CN114139295A - Solving method for contact point of planetary roller screw pair - Google Patents

Solving method for contact point of planetary roller screw pair Download PDF

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Publication number
CN114139295A
CN114139295A CN202111015008.1A CN202111015008A CN114139295A CN 114139295 A CN114139295 A CN 114139295A CN 202111015008 A CN202111015008 A CN 202111015008A CN 114139295 A CN114139295 A CN 114139295A
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Prior art keywords
screw
roller
contact
contact point
thread
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Inventor
陈中
郑继贵
侍威
黄玉平
张兆晶
郭亚星
杨斌
田青
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Beijing Research Institute of Precise Mechatronic Controls
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Beijing Research Institute of Precise Mechatronic Controls
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/10—Geometric CAD
    • G06F30/17—Mechanical parametric or variational design
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
    • F16H—GEARING
    • F16H25/00—Gearings comprising primarily only cams, cam-followers and screw-and-nut mechanisms
    • F16H25/18—Gearings comprising primarily only cams, cam-followers and screw-and-nut mechanisms for conveying or interconverting oscillating or reciprocating motions
    • F16H25/20—Screw mechanisms
    • F16H25/22—Screw mechanisms with balls, rollers, or similar members between the co-operating parts; Elements essential to the use of such members
    • F16H25/2247—Screw mechanisms with balls, rollers, or similar members between the co-operating parts; Elements essential to the use of such members with rollers
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
    • F16H—GEARING
    • F16H25/00—Gearings comprising primarily only cams, cam-followers and screw-and-nut mechanisms
    • F16H25/18—Gearings comprising primarily only cams, cam-followers and screw-and-nut mechanisms for conveying or interconverting oscillating or reciprocating motions
    • F16H25/20—Screw mechanisms
    • F16H25/22—Screw mechanisms with balls, rollers, or similar members between the co-operating parts; Elements essential to the use of such members
    • F16H25/2247—Screw mechanisms with balls, rollers, or similar members between the co-operating parts; Elements essential to the use of such members with rollers
    • F16H25/2252—Planetary rollers between nut and screw
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2111/00—Details relating to CAD techniques
    • G06F2111/04—Constraint-based CAD

Abstract

The invention discloses a method for solving a contact point of a planetary roller screw pair, which comprises the steps of firstly establishing a helical surface equation of a screw and a roller based on a cross section profile of a part thread method, obtaining a unit normal vector of any point of a helical surface, secondly establishing a constraint equation set according to the condition that the unit normal vectors at the contact point of the screw and the roller are collinear, and finally accurately and efficiently solving the theoretical intermediate diameter of the screw and the contact point position at the moment under the condition of no interference by applying a Newton-Raphson iterative algorithm with second-order convergence, thereby laying a foundation for subsequent research.

Description

Solving method for contact point of planetary roller screw pair
Technical Field
The invention belongs to the technical field of mechanical transmission mechanisms, and relates to a contact point solving method of a spatial point contact transmission mechanism such as a planetary roller screw pair.
Background
The planet roller screw pair transfers load by mutual contact of thread curved surfaces, and for a standard planet roller screw, because the lead angle of the screw is inconsistent with the roller, a contact point between the screw and the roller can deviate, so that the interference problem exists in the assembly process. In the actual processing and assembling process, the distance between the axes of the screw rod and the roller is usually kept unchanged, and the interference condition is avoided by adjusting the pitch diameter of the screw rod. Therefore, the determination of the theoretical pitch diameter of the screw and the accurate solution of the position of the contact point are important for subsequent research and analysis.
Regarding the solution of the contact point position, [ mechanical design, meshing calculation of the roller screw pair, 2003 (03): 34-36, dividing a possible contact area into a plurality of planes along the axial direction when solving the contact position, and determining the contact position by the position relation between the roller and the screw profile curve in each plane; CN111199013A, 2020.05.26, determining the relation between contact parameters by constructing a unit normal vector equation of the screw and the roller, and then searching the maximum normal distance to determine the adjustment amount required by the pitch diameter of the screw; [ combined machine tool and automatic processing technique, planetary roller screw meshing calculation and interference elimination, 2018 (08): 4-7, solving the meshing equation set by adopting a numerical iteration method, and obtaining 4 contact parameters by utilizing an improved high-wire Newton iteration method; contact mechanics in the Roller scanner Mechanism, Journal of Mechanical Design,2013,135(5), which is based on the Frenet coordinate system, establishes a curved surface equation of each part, and solves the position of a Contact point according to the curved surface conjugation and the spatial position relationship of each part.
The existing contact point solving method is mostly based on a curved surface equation established by the axial section profile of each part, and the unknown variables in an equation set are more and the solving process is complex according to the conditions that the space coordinates of the screw rod and the roller at the contact point are the same and the normal vectors are collinear during solving.
Disclosure of Invention
The invention aims to overcome the defects and provides a method for solving the contact point of a planetary roller screw pair, which comprises the steps of firstly establishing a helical surface equation of a screw and a roller based on the cross section profile of a part thread method, obtaining a unit normal vector of any point of the helical surface, secondly establishing a constraint equation set according to the condition that the unit normal vectors at the contact point of the screw and the roller are collinear, and finally accurately and efficiently solving the theoretical intermediate diameter of the screw and the contact point position under the condition of no interference by applying a Newton-Raphson iterative algorithm with second-order convergence, thereby laying a foundation for subsequent research.
In order to achieve the above purpose, the invention provides the following technical scheme:
the invention discloses a method for solving a contact point of a planetary roller screw pair, which comprises the following steps of:
(1) in the part coordinate system oxiyiziSecondly, establishing a spiral curved surface parameter equation of the part based on a thread method section profile equation of the part, and calculating unit normal quantity of any point of the spiral curved surface according to the spiral curved surface parameter equation;
(2) obtaining a screw part coordinate system ox according to the position relation of the screw and the rollersyszsCoordinate system ox of roller partryrzrA coordinate transformation matrix therebetween;
(3) according to the condition that the unit normal vectors at the contact points of the screw and the roller are collinear and the coordinate system ox of the screw partsyszsWith roller part coordinate system oxryrzrCoordinate transformation matrix between the two sets of screw part coordinate system oxsyszsThe constraint equation set is simplified;
(4) setting the theoretical intermediate diameter ds of the lead screw and the initial value of the contact parameter; the initial value of the theoretical pitch diameter ds of the lead screw is the nominal pitch diameter value of the lead screw;
(5) solving a constraint equation set by adopting a Newton-Raphson algorithm according to the theoretical intermediate diameter of the screw and the initial value of the contact parameter to obtain the position coordinate and the contact parameter of the side contact of the roller screw;
(6) setting solving precision, judging whether the contact point is interfered according to the position coordinates of the contact point obtained in the step (5), correcting a theoretical diameter value of the screw according to a judgment result and the solving precision, and iterating the step (5) until the contact point is not interfered and the solving precision is met, and outputting the position coordinates and the contact parameters of the contact point;
the contact parameter comprises the contact radius r of the partciDeclination of contact angle theta with partciThe parts comprise a lead screw and a roller;
i-s or r, respectively, denotes a screw or a roller.
Further, in the step (1), 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 the thread starting point corresponding to the small diameter of the screw rod and the thread starting point corresponding to the small diameter of the roller, xiPositive from the origin towards the thread start, yiThe axis conforms to the right hand rule;
the thread method section profile equations of the screw rod and the roller are respectively as follows:
z′s＝ξi[tanβs(rps-rs)+ps cosλs/4]；
Figure BDA0003240068010000031
wherein ξi＝±1，ξiWhen it is-1, it means the upper surface of the thread, xiiWhen 1 denotes the lower surface of the thread, rTIs the profile radius, beta, of the inner roller of the normal sectioniAnd λiNormal section profile half angle and helix angle, p, for each partiThe pitch of the threads of each part, riIs the nominal radius of each part, rpiIs an arbitrary point on the spiral curved surface at xioyiDistance on plane to origin o, thetapiIs any point on the spiral curved surface and xiThe included angle of the axes is set by the angle,
Figure BDA0003240068010000032
further, in the step (1), the cross-sectional profile equation of the thread method is wound around z in the coordinate system of the partiAnd (3) rotating the shaft to obtain a parameter equation of the spiral curved surface:
fi＝[rpi cosθpi,rpi sinθpi,ξih(rpi)/cosλi+θpili/2π]；
wherein, h (r)pi) Is a profile function of the part in a normal section and is simultaneously marked as hi， h(rpi)＝hi＝z′i/ξi，liIs the thread lead of each part.
Further, in the step (1), a unit normal vector of any point of the spiral curved surface of each part is as follows:
Figure BDA0003240068010000033
wherein, h' (r)pi) Is h (r)pi) Is simultaneously recorded as h'i，λiIs the helix angle, /)iIs thread lead, xii＝±1，ξiWhen it is-1, it means the upper surface of the thread, xiiWhen 1 denotes the lower surface of the thread, 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,
Figure BDA0003240068010000041
further, in the step (2), the screw is a 5-head thread screw, and the roller part coordinate system oxryrzrTo the lead screw part coordinate system oxsyszsCoordinate transformation matrix of
Figure BDA0003240068010000042
Wherein alpha issIndicating the position of the contact point in the coordinate system x of the screw partsoysProjection in plane relative xsThe angle through which the shaft rotates, a being the distance between the axis of the screw and the roller, p being the pitch, and ps＝pr＝p，psAnd prRespectively a screw thread pitch of a screw rod and a screw thread pitch of a roller,
Figure BDA0003240068010000043
for a screw part coordinate system oxsyszsCoordinate system ox relative to roller partryrzrThe angle of rotation of (c).
Further, in the step (2), taking
Figure BDA0003240068010000044
Then
Figure BDA0003240068010000045
The coordinate transformation matrix is simplified to:
Figure BDA0003240068010000046
further, in the step (3), the constraint equation system is:
Figure BDA0003240068010000047
Figure BDA0003240068010000048
wherein, F1Is about rcs、rcr、θcs、θcrFunction of (A), F2Is about rcs、rcr、θcs、θcrIs composed ofD, h'sIs hsFirst derivative of, h'rIs hrFirst derivative of, thetas＝αs-θcs，θr＝5αs+θcrContact parameter θcs、 θcrContact declination of screw and roller, rcs、rcrRespectively, the contact radius of the screw and the roller, alphasIndicating the position of the contact point in the lead screw part coordinate system xsoysProjection in plane relative xsAngle, xi, through which the shaft is turnedi＝±1，ξiWhen it is-1, it means the upper surface of the thread, xi i1 denotes the lower surface of the thread,/sFor the thread lead of the lead screw, /)rIs the lead of the roller thread, lambdasFor lead screw lead angle, λrIs the roller helix angle.
Further, in the step (3), the method for simplifying the constraint equation set includes:
for the roller screw side, x in the coordinate system of the part passing through the contact point and parallel to the screwsOysThe cross section of the coordinate plane is a contact parameter thetacs、θcr、rcsAnd rcrSatisfies the relation:
rcs sinθcs＝rcr sinθcr
rcs cosθcs+rcr cosθcr＝a
then, r is obtainedcsAnd rcrExpression (c):
Figure BDA0003240068010000051
Figure BDA0003240068010000052
wherein a is the distance between the axes of the screw and the roller;
will r iscsAnd rcrThe expression of (a) is substituted into a system of constraint equations, canOnly contain the contact parameter thetacsAnd thetacrAnd solving the Jacobi matrix as:
Figure BDA0003240068010000053
further, the specific steps of the step (6) are as follows:
(61) setting a parameter j equal to 1 and solving the precision e;
(62) judging whether the z coordinate of the lead screw is larger than the z coordinate of the roller in the position coordinates of the contact point obtained in the step (5), wherein the z coordinate of the lead screw and the z coordinate of the roller are both the lead screw part coordinate system oxsyszsLower zsAxis coordinates; when the z coordinate of the screw at the contact point is larger than the z coordinate of the roller, the lower surface of the screw and the upper surface of the roller have no interference, executing the step (63), when the z coordinate of the screw at the contact point is not larger than the z coordinate of the roller, the lower surface of the screw and the upper surface of the roller have interference, so that ds is ds-0.1^ (j), and returning to the step (5);
(63) j is equal to j +1, ds is equal to ds +9 x 0.1^ (j) and returns to the step (5), and whether j is equal to e is judged; when j is equal to e, the calculation result reaches the set solving precision e, and the theoretical intermediate diameter ds at the moment and the contact parameter under the intermediate diameter are output;
(64) and (6) ending.
Further, in the step (6), the solution accuracy includes a decimal part, and the theoretical intermediate diameter value is sequentially corrected according to the solution accuracy and the decimal number, and the step (5) is iterated.
Compared with the prior art, the invention has the following beneficial effects:
(1) in the method for solving the contact point of the planetary roller screw pair, a spiral surface equation of a screw and a roller is established based on the section profile of a part by a thread method;
(2) in the method for solving the contact point of the planetary roller screw pair, the number of constraint equation sets is reduced by utilizing the geometric relation among different contact parameters, and the complexity of calculation is greatly reduced;
(3) in the method for solving the contact point of the planetary roller screw pair, a Newton-Raphson iterative algorithm with second-order convergence is applied, and the calculation efficiency is greatly improved on the basis of accurately solving the theoretical intermediate diameter and the contact point position of the screw under the condition of no interference.
Drawings
FIG. 1 is a schematic view of the coordinate system of the components of the drawing of the present invention;
FIG. 2 is a schematic diagram of a screw cross-sectional coordinate system and a cross-sectional profile of the screw according to the present invention;
FIG. 3 is a schematic diagram of a roller normal cross-sectional coordinate system and normal cross-sectional profile of the present invention;
FIG. 4 is a schematic view of the contact parameters in the end cross-section of the roller screw side contact of the present invention;
FIG. 5 is a side curved contact interference diagram of the roller screw of the present invention;
FIG. 6 is a flow chart of the lead screw theoretical pitch diameter solution 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.
A method for solving the numerical value of a contact point of a planetary roller screw pair comprises the following steps:
(1) establishing a screw surface parameter equation of the screw rod and the roller under respective part coordinate systems based on a section profile equation of a thread method, and calculating a unit normal vector of any point of the surface;
(2) determining a coordinate transformation relation between the screw rod and the roller according to the position and phase relation between the screw rod and the roller;
(3) on the basis of the unit normal vector of the arbitrary point of the curved surface obtained in the step (1), according to the unit normal vector common line of the contact point of the screw rod and the rollerPiece, and lead screw part coordinate system ox obtained in step (2)syszsWith roller part coordinate system oxryrzrThe coordinate transformation relationship between the contact parameters is used for establishing a constraint equation set, and the number of variables is reduced based on the geometric relationship between different contact parameters, so that the constraint equation set is simplified;
(4) based on a nominal intermediate diameter value of the screw, solving a constraint equation set by adopting a Newton-Raphson iterative algorithm with second-order convergence to obtain the position of a side contact of the roller screw under the intermediate diameter;
(5) and taking the condition that the interference does not occur at the contact point as a judgment condition, and searching the pitch diameter of the lead screw to determine the theoretical pitch diameter of the lead screw when the interference does not occur.
As shown in FIG. 1, the axis of the screw and the roller is ziAxis, xiThe axis passes through the starting point of the thread and respectively establishes a part coordinate system oxiyiziThe space coordinate of any point on the helical curved surface under the parameter equation coordinate system can be expressed as (r)pi,θpi,zi) The subscript i ═ s, r respectively indicates a screw and a roller, and the relationship between the two satisfies:
Figure BDA0003240068010000071
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 angle of the axes.
Referring to FIGS. 2 and 3, the part coordinate system is wrapped around xiRotation angle of shaft lambdaiObtaining a normal section coordinate system ox'iy′iz′iIn the section of the screw and roller thread track, the screw and roller profiles respectively pass through fixed points (r)i,±pi cosλi/4), it can be determined that the cross-sectional profile of the screw method satisfies the equation:
Figure BDA0003240068010000072
the points on the roller profile satisfy the relation:
Figure BDA0003240068010000073
x′F＝rr-rT sinβr
z′F＝rT cosβr+pr cosλr/4
so the cross-sectional profile of the roller method satisfies the equation:
Figure BDA0003240068010000081
by a curved normal section profile (normal section) around ziThe helical surface equation of the screw rod and the roller can be obtained by rotating the shaft as follows:
zs＝ξs[tanβs(rps-rs)+ps cosλs/4]/cosλs+θpsls/2π
Figure BDA0003240068010000082
wherein ξiFor each part curved surface, coefficient, xiiWhen it is-1, it means the upper surface of the thread, xiiThe thread lower surface is denoted by 1, and the upper half of the thread is generally considered as the upper surface and the lower half is considered as the lower surface along the positive direction of the axis. Beta is aiAnd λiNormal section profile half angle and helix angle, p, of the partiAnd liRespectively, pitch and lead, riIs the nominal radius of the part, rTIs the contour radius of the inner roller of the normal section; x'FX coordinate, z 'in the normal section coordinate system of the center (F point) of the circular arc of the roller'FIs the z coordinate of the center of the circular arc of the roller (F point) in the normal section coordinate system.
Therefore, the helical surface equation of each part can be uniformly expressed as:
Figure BDA0003240068010000085
in the formula, h (r)pi) As a function of the profile of the respective part in normal section, h (r)pr)＝z′r/ξr，h(rps)＝z′s/ξs。
Then the unit normal vector of the part contour surface can be expressed as:
Figure BDA0003240068010000083
substituting the helical surface equation into the above formula to obtain:
Figure BDA0003240068010000084
wherein, h' (r)pi) Is h (r)pi) The first derivative of (a).
Taking a 5-start threaded screw as an example, selecting a global coordinate system to coincide with a screw part coordinate system, and when the lower surface of the screw is in contact with the upper surface of the roller, taking xis＝1、ξrIs-1. Obtaining a coordinate transformation matrix from a roller coordinate system to a global coordinate system according to the position relation of each part in the planetary roller screw pair:
Figure BDA0003240068010000091
in the formula, alphasIndicating that the contact point is located at xsOysProjection relative lead screw x in planesThe angle through which the shaft rotates, a being the distance between the screw and the roller axis, p being the pitch, and ps＝pr＝p，
Figure BDA0003240068010000092
As global coordinatesThe system is transformed to the rotation angle of the roller coordinate system,
Figure BDA0003240068010000093
because the contact state at any point on the spiral line where the contact point is located is the same, in order to simplify the subsequent calculation process, the contact state is taken
Figure RE-GDA0003495237280000094
Then
Figure RE-GDA0003495237280000095
The coordinate transformation matrix of the roller at this time is:
Figure BDA0003240068010000096
for the roller screw side, see FIG. 4, at the over-contact point and parallel to xsOysIn the section of the coordinate plane, the contact parameters satisfy the following relation:
rcs sinθcs＝rcr sinθcr
rcs cosθcs+rcr cosθcr＝a
in the formula, rcs、rcrThe contact radii of the screw and the roller respectively represent the distance from the position of the contact point to the axis of the screw and the roller respectively; thetacs、θcrThe contact declination of the screw and the roller represents the angle of the vertical line from the contact point position to the axes of the screw and the roller respectively deviating from the central connecting line of the screw and the roller.
Thus, r can be deducedcsAnd rcrExpression (c):
Figure BDA0003240068010000097
Figure BDA0003240068010000098
at the contact point, the unit normal vectors of the screw rod and the roller meet the collinear reversal condition, and a constraint equation set of the contact point can be obtained by carrying out coordinate transformation on the unit normal vectors of the roller:
Figure BDA0003240068010000099
Figure BDA0003240068010000101
wherein, thetas＝αs-θcs，θr＝5αs+θcr，F1Is about rcs、rcr、θcs、θcrFunction of (A), F2Is about rcs、 rcr、θcs、θcrFunction of h'sIs hsFirst derivative of, h'rIs hrThe first derivative of (a).
Will r iscsAnd rcrBy substituting the expression into the equation system, only the contact parameter theta can be obtainedcsAnd thetacrAnd solving the Jacobi matrix as:
Figure BDA0003240068010000102
and (3) obtaining each contact parameter and the coordinate position of the contact point by using a Newton-Raphson algorithm and matlab software. As shown in fig. 5, the lead angle of the screw is not consistent with the roller, so that the screw and the roller interfere with each other when the pitch diameter of the screw is the nominal pitch diameter, and therefore, the theoretical pitch diameter of the screw under the condition of no interference needs to be determined. The contact point coordinates obtained by utilizing the unit normal vector collinear condition are sequentially searched for the screw pitch diameter according to the decimal number, and the theoretical pitch diameter of the screw is determined only by taking the condition that interference does not occur at the point where the contact point is obtained each time as a judgment condition, so that the calculation amount can be obviously reduced, meanwhile, the calculation precision e (e is effective after the decimal point is calculated) can be freely set, and the theoretical pitch diameter of the screw and each contact parameter under the pitch diameter are calculated, and the specific process is shown in fig. 6.
Example 1
According to the structural parameters of the planetary roller screw pair listed in the table 1, the solving precision e is set to be 5, and the theoretical pitch diameter of the screw when the method is not interfered and the side contact parameters of the roller screw are obtained by solving and are listed in the table 2.
TABLE 1 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
Normal section profile radius rT/mm - 7.0711 -
TABLE 2 calculation of contact parameters for planetary roller screw pairs
Figure BDA0003240068010000111
From the contact parameter calculations, it can be seen that the unit normal vectors of the screw and roller at the contact point are very close to collinear reversal, while the contact gap (the distance between the screw surface and the roller surface at the contact point) reaches 10-6And mm magnitude, the accuracy of solving the contact point position is verified.
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 in the technical solution of the present invention and the embodiments thereof 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 solving a contact point of a planetary roller screw pair is characterized by comprising the following steps:
(1) in the part coordinate system oxiyiziSecondly, establishing a spiral curved surface parameter equation of the part based on a thread method section profile equation of the part, and calculating a unit normal vector of any point of the spiral curved surface according to the spiral curved surface parameter equation;
(2) obtaining a screw part coordinate system ox according to the position relation of the screw and the rollersyszsWith roller part coordinate system oxryrzrA coordinate transformation matrix therebetween;
(3) according to the condition that the unit normal vectors at the contact points of the screw and the roller are collinear and the coordinate system ox of the screw partsyszsWith roller part coordinate system oxryrzrCoordinate transformation matrix between the two sets of screw part coordinate system oxsyszsThe constraint equation set is simplified;
(4) setting the theoretical intermediate diameter ds of the lead screw and the initial value of the contact parameter; the initial value of the theoretical pitch diameter ds of the lead screw is the nominal pitch diameter value of the lead screw;
(5) solving a constraint equation set by adopting a Newton-Raphson algorithm according to the theoretical intermediate diameter of the screw and the initial value of the contact parameter to obtain the position coordinate and the contact parameter of the side contact of the roller screw;
(6) setting solving precision, judging whether the contact point is interfered according to the position coordinates of the contact point obtained in the step (5), correcting a theoretical mean diameter value of the screw according to a judgment result and the solving precision, and iterating the step (5) until the contact point is not interfered and the solving precision is met, and outputting the position coordinates and the contact parameters of the contact point;
the contact parameter comprises the contact radius r of the partciDeclination of contact angle theta with partciThe parts comprise a lead screw and a roller;
i-s or r, respectively, denotes a screw or a roller.
2. A method for solving the contact point of a planetary roller screw pair according to claim 1, wherein in the step (1), the part coordinate system oxiyiziWith the axis and thread of the partThe intersection point of the cross section of the end where the starting point is located is the origin point, ziThe axis being the axis of the respective part, xiThe shaft passes through the thread starting point corresponding to the small diameter of the screw rod and the thread starting point corresponding to the small diameter of the roller, xiThe positive direction is from the origin to the starting point of the thread, yiThe axis conforms to the right hand rule;
the thread method section profile equations of the screw rod and the roller are respectively as follows:
z′s＝ξi[tanβs(rps-rs)+pscosλs/4]；
Figure FDA0003240067000000021
wherein ξi＝±1，ξiWhen it is-1, it means the upper surface of the thread, xiiWhen 1 denotes the lower surface of the thread, rTIs the profile radius, beta, of the inner roller of the normal sectioniAnd λiNormal section profile half angle and helix angle, p, for each partiThe pitch of the threads of each part, riIs the nominal radius of each part, 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,
Figure FDA0003240067000000022
3. the method for solving the contact point of the planetary roller screw pair according to claim 2, wherein in the step (1), the cross-sectional profile equation of the screw method is wound around z in the coordinate system of the partiRotating the shaft to obtain a parameter equation of the spiral curved surface:
fi＝[rpicosθpi,rpisinθpi,ξih(rpi)/cosλi+θpili/2π]；
wherein, h (r)pi) For the contour of the part in the normal sectionFunction, simultaneously denoted as hi，h(rpi)＝hi＝z′i/ξi，liIs the thread lead of each part.
4. The method for solving the contact point of the planetary roller screw pair according to claim 1, wherein in the step (1), the unit normal vector of any point of the helical surface of each part is as follows:
Figure FDA0003240067000000023
wherein, h' (r)pi) Is h (r)pi) Is simultaneously recorded as h'i，λiIs the helix angle, /)iIs the lead of the thread, xii＝±1，ξiWhen it is-1, it means the upper surface of the thread, xiiWhen 1 denotes the lower surface of the thread, 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,
Figure FDA0003240067000000024
5. the method for solving the contact point of the planetary roller screw pair as claimed in claim 1, wherein in the step (2), the screw is a 5-head thread screw, and the roller part coordinate system oxryrzrTo the lead screw part coordinate system oxsyszsCoordinate transformation matrix of
Figure FDA0003240067000000031
Wherein alpha issIndicating the position of the contact point in the coordinate system x of the screw partsoysProjection in plane relative xsThe angle of the shaft is rotated, a is a lead screw and a rollerDistance between column axes, p is pitch, and ps＝pr＝p，psAnd prRespectively the thread pitch of the screw rod and the thread pitch of the roller,
Figure FDA0003240067000000032
for a screw part coordinate system oxsyszsRelative to the roller part coordinate system oxryrzrThe angle of rotation of (c).
6. The method for solving the contact point of the planetary roller screw pair according to claim 5, wherein in the step (2), the contact point is taken
Figure FDA0003240067000000033
Then
Figure FDA0003240067000000034
The coordinate transformation matrix is simplified as:
Figure FDA0003240067000000035
7. the method for solving the contact point of the planetary roller screw pair according to claim 1, wherein in the step (3), the constraint equation set is as follows:
Figure FDA0003240067000000036
Figure FDA0003240067000000037
wherein, h'sIs hsFirst derivative of, h'rIs hrFirst derivative of, thetas＝αs-θcs，θr＝5αs+θcrContact parameter θcs、θcrContact declination of screw and roller, rcs、rcrRespectively, the contact radius of the screw and the roller, alphasIndicating the position of the contact point in the coordinate system x of the screw partsoysProjection in plane relative xsAngle, xi, through which the shaft is turnedi＝±1，ξiWhen it is-1, it means the upper surface of the thread, xii1 denotes the lower surface of the thread,/sIs the lead of the screw thread, /)rIs the lead of the roller thread, lambdasFor lead screw lead angle, λrIs the roller helix angle.
8. The method for solving the contact point of the planetary roller screw pair according to claim 7, wherein in the step (3), the method for simplifying the constraint equation set comprises the following steps:
for the roller screw side, x in the coordinate system of the part passing through the contact point and parallel to the screwsOysIn a cross-section of the coordinate plane, a contact parameter thetacs、θcr、rcsAnd rcrSatisfies the relation:
rcssinθcs＝rcrsinθcr
rcscosθcs+rcrcosθcr＝a
then, r is obtainedcsAnd rcrExpression (c):
Figure FDA0003240067000000041
Figure FDA0003240067000000042
wherein a is the distance between the axes of the screw and the roller;
will r iscsAnd rcrThe expression is substituted into a constraint equation system, and only the contact parameter theta can be obtainedcsAnd thetacrAnd solving the Jacobi matrix as:
Figure FDA0003240067000000043
9. the method for solving the contact point of the planetary roller screw pair according to claim 1, wherein the step (6) comprises the following specific steps:
(61) setting a parameter j equal to 1 and solving the precision e;
(62) judging whether the z coordinate of the screw is larger than the z coordinate of the roller in the position coordinates of the contact point obtained in the step (5), wherein the z coordinate of the screw and the z coordinate of the roller are both the screw part coordinate system oxsyszsZ ofsAxis coordinates; when the z coordinate of the screw at the contact point is larger than the z coordinate of the roller, the lower surface of the screw and the upper surface of the roller have no interference, executing the step (63), when the z coordinate of the screw at the contact point is not larger than the z coordinate of the roller, the lower surface of the screw and the upper surface of the roller have interference, so that ds is ds-0.1^ (j), and returning to the step (5);
(63) j is equal to j +1, ds is equal to ds +9 x 0.1^ (j) and returns to the step (5), and whether j is equal to e is judged; when j is equal to e, the calculation result reaches the set solving precision e, and the theoretical pitch diameter ds at the moment and the contact parameter under the pitch diameter are output;
(64) and (6) ending.
10. The method for solving the contact point of the planetary roller screw pair according to claim 1, wherein in the step (6), the solution precision comprises a decimal part, and the step (5) is iterated by sequentially correcting the theoretical intermediate diameter value according to the solution precision by decimal numbers.
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