roller screw pair, according to the running characteristics of the planetary roller screw pair, the friction loss is analyzed, and the friction loss comprises rolling friction loss caused by elastic hysteresis, sliding friction loss caused by spinning, relative sliding friction loss caused by contact point deviation, friction loss between the roller and the retainer, viscous friction loss caused by lubrication, other losses and the like. The friction loss calculation method is as follows:
1. rolling friction caused by elastic hysteresis
The contact point is deformed and converted into a contact surface under the action of an external load, and the contact deformation is slowly recovered in the load releasing process, but the deformation degrees generated in the two stages are different, and the rotation of the roller is hindered along with friction loss.
Rolling friction moment M on the roller screw side caused by elastic hysteresisfsRolling friction moment M with roller nut sidefn：
Wherein γ is an energy loss coefficient; b issAnd BnParameters related to the curvatures of the screw rod side and the nut side and the contact surface; m isbsAnd mbnThe minor axis coefficients of the Hertz contact ellipses at the screw side and the nut side; e'sAnd E'nThe equivalent elastic modulus of the screw rod and the nut; sigma rhosSum Σ ρnThe curvature sum of parts at the contact points of the screw rod side and the nut side is shown; n is the number of the rollers; tau is the number of threads of a single roller; fkThe contact load on the kth thread of the roller is shown, and k is more than or equal to 1 and less than or equal to tau;
as shown in fig. 5, the rotational axis of the roller does not coincide with the force transmission direction (common normal direction), and the angular velocity is divided into a tangential direction and a normal direction according to the force transmission direction vector, and corresponds to the rotational angular velocity of the roller during rolling
And
and angular velocity of rotation of the roller during spinning sliding
And
rolling friction is generated when the contact point is deformed and exists on the side of the roller screw and the side of the roller nut at the same time, and the corresponding rolling friction loss power is as follows:
In the formula (I), the compound is shown in the specification,
and
the tangential components of the angular velocity of rotation of the rollers on the side of the roller screw and on the side of the roller nut, respectively.
2. Spin induced sliding friction
The rotation angular velocity of the roller has a component in the common normal direction of the thread curved surface, which can generate a self-rotating sliding phenomenon, and the self-rotating sliding friction moment M at the side of the roller screw rodksAnd sliding friction moment M of the roller nut sidekn：
Wherein f is a sliding friction coefficient; a isskAnd bskThe length of a long semi-axis and the length of a short semi-axis of a Hertz contact ellipse on the kth thread tooth on the side of the roller screw; a isnkAnd bnkThe length of a long semi-axis and the length of a short semi-axis of a Hertz contact ellipse on a kth thread tooth on the roller nut side; fkThe contact load on the kth thread of the roller is shown, and k is more than or equal to 1 and less than or equal to tau; as shown in FIG. 2, (X, Y) are coordinates of each point in the Hertz contact ellipse with the center of the ellipse as the origin, the minor axis as the Y-axis, and the major axis as the X-axis.
Then the corresponding spin-slip friction losses power:
In the formula (I), the compound is shown in the specification,
and
the normal components of the roller rotational angular velocity of the roller screw side and the roller nut side, respectively.
Because the sliding friction loss caused by rolling friction and spin caused by elastic hysteresis is smaller than the sliding friction loss caused by contact point offset, in order to simplify the calculation process, the following steps are carried out:
in the formula, ωrIs the rotational angular velocity of the roller.
3. Sliding friction (main loss) caused by contact point offset
For a standard planetary roller screw, because the lead screw and the roller have different lead angles, the movement speeds of the contact points are inevitably different in the contact process of the lead screw and the roller, and therefore, the relative sliding cannot be avoided. The direction of the friction force generated by the relative sliding is opposite to the direction of the relative movement speed of the two, and the magnitude of the friction force is proportional to the contact load.
As shown in fig. 4, in the course of the planetary roller screw pair motion, assuming that the roller and the nut are pure rolling, the contact point (point a) of the roller and the nut is the instant center of speed, and the speed of the central point (point B) of the roller satisfies the following conditions:
vB＝ωr·rr＝ωp·a
the relationship between the revolution and the rotation angular speed of the roller can be deduced:
in the formula, ωrIs the rotational angular velocity of the roller, omegaPThe rotational angular velocity of the roller, namely the rotational angular velocity of the retainer; a is the distance between the roller and the axis of the screw.
As shown in fig. 6, in an ideal case, i.e., without considering the relative slip introduced by the contact point offset, the cage rotational angular velocity (i.e., the roller revolution angular velocity ω)P) Angular velocity omega of lead screwsSatisfy the relation:
namely, it is
In the formula, zeta is the theoretical speed ratio of the angular speed of the retainer and the angular speed of the lead screw under an ideal condition; point C is the intersection point of the roller and the screw at the nominal pitch diameter, vCRepresenting the velocity at the intersection;
however, in consideration of the influence of the contact point offset, the speed ratio is determined by the friction between the roller and the screwζ is reduced, and thus a speed ratio coefficient K is introduced, so that a real speed ratio ζ is obtained1And the theoretical speed ratio zeta meets the following conditions:
ζ1＝K·ζ，0≤K≤1
in the working process of the planetary roller screw pair, the screw only rotates, and the speed at the contact point is only the rotation speed
The roller rotates and simultaneously has revolution motion and linear motion, and the corresponding contact point velocity vectors are respectively
And
the velocity magnitude calculation formula is as follows:
vR＝ωr·rcr、vp＝ωp·rcs、vL＝n·ls
wherein n is the rotation speed of the screw rod, lsIs a lead screw lead.
The speed of the roller at the contact point is then:
therefore, the relative sliding speed of the roller and the screw at the contact point:
the direction of the sliding friction force applied to the screw is opposite to the direction of the relative sliding speed, so the power loss of the relative sliding friction is as follows:
wherein f is sliding frictionCoefficient, τ being the number of threads of a single roller, FkThe contact load on the kth thread of the roller is shown, and k is more than or equal to 1 and less than or equal to tau.
4. Friction between cage and roller
Because the direction of the contact force between the roller and the screw rod and the nut is not consistent with the direction of the angular speed of the roller, the roller is influenced by the overturning moment in the running process, so that the friction loss inevitably exists between the roller and the retainer, but the friction loss of the roller is smaller.
5. Viscous friction caused by lubrication
In order to ensure smooth running of the planetary roller screw pair, a lubricant, usually grease, is added to the nut, so as to reduce friction loss. As the roller performs planetary motion in the roller screw pair, the viscous resistance of lubricating grease needs to be overcome, viscous friction loss is generated, the loss is small when the speed is related to the rotating speed of the screw, and the loss is small when the speed is low.
In the working process of the planetary roller screw pair, the nut outputs linear motion, so that the output power of the roller screw pair is as follows:
Po＝Fa·vL
the transmission efficiency can be expressed as the ratio of output power to input power. In the transmission process of the planetary roller screw pair, friction loss is the main energy loss, so that the input power can be approximately equal to the sum of the output power and the friction loss power, the transmission efficiency of the planetary roller screw pair is as follows:
in the formula, PfPower is lost as a total friction.
Example 1
The basic structural parameters of the planetary roller screw pair used in the embodiment are shown in table 1, and other parameters used in the calculation process are shown in table 2; where the number of starts is used to calculate the thread lead.
TABLE 1 basic structural parameters of planetary roller screw pair
| Parameter(s) | Screw rod | Roller pin | Nut |
| Nominal radius ri/mm | 15 | 5 | 25 |
| Number of heads ni | 5 | 1 | 5 |
| Pitch p of the threadi/mm | 1 | 1 | 1 |
| Tooth form half angle betai/° | 45 | 45 | 45 |
| Roller profile radius rR/mm | - | 7.0711 | - |
TABLE 2 other parameters
From the parameters in tables 1 and 2, the contact parameters of the roller screw side contact points were calculated by the calculation method according to the present invention as shown in table 3, the speed ratio coefficient K was 0.99925, and the results of the power calculations are shown in table 4, and the transmission efficiency η was 0.825 was calculated, which is more accurate than other methods in the prior art. FIG. 7 is a roller load distribution graph, F, obtained according to the thread load distribution conditions in the text using the structural parameters of the examplekAs can be seen from fig. 7, the load distribution of the thread on the roller is uneven, and the subsequent calculation performed by the present patent according to the distribution rule calculates the friction loss on each thread by using the load on each thread and then summarizes the friction loss.
TABLE 3 roller screw side contact parameters
TABLE 4 calculation of frictional loss power
The invention has been described in detail with reference to specific embodiments and illustrative examples, but the description is not intended to be construed in a limiting sense. Those skilled in the art will appreciate that various equivalent substitutions, modifications or improvements may be made to the technical solution of the present invention and its embodiments without departing from the spirit and scope of the present invention, which fall within the scope of the present invention. The scope of the invention is defined by the appended claims.
Those skilled in the art will appreciate that those matters not described in detail in the present specification are well known in the art.
Claims (10)
1. A method for calculating the transmission efficiency of a planetary roller screw pair is characterized by comprising the following steps:
(1) establishing a thread surface equation of the screw rod, the roller and the nut, and solving the position of a side contact of the roller screw rod according to the thread surface equation;
(2) determining the contact load distribution of the screw thread of the roller based on the deformation coordination relationship of the screw, the roller and the nut;
(3) calculating friction loss P in the running process of the planetary roller screw pair according to the position of the side contact of the roller screw obtained in the step (1) and the contact load distribution of the roller thread obtained in the step (2)f(ii) a The friction loss includes a rolling friction loss power P on the roller screw side caused by elastic hysteresisfsRolling friction loss power P with roller nut sidefnSelf-rotating sliding friction loss power P at roller screw sideksAnd the spin sliding friction loss power P of the roller nut sideknAnd sliding friction loss P caused by contact deviation on roller screw sides；
(4) And (4) calculating the output power of the roller screw pair, and obtaining the transmission efficiency of the roller screw pair according to the output power and the friction loss obtained in the step (3).
2. A method for calculating the transmission efficiency of a planetary roller screw pair according to claim 1, characterized in that the part coordinate system oxiyiziIn the middle, the equation of the thread curved surface of the lead screw is as follows:
zs＝ξs[tanβs(rps-rs)+pscosλs/4]/cosλs+θpsls/2π；
the equation of the thread curved surface of the roller is as follows:
the equation of the thread curved surface of the nut is as follows:
zn＝ξn[tanβn(rn-rpn)+pncosλn/4]/cosλn+θpnln/2π；
wherein the part coordinate system oxiyiziUsing the intersection point of the axis of the part and the cross section of the end where the starting point of the thread is as the origin, ziThe axis being the axis of the respective part, xiThe shaft passes through a thread starting point corresponding to the small diameter of the screw rod, a thread starting point corresponding to the small diameter of the roller and a thread starting point corresponding to the large diameter of the nut, xiThe positive direction is from the origin to the starting point of the thread, yiThe axis conforms to the right hand rule;
ξi＝±1，ξiwhen it is-1, it means the upper surface of the thread, xii1 denotes the lower thread surface, βiAnd λiNormal section profile half angle and helix angle, p, for each partiAnd liThe pitch and lead of the thread of each part, riIs the nominal radius of each part, rTIs the profile radius of the inner roller of the normal section, rpiIs an arbitrary point on the spiral curved surface at xioyiDistance on the plane to the origin o, thetapiIs any point on the spiral curved surface and xiThe included angle of the axes is set by the angle,
the parts include a screw, a roller and a nut, i ═ s, r, n, which respectively denote the screw, the roller and the nut.
3. The method for calculating the transmission efficiency of the planetary roller screw pair according to claim 1, wherein in the step (1), a constraint equation set is established by utilizing a collinear reversal condition of unit normal vectors at the contact points according to a thread surface equation, so that the positions of the contact points on the side of the roller screw are obtained.
4. The method for calculating the transmission efficiency of the planetary roller screw pair according to claim 1, wherein in the step (2), the thread deformation coordination relationship of each part is the deformation coordination relationship between the axial tension-compression deformation of the roller and the Hertz contact deformation at the contact point;
the contact load distribution formula of the roller thread ridge is as follows:
in the formula, FkIs the contact load on the kth thread ridge of the roller; faThe axial load of the roller thread ridge is the load; p is a radical ofrIs the pitch of the thread of the roller, betarIs a roller method section tooth type half angle; lambda [ alpha ]rThe helix angle of the roller; n is the number of the rollers; tau is the number of threads of a single roller; a. thesAnd AnThe effective areas of the screw rod and the nut when in contact with the roller are respectively; csAnd CnThe contact rigidity of the screw rod and the nut when the screw rod and the nut are in contact with the roller respectively, and E is the elastic modulus of the roller material.
5. The method for calculating the transmission efficiency of a planetary roller screw pair according to claim 1, wherein in the step (3), the rolling friction loss power P on the roller screw side caused by elastic hysteresisfsRolling friction loss power P with roller nut sidefnThe calculation method comprises the following steps:
obtaining the rolling friction moment M on the side of the roller screw rod caused by elastic hysteresis according to the contact load distribution of the roller thread ridge obtained in the step (2)fsRolling friction moment M with roller nut sidefn：
Wherein N is the number of the rollers; tau is the number of threads of a single roller; gamma is the energy loss coefficient; b issAnd BnParameters related to the curvature of the contact surface are taken as the side of the roller screw and the side of the roller nut; m isbsAnd mbnThe minor axis coefficients of the roller screw side and roller nut side Hertz contact ellipses; e'sAnd E'nThe equivalent elastic modulus of the screw rod and the nut; sigma rhosSum Σ ρnThe curvature sum of the parts at the contact points of the side of the roller screw and the side of the roller nut is taken as the curvature sum; fkThe contact load on the kth thread of the roller is shown, and k is more than or equal to 1 and less than or equal to tau;
then according to the rolling friction moment M of the roller screw sidefsRolling friction moment M with roller nut sidefnObtaining rolling friction loss power P of roller screw sidefsRolling friction loss power P with roller nut sidefn：
Wherein the content of the first and second substances,
and
the tangential components of the angular velocity of rotation of the rollers on the side of the roller screw and on the side of the roller nut, respectively.
6. The method for calculating the transmission efficiency of a planetary roller screw pair according to claim 1, wherein in the step (3), the step (c) is carried outSpin-induced spin-slip friction loss power P on the roller screw sideksAnd the spin sliding friction loss power P of the roller nut sideknThe calculation method comprises the following steps:
calculating the sliding friction moment M of the roller screw rod side caused by spin according to the contact load distribution of the roller thread ridge obtained in the step (2)ksAnd sliding friction moment M of the roller nut sidekn：
Wherein N is the number of the rollers; f is the sliding friction coefficient; tau is the number of threads of a single roller; a isskAnd bskThe length of a long semi-axis and the length of a short semi-axis of a Hertz contact ellipse on the kth thread tooth on the side of the roller screw; a isnkAnd bnkThe length of a long semi-axis and the length of a short semi-axis of a Hertz contact ellipse on a kth thread tooth on the roller nut side; fkThe contact load on the kth thread of the roller is shown, and k is more than or equal to 1 and less than or equal to tau; (X, Y) is the coordinate of each point in the Hertz contact ellipse with the center of the ellipse as the origin, the minor axis direction as the Y axis and the major axis direction as the X axis;
then according to the sliding friction moment M of the roller screw sideksAnd sliding friction moment M of the roller nut sideknObtaining the self-rotating sliding friction loss power P of the roller screw sideksAnd the spin sliding friction loss power P of the roller nut sidekn：
Wherein the content of the first and second substances,
and
the normal components of the roller rotational angular velocity of the roller screw side and the roller nut side, respectively.
7. The method for calculating the transmission efficiency of a planetary roller screw pair according to claim 1, wherein in the step (3), the contact point deviation is the contact point deviation of the screw and the roller; the method for calculating the sliding friction loss caused by the contact point deviation comprises the following steps:
calculating the relative sliding velocity v of the roller and the screw at the contact pointrs：
Wherein v isrIs the speed of the roller at the contact point; v. ofsIs the speed of the lead screw at the contact point;
according to the contact load distribution of the thread ridges of the roller and the relative sliding speed v of the roller and the screw rod at the contact point obtained in the step (2)rsCalculating the sliding friction loss caused by the contact point deviation:
wherein F is the sliding friction coefficient, tau is the number of threads of a single roller, FkThe contact load on the kth thread of the roller is shown, and k is more than or equal to 1 and less than or equal to tau.
8. A method for calculating the transmission efficiency of a planetary roller screw pair according to claim 7, wherein in the step (3), the speed v of the roller at the contact pointrIs calculated byComprises the following steps:
wherein v isR，vPAnd vLThe rotation speed, revolution speed and linear speed of the roller at the contact point are respectively:
vR＝ωr·rcr；vp＝ωp·rcs；vL＝n·ls；
wherein, ω isrThe rotational angular velocity of the roller; omegaPIs the revolution angular velocity of the roller, omegaP＝Kζ·ωsK is a speed ratio coefficient, K is more than or equal to 0 and less than or equal to 1, and zeta is a theoretical speed ratio omega of angular speed of the retainer and angular speed of the lead screw when relative sliding caused by contact point deviation is not consideredsIn order to determine the angular velocity of the screw,
rsis the nominal radius of the screw, a is the distance between the roller and the axis of the screw; n is the rotating speed of the lead screw; lsIs a lead screw lead; r iscrAnd rcsThe distances from the contact point position to the axes of the screw and the roller are respectively.
9. A method for calculating the transmission efficiency of a planetary roller screw pair according to any one of claims 1 to 8, wherein in step (4), the output power P of the roller screw pairo＝Fa·vLWherein v isLIs the linear velocity of the roller, FaIs a load;
transmission efficiency of roller screw pair
10. The method for calculating the transmission efficiency of the planetary roller screw pair according to claim 1, wherein in the step (3), the friction loss further comprises friction loss between the cage and the roller caused by the inconsistency of the direction of the contact force between the roller and the screw and the nut with the direction of the angular velocity of the roller, and viscous friction loss caused by the lubricant in the nut.
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