CN112016196A - Double-nut planetary roller screw dynamics research method based on elastic deformation - Google Patents

Double-nut planetary roller screw dynamics research method based on elastic deformation Download PDF

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CN112016196A
CN112016196A CN202010803575.2A CN202010803575A CN112016196A CN 112016196 A CN112016196 A CN 112016196A CN 202010803575 A CN202010803575 A CN 202010803575A CN 112016196 A CN112016196 A CN 112016196A
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nut
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CN112016196B (en
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付晓军
刘更
李欣
王海伟
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Northwestern Polytechnical University
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    • G06—COMPUTING; CALCULATING OR COUNTING
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    • G06—COMPUTING; CALCULATING OR COUNTING
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    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
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    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
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    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
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Abstract

The invention discloses a double-nut planetary roller screw dynamics research method based on elastic deformation, which comprises the following steps of S1: according to the structural characteristics of the double-nut planetary roller screw, a double-nut planetary roller screw spring mass system comprehensively considering elastic deformation, inertia force and pretightening force is established; s2: calculating an adjoint matrix and a stiffness matrix of the spring mass system; s3: establishing an elastic dynamic equation of a double-nut planetary roller screw with coupled stress-deformation-motion parameters; s4: establishing rigid motion equations of a screw rod and a roller; s5: and (5) solving the elastic kinetic equation in the step S3 by combining the rigid body motion equations of the screw and the roller in the step S4. The research method of the invention provides an elastic dynamic equation of the double-nut planetary roller screw with coupled stress-deformation-motion parameters, and by solving the equation, the pretightening force, deformation, load distribution and motion state of the mechanism under different use conditions are obtained.

Description

Double-nut planetary roller screw dynamics research method based on elastic deformation
Technical Field
The invention relates to the technical field of planetary roller screw transmission dynamics, in particular to a double-nut planetary roller screw dynamics research method based on elastic deformation.
Background
Currently, researchers focus on the dynamics of the planetary roller screw, mainly focus on the planetary roller screw with a single nut and without pretightening force, and are limited to the field of rigid body dynamics analysis. The important point of research on the elastic deformation of the planetary roller screw is mainly focused on a single-nut planetary roller screw rigidity and load distribution model which is static and has no pretightening force. Rigid-body dynamic models, such as the "Anonelar six dimensions of free dynamic model of planar roller mill mechanics" and the "An effective method for the dynamic analysis of planar roller mill mechanics", do not allow to calculate the deformation state of each part and therefore the pre-tightening force to which the double nut is subjected. The rigidity and load distribution models of the single-nut planetary roller screw, such as the research on the design method for uniform loading of the thread and the tooth of the planetary roller screw pair and the load distribution of the planetary roller screw pair considering errors, cannot consider the influence of the change of the motion state on the stress and deformation of each part. From the published calculation results of the stiffness and load distribution models, it is known that elastic deformation of the screw threads, the rollers and the nut threads has a significant effect on the load distribution between the thread teeth, but this important influencing factor is ignored in the prior kinetic analysis. In addition, due to the pretensioning force, a double nut planetary roller screw will generally have a higher friction torque than a single nut planetary roller screw without pretensioning force. The friction between the engagement points of the screw and the rollers and of the nut and the rollers has an influence on the load distribution of the thread ridge, the movement of the rollers and the elastic deformation of the thread. However, at present, there is only a literature concerning the elastic dynamics research method of coupling stress-deformation-motion parameters for the transmission of the double-nut planetary roller screw.
Therefore, a double-nut planetary roller screw dynamics analysis method considering elastic deformation is needed to be provided, an elastic dynamics equation with coupled stress-deformation-motion parameters is established, solution is completed, the stress, deformation and motion state analysis of parts of the mechanism under different use conditions is realized, and a more accurate basis is provided for strength and rigidity checking, friction and wear analysis, structural design and pretightening force selection of the double-nut planetary roller screw.
Disclosure of Invention
Aiming at the existing problems, the invention aims to provide a double-nut planetary roller screw dynamics research method based on elastic deformation, which adopts a spring mass unit to realize the structural dispersion of a screw, a roller and a nut, utilizes a nonlinear contact unit to simulate the contact deformation of each meshing point, and sets the spring unit to simulate the deformation of a pre-tightening gasket, forms a spring mass system comprehensively considering the elastic deformation, the inertia force and the pre-tightening force, establishes an elastic dynamics equation of the double-nut planetary roller screw with coupled stress-deformation-motion parameters, completes the solution, and obtains the pre-tightening force, the deformation, the load distribution and the motion state of the mechanism under different use working conditions.
In order to achieve the purpose, the technical scheme adopted by the invention is as follows:
a double-nut planetary roller screw dynamics research method based on elastic deformation is disclosed, wherein the double-nut planetary roller screw comprises a 1# nut, a 2# nut, a 1# roller, a 2# roller, a screw and two inner gear rings, and a pre-tightening gasket is clamped between the 1# nut and the 2# nut; which is characterized by comprising the following steps of,
s1: according to the structural characteristics of the double-nut planetary roller screw, the structural dispersion of the screw, the roller and the nut is realized by adopting the spring mass unit, the contact deformation of the screw and the roller and the contact deformation of each meshing point between the nut and the roller are simulated by utilizing the nonlinear contact unit, and the deformation of the pre-tightening gasket is simulated by arranging the spring unit, so that a double-nut planetary roller screw spring mass system comprehensively considering elastic deformation, inertia force and pre-tightening force is formed;
s2: calculating an adjoint matrix and a stiffness matrix of the spring mass system;
s3: establishing an elastic dynamic equation of a double-nut planetary roller screw with coupled stress-deformation-motion parameters;
s4: establishing rigid motion equations of a screw rod and a roller;
s5: and (5) solving the elastic kinetic equation in the step (S3) by combining the rigid motion equations of the screw and the roller in the step (S4) to complete the dynamic calculation of the double-nut planetary roller screw based on elastic deformation.
Further, the specific operation of step S1 includes,
s11: calculating the stiffness k of the screw, nut and roller unit of a double-nut planetary roller screweS、keNAnd keR；
Figure BDA0002628281760000031
Wherein i-S, N or R-a lead screw, nut or roller;
Ei、Aeiand Lei-the corresponding modulus of elasticity, cross-sectional area and length of the screw, nut or roller unit;
s12: calculating the rigidity of the nonlinear contact unit between the meshing points of the screw rod and the roller and the meshing points of the nut and the roller, respectively
Figure BDA0002628281760000032
Figure BDA0002628281760000033
In the formula, FRszAnd FRnzRespectively the contact forces between the screw and the roller and between the nut and the roller,RszandRnzaxial components of contact deformation between the screw rod and the roller and between the nut and the roller respectively;
λRsand betaRsThe rollers being on the screwHelix angle and flank angle at the flank contact point;
λRnand betaRn-the helix angle and flank angle of the roller at the nut side contact point;
ERs、RRsand
Figure BDA0002628281760000034
-equivalent modulus of elasticity, equivalent radius of curvature and curvature ratio at the point of engagement of the screw and the roller;
ERn、RRnand
Figure BDA0002628281760000035
-equivalent modulus of elasticity, equivalent radius of curvature and curvature ratio at the point of engagement of the nut and the roller.
Further, the specific operation of step S2 includes,
s21: according to the relation between the deformation of each unit and the elastic displacement of the node in the spring mass system, obtaining the value of A & u;
wherein, A is a conversion matrix between node elastic displacement and unit deformation;
u-node elastic displacement vector;
-a unit deformation vector;
Figure BDA0002628281760000041
wherein, a1And a2-element numbering of rows and columns in the matrix;
neland nnodeThe number of units and nodes in the spring mass system;
most of the elements in the matrix a have values of 0, and the non-zero elements therein are:
Figure BDA0002628281760000042
and
Figure BDA0002628281760000043
in the formula, neNAnd neNR-the number of nut elements and the number of contact elements between the nut and the roller;
nnoNand nnoR-the number of nut nodes and the number of roller nodes;
neRand neRS-the number of roller means and the number of contact means between the screw and the rollers;
nWNR-the sum of the number of nut units, the number of roller units and the number of contact units between the nut and the roller, nWNR＝neN+neNR+neR；
S22: on the basis of step S21, based on the constraint conditions of the double-nut planetary roller screw, the relationship between the deformation of each unit and the elastic displacement of the node may be expressed as a '· u';
wherein A' is a companion matrix of the spring mass system;
u' — unconstrained node elastic displacement;
Figure BDA0002628281760000051
Figure BDA0002628281760000052
wherein n isnoS-number of nodes of the screw unit;
s23: according to the stress balance relationship, the relationship between the force acting on the unit and the elastic displacement of each node is Fd＝K·A′·u′；
In the formula, Fd-forces acting on the individual cells;
k is the stiffness matrix of the spring mass system;
Figure BDA0002628281760000053
wherein the content of the first and second substances,
Figure BDA0002628281760000054
1, 2, …, nelThe stiffness of the individual cells.
Further, the specific operation of step S3 includes,
s31: establishing a relation between deformation coordination and stress balance of the double nuts and the pre-tightening gaskets;
s32: and (3) establishing an elastic dynamic equation of the double-nut planetary roller screw with coupled stress-deformation-motion parameters by using the adjoint matrix obtained in the step (1).
Further, the specific operation of step S31 includes,
s311: in the unloaded state, the pressure acting on the pre-tightening washer between the two nuts can be expressed as
Figure BDA0002628281760000061
In the formula:
Figure BDA0002628281760000062
-initial deformation of the pre-tensioning pad;
Figure BDA0002628281760000063
and
Figure BDA0002628281760000064
n thTAnd (n) thT+1) initial elastic displacement of the node;
Figure BDA0002628281760000065
SpandSp-initial deformation, stiffness and thickness of the pre-tensioned gasket;
gN-a gap between the # 1 nut and the # 2 nut;
s312: in the loaded state, the pressure acting on the pre-tightening gasket between the two nuts can be expressed as
Figure BDA0002628281760000066
In the formula:
Sp-deformation of the pre-tightening pad under load;
Figure BDA0002628281760000067
and
Figure BDA0002628281760000068
when bearing the load nTAnd (n) thT+1) elastic displacement of the node;
Sp-deformation of the pre-tightening pad under load;
s313: according to the stress balance relationship, the initial pretightening force, the load, the stress of the pretightening gasket and the actual predicted force of the two nuts have the following relationship:
Figure BDA0002628281760000069
Figure BDA00026282817600000610
in the formula, Fpre0-initial pre-tightening force of the double-nut planetary roller screw;
Fpre1and Fpre2And the 1# nut and the 2# nut are subjected to pre-tightening force when bearing load.
Further, in step S32, the adjoint matrix obtained in step 1 is used to obtain an elastic dynamic equation of the double-nut planetary roller screw with coupled stress-deformation-motion parameters as
F′noN+F′in+(A′)TfeSq-(A′)TFe＝0；
In the formula: f'noN-an external force exerted on the node,
Figure BDA0002628281760000071
F′inthe inertial force to which the node is subjected,
Figure BDA0002628281760000072
wherein the content of the first and second substances,
Figure BDA0002628281760000073
-acceleration of the nut;
meN1and
Figure BDA0002628281760000074
-1 st and n theNThe mass of each nut unit;
meR1and
Figure BDA0002628281760000075
-1 st and n theRThe mass of each roller unit;
feSqthe friction to which the unit is subjected,
Figure RE-GDA0002720309450000074
wherein f isRsz1，1And
Figure BDA0002628281760000077
-1 st and n thTFriction force of a contact unit between the lead screw and the 1# roller;
fRsz2，1and
Figure BDA0002628281760000078
-1 st and n thTFriction force of a contact unit between the lead screw and the 2# roller;
Fe-the forces formed by the elastic deformation of the unit and by the overturning of the balancing roller,
Figure BDA0002628281760000081
wherein the content of the first and second substances,
Figure BDA0002628281760000082
further, in step S4, the rigid body motion equations of the screw and the roller are specifically:
equation of motion of roller movement
Figure BDA0002628281760000083
Rotational equation of motion of roller about axis
Figure BDA0002628281760000084
And the rotational equation of motion of the screw about its axis
Figure BDA0002628281760000085
In the formula:
Figure BDA0002628281760000086
and
Figure BDA0002628281760000087
-friction between the screw and the roller;
Figure BDA0002628281760000088
and
Figure BDA0002628281760000089
-nuts and rollersAnd the contact force of the inner gear ring and the roller;
Figure BDA00026282817600000810
and
Figure BDA00026282817600000811
contact forces and friction forces between the cage and the rollers.
mR-the mass of the rollers;
Figure BDA00026282817600000812
and
Figure BDA00026282817600000813
-the speed and acceleration of the cage;
rSand rR-nominal radius of the screw and nut;
Figure BDA00026282817600000814
and
Figure BDA00026282817600000815
-the position vectors of the screw, the nut, the cage and the inner ring gear and the roller contact point;
nSand IR-the number of heads of the screw and the moment of inertia of the rollers;
μSR-the coefficient of friction of the screw and the roller;
Figure BDA0002628281760000091
-the common normal direction at the contact point of the screw and the roller;
LSand MSz-lead and drive torque of the lead screw;
Figure BDA0002628281760000092
wherein the content of the first and second substances,
rSrand rRs-the meshing radius of the screw and the roller;
Figure BDA0002628281760000093
-the rotational speed of the screw.
Further, the concrete operation of solving the elastic dynamic equation of step S3 in step S5 includes:
s51: in the static and non-nut-loaded condition,
Figure BDA0002628281760000094
and F Nz0, which is substituted into elastodynamic equation F 'in step S3'noN+F′in+(A′)TfeSq-(A′)TFeCalculating the deformation and stress of a pre-tightening gasket in the double-nut planetary roller screw under the condition of static state and no nut load
Figure BDA0002628281760000095
And
Figure BDA0002628281760000096
s52: substituting the specific nut load F into step S51NzIn a
Figure BDA0002628281760000097
Under the condition (1), calculating the pretightening force to which the nut # 1 and the nut # 2 are subjected by using the elastic kinetic equation in the step S3;
s53: the pretightening force to which the 1# nut and the 2# nut are subjected, which is obtained by calculation in the step S52, is taken as a known quantity, and the rotating speed of the screw rod is considered
Figure BDA0002628281760000098
And acceleration
Figure BDA0002628281760000099
In the elasticity of the screw, roller and nutUnder the condition that the deformation is zero, solving the elastic kinetic equation in the step S3 and the rigid motion equation of the screw and the roller in the step S4 in a simultaneous mode to obtain initial results of the motion and stress of each part in the double-nut planetary roller screw;
s54: substituting the initial calculated values of the motion and stress of each part as known quantities into the elastic kinetic equation in the step S3, and calculating to obtain the initial result of load distribution of the screw rod, the roller and the nut by considering elastic deformation;
s55: and taking the initial results of the motion, stress and load distribution of each part as initial values, considering the motion of the screw, the deformation and the pretightening force of the part, simultaneously solving the elastic dynamic equation in the step S3 and the rigid motion equation of the screw and the roller in the step S4, and completing the dynamic calculation of the double-nut planetary roller screw based on the elastic deformation.
The invention has the beneficial effects that: according to the double-nut planetary roller screw dynamics research method based on elastic deformation, a spring mass system comprehensively considering elastic deformation, inertia force and pretightening force is formed, a stress-deformation-motion parameter coupled double-nut planetary roller screw elastic dynamics equation is established, motion state calculation, pretightening force change analysis, motion part stress and elastic deformation calculation of the motion parts under different use conditions can be realized, and a basis is provided for strength and rigidity check, friction and wear analysis, structural design and pretightening force selection of the double-nut planetary roller screw.
Drawings
FIG. 1 is a schematic structural view of a double nut planetary roller screw;
FIG. 2 is a flow chart of a double-nut planetary roller screw dynamics research method based on elastic deformation in the invention;
FIG. 3 is a schematic diagram showing the structural dispersion of a double nut planetary roller screw;
FIG. 4 is a schematic diagram of the stress and deformation relationship between a double nut and a pre-tightening gasket of the double nut planetary roller screw in a no-load state;
FIG. 5 is a schematic diagram of the stress and deformation relationship between a double nut and a pre-tightening gasket when the double nut planetary roller screw bears a load;
FIG. 6 is a schematic view of a force analysis of a double nut planetary roller screw;
FIG. 7 is a force analysis diagram of a screw in a double nut planetary roller screw;
FIG. 8 is a flow chart of the solution of the elastic dynamic equation of the double-nut planetary roller screw in the invention;
FIG. 9 is a schematic diagram of the variation of the pre-tightening force of the double-nut planetary roller screw acting on the # 1 nut and the # 2 nut according to the load in the embodiment of the invention;
FIG. 10 is a result of a dynamic simulation of a double nut planetary roller screw in an embodiment of the present invention;
FIG. 11 is a diagram showing the load distribution between the screw and the 1# roller and between the 1# nut and the 1# roller according to the embodiment of the present invention;
FIG. 12 is a diagram showing the load distribution between the screw and the # 2 roller and between the # 2 nut and the # 2 roller in the embodiment of the present invention.
Wherein: the nut comprises a 1-1# nut, a 2-2# nut, a 3-1# roller, a 4-2# roller, a 5-1# retainer, a 6-2# retainer, a 7-1# inner gear ring, a 8-2# inner gear ring, a 9-lead screw and a 10-pre-tightening gasket.
Detailed Description
In order to make those skilled in the art better understand the technical solution of the present invention, the following further describes the technical solution of the present invention with reference to the drawings and the embodiments.
The structure composition of the double-nut planetary roller screw is shown in figure 1, and the double-nut planetary roller screw comprises a 1# nut 1, a 2# nut 2, a 1# roller 3, a 2# roller 4, a 1# retainer 5, a 2# retainer 6, a 1# inner gear ring 7, a 2# inner gear ring 8 and a screw 9, wherein a pre-tightening gasket 10 is clamped between the 1# nut 1 and the 2# nut 2, the 1# roller 3 and the 2# roller 4 are respectively positioned inside the 1# nut 1 and the 2# nut 2 and are both in contact with the screw 9, and the 1# retainer 5 and the 2# retainer 6 are respectively installed at two ends of the 1# nut 1 and the 2# nut 2 to ensure that the rollers always keep the same interval. The # 1 ring gear 7 is mounted between the # 1 nut 1 and the # 1 holder 5, and the # 2 ring gear 8 is mounted between the # 2 nut 2 and the # 2 holder 6.
Based on the structural characteristics of the double-nut planetary roller screw, the double-nut planetary roller screw dynamics research method based on elastic deformation, as shown in figure 2, comprises the following steps,
s1: according to the structural characteristics of the double-nut planetary roller screw, the structural dispersion of the screw, the roller and the nut is realized by adopting the spring mass unit, the contact deformation of the screw and the roller and the contact deformation of each meshing point between the nut and the roller are simulated by utilizing the nonlinear contact unit, and the deformation of the pre-tightening gasket is simulated by arranging the spring unit, so that a double-nut planetary roller screw spring mass system comprehensively considering elastic deformation, inertia force and pre-tightening force is formed;
specifically, a double-nut planetary roller screw is dispersed into a spring mass system, as shown in fig. 3, the numbering modes of each node and unit are as follows: the nodes are numbered according to the sequence from 1 # nut 1, 2 # nut 2, 1 # roller 3, 2# roller 4 and screw 9, and the units are numbered according to the sequence from 1 # nut 1, 2# nut 2, the meshing point between 1 # nut 1 and 1# roller 3, the meshing point between 2 # nut 2 and 2 # roller 4, 1 # roller 3, 2# roller 4, the meshing point between 1# roller 3 and screw 9, the meshing point between 2# roller 4 and screw 9.
Further, calculating the rigidity k of the screw, nut and roller unit of the double-nut planetary roller screweS、keNAnd keR；
Figure BDA0002628281760000121
Wherein i-S, N or R-a lead screw, nut or roller;
Ei、Aeiand Lei-the corresponding modulus of elasticity, cross-sectional area and length of the screw, nut or roller unit;
calculating the rigidity of the nonlinear contact unit between the meshing points of the screw rod and the roller and the meshing points of the nut and the roller, respectively
Figure BDA0002628281760000122
Figure BDA0002628281760000123
In the formula, FRszAnd FRnzRespectively the contact forces between the screw and the roller and between the nut and the roller,RszandRnzaxial components of contact deformation between the screw rod and the roller and between the nut and the roller respectively;
λRsand betaRs-the lead angle and flank angle of the roller at the screw-side contact point;
λRnand betaRn-the helix angle and flank angle of the roller at the nut side contact point;
ERs、RRsand
Figure BDA0002628281760000124
-equivalent modulus of elasticity, equivalent radius of curvature and curvature ratio at the point of engagement of the screw and the roller.
ERn、RRnAnd
Figure BDA0002628281760000133
-equivalent modulus of elasticity, equivalent radius of curvature and curvature ratio at the point of engagement of the nut and the roller.
Further, step S2: calculating a adjoint matrix and a stiffness matrix of the spring mass system, the specific operations including,
s21: according to the relation between the deformation of each unit and the elastic displacement of the node in the spring mass system, obtaining the value of A & u;
wherein, A is a conversion matrix between node elastic displacement and unit deformation;
u-node elastic displacement vector;
-a unit deformation vector;
Figure BDA0002628281760000131
wherein，a1And a2-element numbering of rows and columns in the matrix;
neland nnodeThe number of units and nodes in the spring mass system;
most of the elements in the matrix a have values of 0, and the non-zero elements therein are:
Figure BDA0002628281760000132
and
Figure BDA0002628281760000141
in the formula, neNAnd neNR-the number of nut elements and the number of contact elements between the nut and the roller;
nnoNand nnoR-the number of nut nodes and the number of roller nodes;
neRand neRS-the number of roller means and the number of contact means between the screw and the rollers;
nWNR-the sum of the number of nut units, the number of roller units and the number of contact units between the nut and the roller, nWNR＝neN+neNR+neR；
S22: on the basis of step S21, based on the constraint conditions of the double-nut planetary roller screw, the relationship between the deformation of each unit and the elastic displacement of the node may be expressed as a '· u';
wherein A' is a companion matrix of the spring mass system;
u' — unconstrained node elastic displacement;
Figure BDA0002628281760000142
Figure BDA0002628281760000143
wherein n isnoS-number of nodes of the screw unit;
s23: according to the stress balance relationship, the relationship between the force acting on the unit and the elastic displacement of each node is Fd＝K·A′·u′；
In the formula, Fd-forces acting on the individual cells;
k is the stiffness matrix of the spring mass system;
Figure BDA0002628281760000151
wherein k is1、k2、…、 k nel1, 2, …, nelThe stiffness of the individual cells.
Further, step S3, establishing an elastic dynamic equation of the double-nut planetary roller screw with coupled stress-deformation-motion parameters; the specific operation of the method comprises the following steps of,
s31: establishing a relation between deformation coordination and stress balance of the double nuts and the pre-tightening gaskets;
s32: establishing an elastic dynamic equation of the double-nut planetary roller screw with coupled stress-deformation-motion parameters by using the adjoint matrix obtained in the step 1;
wherein, the specific operations of step S31 include,
s311: as shown in FIG. 4, the pressure applied to the pre-load pad between the two nuts in the unloaded state can be expressed as
Figure BDA0002628281760000152
In the formula:
Figure BDA0002628281760000153
-initial deformation of the pre-tensioning pad;
Figure BDA0002628281760000154
and
Figure BDA0002628281760000155
n thTAnd (n) thT+1) initial elastic displacement of the node;
Figure BDA0002628281760000156
and
Figure BDA0002628281760000157
-initial deformation, stiffness and thickness of the pre-tensioned gasket;
gN-a gap between the # 1 nut and the # 2 nut;
s312: as shown in FIG. 5, the compressive force applied to the preload pad between the two nuts under load is expressed as
Figure BDA0002628281760000158
In the formula:
Sp-deformation of the pre-tightening pad under load;
Figure BDA0002628281760000161
and
Figure BDA0002628281760000162
when bearing the load nTAnd (n) thT+1) elastic displacement of the node;
Sp-deformation of the pre-tightening pad under load;
s313: according to the stress balance relationship, the initial pretightening force, the load, the stress of the pretightening gasket and the actual predicted force of the two nuts have the following relationship:
Figure BDA0002628281760000163
Figure BDA0002628281760000164
in the formula, Fpre0-initial pre-tightening force of the double-nut planetary roller screw;
Fpre1and Fpre2And the 1# nut and the 2# nut are subjected to pre-tightening force when bearing load.
Further, the specific operation of step S32 includes,
the force of the double-nut planetary roller screw is analyzed as shown in figure 6.
According to the stress analysis shown in the attached figure 6, the adjoint matrix obtained in the step 1 is used to obtain an elastic dynamic equation of the double-nut planetary roller screw with coupled stress-deformation-motion parameters, wherein the elastic dynamic equation is as follows
F′noN+F′in+(A′)TfeSq-(A′)TFe＝0；
In the formula: f'noN-an external force exerted on the node,
Figure BDA0002628281760000165
F′inthe inertial force to which the node is subjected,
Figure BDA0002628281760000166
wherein the content of the first and second substances,
Figure BDA0002628281760000171
-acceleration of the nut;
meN1and
Figure BDA0002628281760000172
-1 st and n theNThe mass of each nut unit;
meR1and
Figure BDA0002628281760000173
-1 st and n theRThe mass of each roller unit;
feSqthe friction to which the unit is subjected,
Figure RE-GDA0002720309450000172
wherein f isRsz1，1And
Figure BDA0002628281760000175
-1 st and n thTFriction force of a contact unit between the lead screw and the 1# roller;
fRsz2，1and
Figure BDA0002628281760000176
-1 st and n thTFriction force of a contact unit between the lead screw and the 2# roller;
Fe-the forces formed by the elastic deformation of the unit and by the overturning of the balancing roller,
Figure BDA0002628281760000177
wherein the content of the first and second substances,
Figure BDA0002628281760000178
further, step S4: establishing rigid motion equations of a screw rod and a roller;
specifically, the above-mentioned double-nut planetary roller screw motion equation considering elastic deformation does not include radial and tangential motions of the roller and rotational motions of each part, so that in the case of considering radial and tangential motions of the roller and rotational motions of each part, a screw and roller rigid motion equation of the double-nut planetary roller screw can be obtained, specifically:
according to the stress analysis of the double-nut planetary roller screw shown in the attached figure 6, a roller movement motion equation can be obtained
Figure BDA0002628281760000181
From the force analysis of the screw shown in FIG. 7, the equation of rotational motion of the roller about the axis can be derived
Figure BDA0002628281760000182
And the rotational equation of motion of the screw about its axis
Figure BDA0002628281760000183
In the formula:
Figure BDA0002628281760000184
and
Figure BDA0002628281760000185
-friction between the screw and the roller;
Figure BDA0002628281760000186
and
Figure BDA0002628281760000187
-the contact forces of the nut and the rollers and of the inner ring gear and the rollers;
Figure BDA0002628281760000188
and
Figure BDA0002628281760000189
contact forces and friction forces between the cage and the rollers.
mR-the mass of the rollers;
Figure BDA00026282817600001810
and
Figure BDA00026282817600001811
-the speed and acceleration of the cage;
rSand rR-nominal radius of the screw and nut;
Figure BDA00026282817600001812
and
Figure BDA00026282817600001813
-the position vectors of the screw, the nut, the cage and the inner ring gear and the roller contact point;
nSand IR-the number of heads of the screw and the moment of inertia of the rollers;
μSR-the coefficient of friction of the screw and the roller;
Figure BDA00026282817600001814
-the common normal direction at the contact point of the screw and the roller;
LSand MSz-lead and drive torque of the lead screw;
Figure BDA00026282817600001815
wherein the content of the first and second substances,
rSrand rRs-the meshing radius of the screw and the roller;
Figure BDA0002628281760000191
-the rotational speed of the screw.
Further, step S5: and (2) solving the elastic kinetic equation in the step (S3) in combination with the rigid motion equation of the screw and the roller in the step (S4) to complete the dynamic calculation of the double-nut planetary roller screw based on elastic deformation, wherein the specific operation flow is shown in figure 8 and comprises,
s51: in the static and non-nut-loaded condition,
Figure BDA0002628281760000192
and F Nz0, which is substituted into elastodynamic equation F 'in step S3'noN+F′in+(A′)TfeSq-(A′)TFeCalculating the deformation and stress of a pre-tightening gasket in the double-nut planetary roller screw under the condition of static state and no nut load
Figure BDA0002628281760000193
And
Figure BDA0002628281760000194
s52: substituting the specific nut load F into step S51NzIn a
Figure BDA0002628281760000195
Under the condition (1), calculating the pretightening force to which the nut # 1 and the nut # 2 are subjected by using the elastic kinetic equation in the step S3;
s53: the pretightening force to which the 1# nut and the 2# nut are subjected, which is obtained by calculation in the step S52, is taken as a known quantity, and the rotating speed of the screw rod is considered
Figure BDA0002628281760000196
And acceleration
Figure BDA0002628281760000197
Under the condition that the elastic deformation of the screw, the roller and the nut is zero, solving an elastic kinetic equation in the step S3 and a rigid motion equation of the screw and the roller in the step S4 in a simultaneous mode to obtain initial results of the motion and stress of each part in the double-nut planetary roller screw;
s54: substituting the initial calculated values of the motion and stress of each part as known quantities into the elastic kinetic equation in the step S3, and calculating to obtain the initial result of load distribution of the screw rod, the roller and the nut by considering elastic deformation;
s55: and taking the initial results of the motion, stress and load distribution of each part as initial values, considering the motion of the screw, the deformation and the pretightening force of the part, simultaneously solving the elastic dynamic equation in the step S3 and the rigid motion equation of the screw and the roller in the step S4, and completing the dynamic calculation of the double-nut planetary roller screw based on the elastic deformation.
Through the calculation, under the conditions of known structural parameters, quality parameters, rigidity parameters, constraint conditions, screw motion states, nut loads and pre-tightening forces of the double-nut planetary roller screw, the roller autorotation speed, the rotating speed of the retainer, load distribution among threads, stress between the roller and the retainer, stress between the roller and the inner gear ring, pre-tightening force borne by the nut, screw deformation, roller deformation, nut deformation and pre-tightening gasket deformation can be obtained.
Example (b):
the working condition parameters are selected as that the input rotating speed of the screw rod changes in a sine form, namely
Figure BDA0002628281760000201
In the formula (I), the compound is shown in the specification,
Figure BDA0002628281760000202
-the rotational speed of the screw; t is simulation time;
the angular acceleration of the screw is:
Figure BDA0002628281760000203
the nut load of the double-nut planetary roller screw is as follows:
Figure BDA0002628281760000204
in the formula:
FNz-nut loading; l isS-lead of lead screw;
the structural parameters and the quality parameters of the double-nut planetary roller screw are respectively shown in the table 1 and the table 2. Selecting the initial pretightening force between the double nuts as Fpre03000N, then the 1# nut and the 2# nut are subjected to a pretension force, Fpre1And Fpre2The change of the slide-rolling ratio between the screw and the rollers and the contact force between the retainer and the inner ring gear and the rollers along with the change of the nut load are shown in fig. 9 and fig. 10, wherein, (a) is a change curve of the slide-rolling ratio between the screw and the rollers, (b) is a change curve of the contact force between the retainer and the rollers, (c) is a change curve of the contact force between the inner ring gear and the # 1 roller, and (d) is a change curve of the contact force between the inner ring gear and the # 2 roller; the load distribution between the screw and the 1# roller and between the 1# nut and the 1# roller is shown in fig. 11, in which (a) is the load distribution between the screw and the 1# roller, and (b) is the load distribution between the 1# nut and the 1# roller; the load distribution between the screw and the 2# roller and between the 2# nut and the 2# roller is shown in fig. 12, in which (a) is the load distribution between the screw and the 2# roller, and (b) is the load distribution between the 2# nut and the 2# roller.
TABLE 1 structural parameters of a double-nut planetary roller screw
Figure BDA0002628281760000211
TABLE 2 quality parameters of the double-nut planetary roller screw
Figure BDA0002628281760000212
As can be seen from fig. 9, the preload of the 1# nut is less than the initial value and the preload of the 2# nut is greater than the initial value under the influence of the load. With the reduction of the load, the pretightening force of the 1# nut is increased, and the pretightening force of the 2# nut is reduced. As can be seen from the attached figures 10-12, the stress and motion state of each part corresponding to the 1# nut and the 2# nut are different, when the rotation direction of the screw rod is changed, the motion and stress of each part are changed suddenly, although the nominal radius of the 1# roller and the nominal radius of the 2# roller are the same, the maximum value of the stress of the 2# roller is much higher than that of the stress of the 1# roller.
The foregoing shows and describes the general principles, essential features, and advantages of the 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 given by way of illustration of the principles of the present invention, and that various changes and modifications may be made without departing from the spirit and scope of the invention as defined by the appended claims. The scope of the invention is defined by the appended claims and equivalents thereof.

Claims (8)

1. A double-nut planetary roller screw dynamics research method based on elastic deformation is disclosed, wherein the double-nut planetary roller screw comprises a 1# nut, a 2# nut, a 1# roller, a 2# roller, a screw and two inner gear rings, and a pre-tightening gasket is clamped between the 1# nut and the 2# nut; which is characterized by comprising the following steps of,
s1: according to the structural characteristics of the double-nut planetary roller screw, the spring mass unit is adopted to realize the structural dispersion of the screw, the roller and the nut, the nonlinear contact unit is utilized to simulate the contact deformation of each meshing point between the screw and the roller as well as between the nut and the roller, and the spring unit is arranged to simulate the deformation of a pre-tightening gasket, so that a double-nut planetary roller screw spring mass system which comprehensively considers the elastic deformation, the inertia force and the pre-tightening force is formed;
s2: calculating an adjoint matrix and a stiffness matrix of the spring mass system;
s3: establishing an elastic dynamic equation of a double-nut planetary roller screw with coupled stress-deformation-motion parameters;
s4: establishing rigid motion equations of a screw rod and a roller;
s5: and (5) solving the elastic kinetic equation in the step (S3) by combining the rigid motion equations of the screw and the roller in the step (S4) to complete the dynamic calculation of the double-nut planetary roller screw based on elastic deformation.
2. The double-nut planetary roller screw dynamics research method based on elastic deformation according to claim 1, characterized in that, the concrete operations of step S1 include,
s11: calculating the stiffness k of the screw, nut and roller unit of a double-nut planetary roller screweS、keNAnd keR；
Figure FDA0002628281750000011
Wherein i-S, N or R-a lead screw, nut or roller;
Ei、Aeiand Lei-the corresponding modulus of elasticity, cross-sectional area and length of the screw, nut or roller unit;
s12: calculating the rigidity of the nonlinear contact unit between the meshing points of the screw rod and the roller and the meshing points of the nut and the roller, respectively
Figure FDA0002628281750000021
Figure FDA0002628281750000022
In the formula, FRszAnd FRnzRespectively the contact forces between the screw and the roller and between the nut and the roller,RszandRnzaxial components of contact deformation between the screw rod and the roller and between the nut and the roller respectively;
λRsand betaRs-the lead angle and flank angle of the roller at the screw-side contact point;
λRnand betaRn-the helix angle and flank angle of the roller at the nut side contact point;
ERs、RRsand thetaRsEquivalent elastic modulus at the point of engagement of the screw and the rollerAmount, equivalent radius of curvature and curvature ratio;
ERn、RRnand thetaRn-equivalent modulus of elasticity, equivalent radius of curvature and curvature ratio at the point of engagement of the nut and the roller.
3. The double-nut planetary roller screw dynamics research method based on elastic deformation according to claim 2, characterized in that, the concrete operations of step S2 include,
s21: according to the relation between the deformation of each unit and the elastic displacement of the node in the spring mass system, obtaining the value of A & u;
wherein, A is a conversion matrix between node elastic displacement and unit deformation;
u-node elastic displacement vector;
-a unit deformation vector;
Figure FDA0002628281750000031
wherein, a1And a2-element numbering of rows and columns in the matrix;
neland nnodeThe number of units and nodes in the spring mass system;
most of the elements in the matrix a have values of 0, and the non-zero elements therein are:
Figure FDA0002628281750000032
and
Figure FDA0002628281750000033
in the formula, neNAnd neNR-the number of nut elements and the number of contact elements between the nut and the roller;
nnoNand nnoR-nut sectionCounting the number of points and the number of roller nodes;
neRand neRS-the number of roller means and the number of contact means between the screw and the rollers;
nWNR-the sum of the number of nut units, the number of roller units and the number of contact units between the nut and the roller, nWNR＝neN+neNR+neR；
S22: on the basis of step S21, based on the constraint conditions of the double-nut planetary roller screw, the relationship between the deformation of each unit and the elastic displacement of the node may be expressed as a '· u';
wherein A' is a companion matrix of the spring mass system;
u' — unconstrained node elastic displacement;
Figure FDA0002628281750000041
Figure FDA0002628281750000042
wherein n isnoS-number of nodes of the screw unit;
s23: according to the stress balance relationship, the relationship between the force acting on the unit and the elastic displacement of each node is Fd＝K·A′·u′；
In the formula, Fd-forces acting on the individual cells;
k is the stiffness matrix of the spring mass system;
Figure FDA0002628281750000043
wherein k is1、k2、...、
Figure FDA0002628281750000044
1, 2, …, nelThe stiffness of the individual cells.
4. The double-nut planetary roller screw dynamics research method based on elastic deformation according to the claim 3, characterized in that the concrete operations of the step S3 include,
s31: establishing a relation between deformation coordination and stress balance of the double nuts and the pre-tightening gaskets;
s32: and (3) establishing an elastic dynamic equation of the double-nut planetary roller screw with coupled stress-deformation-motion parameters by using the adjoint matrix obtained in the step (1).
5. The double-nut planetary roller screw dynamics research method based on elastic deformation according to the claim 4, characterized in that, the concrete operations of the step S31 include,
s311: in the unloaded state, the pressure acting on the pre-tightening washer between the two nuts can be expressed as
Figure FDA0002628281750000051
In the formula:
Figure FDA0002628281750000052
-initial deformation of the pre-tensioning pad;
Figure FDA0002628281750000053
and
Figure FDA0002628281750000054
n thTAnd (n) thT+1) initial elastic displacement of the node;
Figure FDA0002628281750000055
kSpand hSp-initial deformation, stiffness and thickness of the pre-tensioned gasket;
gN-1# nut and 2# nutThe gap therebetween;
s312: in the loaded state, the pressure acting on the pre-tightening gasket between the two nuts can be expressed as
Figure FDA0002628281750000056
In the formula:
Sp-deformation of the pre-tightening pad under load;
Figure FDA0002628281750000057
and
Figure FDA0002628281750000058
when bearing the load nTAnd (n) thT+1) elastic displacement of the node;
Sp-deformation of the pre-tightening pad under load;
s313: according to the stress balance relationship, the initial pretightening force, the load, the stress of the pretightening gasket and the actual predicted force of the two nuts have the following relationship:
Figure FDA0002628281750000059
Figure FDA00026282817500000510
in the formula, Fpre0-initial pre-tightening force of the double-nut planetary roller screw;
Fpre1and Fpre2And the 1# nut and the 2# nut are subjected to pre-tightening force when bearing load.
6. The method for researching the dynamics of the double-nut planetary roller screw based on the elastic deformation as claimed in claim 5, wherein the adjoint matrix obtained in the step 1 is used in the step S32 to obtain the elastic dynamics equation of the double-nut planetary roller screw with the coupled stress-deformation-motion parameters as
F′noN+F′in+(A′)TfeSq-(A′)TFe＝0；
In the formula: f'noN-an external force exerted on the node,
Figure RE-FDA0002720309440000061
F′inthe inertial force to which the node is subjected,
Figure RE-FDA0002720309440000062
wherein the content of the first and second substances,
Figure RE-FDA0002720309440000063
-acceleration of the nut;
meN1and
Figure RE-FDA0002720309440000064
-1 st and n theNThe mass of each nut unit;
meR1and
Figure RE-FDA0002720309440000065
-1 st and n theRThe mass of each roller unit;
feSqthe friction to which the unit is subjected,
Figure RE-FDA0002720309440000066
wherein f isRsz1，1And
Figure RE-FDA0002720309440000068
-1 st and n thTFriction force of a contact unit between the lead screw and the 1# roller;
fRsz2，1and
Figure RE-FDA0002720309440000067
-1 st and n thTFriction force of a contact unit between the lead screw and the 2# roller;
Fe-the forces formed by the elastic deformation of the unit and by the overturning of the balancing roller,
Fe＝Fd+Fζ；
wherein the content of the first and second substances,
Figure RE-FDA0002720309440000071
7. the method for researching the dynamics of the double-nut planetary roller screw based on the elastic deformation according to the claim 6, wherein the rigid body motion equations of the screw and the roller in the step S4 are specifically as follows:
equation of motion of roller movement
Figure FDA0002628281750000072
Rotational equation of motion of roller about axis
Figure FDA0002628281750000073
And the rotational equation of motion of the screw about its axis
Figure FDA0002628281750000074
In the formula:
Figure FDA0002628281750000075
and
Figure FDA0002628281750000076
-friction between the screw and the roller;
Figure FDA0002628281750000077
and
Figure FDA0002628281750000078
-the contact forces of the nut and the rollers and of the inner ring gear and the rollers;
Figure FDA0002628281750000079
and
Figure FDA00026282817500000710
contact forces and friction forces between the cage and the rollers.
mR-the mass of the rollers;
Figure FDA00026282817500000711
and
Figure FDA00026282817500000712
-the speed and acceleration of the cage;
rSand rR-nominal radius of the screw and nut;
Figure FDA0002628281750000081
and
Figure FDA0002628281750000082
-the position vectors of the contact points of the screw, the nut, the cage and the inner ring gear with the rollers;
nSand IR-the number of heads of the screw and the moment of inertia of the rollers;
μSR-the coefficient of friction of the screw and the roller;
Figure FDA0002628281750000083
-the common normal direction at the contact point of the screw and the roller;
LSand MSz-lead and drive torque of the lead screw;
Figure FDA0002628281750000084
wherein the content of the first and second substances,
rSrand rRs-the meshing radius of the screw and the roller;
Figure FDA0002628281750000085
-the rotational speed of the screw.
8. The double-nut planetary roller screw dynamics research method based on elastic deformation of claim 7, wherein the concrete operation of solving the elastic dynamics equation of the step S3 in the step S5 comprises:
s51: in the static and non-nut-loaded condition,
Figure FDA0002628281750000086
and FNz0, this is substituted into the elasto-kinetic equation F 'in step S3'noN+F′in+(A′)TfeSq-(A′)TFeCalculating the deformation and stress of a pre-tightening gasket in the double-nut planetary roller screw under the condition of static state and no nut load
Figure FDA0002628281750000087
And
Figure FDA0002628281750000088
s52: substituting the specific nut load F into step S51NzIn a
Figure FDA0002628281750000089
Under the condition (1), calculating the pretightening force to which the nut # 1 and the nut # 2 are subjected by using the elastic kinetic equation in the step S3;
s53: the pretightening force to which the 1# nut and the 2# nut are subjected, which is obtained by calculation in the step S52, is taken as a known quantity, and the rotating speed of the screw rod is considered
Figure FDA00026282817500000810
And acceleration
Figure FDA00026282817500000811
Under the condition that the elastic deformation of the screw, the roller and the nut is zero, solving the elastic kinetic equation in the step S3 and the rigid motion equation of the screw and the roller in the step S4 in a simultaneous mode to obtain initial results of the motion and stress of each part in the double-nut planetary roller screw;
s54: substituting the initial calculated values of the motion and stress of each part as known quantities into the elastic kinetic equation in the step S3, and calculating to obtain the initial result of load distribution of the screw rod, the roller and the nut by considering elastic deformation;
s55: and taking the initial results of the motion, stress and load distribution of each part as initial values, considering the motion of the screw, the deformation and the pretightening force of the part, simultaneously solving the elastic kinetic equation in the step S3 and the rigid motion equation of the screw and the roller in the step S4, and completing the dynamic calculation of the double-nut planetary roller screw based on elastic deformation.
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Cited By (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN112597636A (en) * 2020-12-09 2021-04-02 西北工业大学 Multistage planetary roller screw motion and stress state analysis method
CN113297708A (en) * 2021-06-23 2021-08-24 江苏理工学院 Pre-tightening force calculation method for stack type central solenoid coil
CN113392544A (en) * 2021-05-28 2021-09-14 东北林业大学 Method for calculating contact load of planetary threaded roller bearing based on deformation coordination theory
CN113434972A (en) * 2021-06-15 2021-09-24 汕头大学 Method for calculating axial static stiffness of planetary roller screw
CN113609616A (en) * 2021-08-05 2021-11-05 西北工业大学 Design method for double-nut planetary roller screw pre-tightening part
CN114801278A (en) * 2022-04-28 2022-07-29 南京理工大学 Intelligent press machine transmission efficiency monitoring system and method

Citations (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN104565252A (en) * 2015-01-30 2015-04-29 山东大学 Dual-nut ball screw assembly with controllable pre-tightening force
CN204512340U (en) * 2015-01-30 2015-07-29 山东大学 The double nut ball screw pair that a kind of pretightening force is controlled
CN106230308A (en) * 2016-09-05 2016-12-14 山东大学 A kind of ball screw assembly, pretightning force TT&C system having from perceptive function and method
CN108984831A (en) * 2018-06-07 2018-12-11 武汉理工大学 A kind of double lead-screw drive system transmission chain rigidity modeling method
CN110020486A (en) * 2019-04-11 2019-07-16 西北工业大学 A kind of planetary roller screw pair contact performance calculation method considering friction
US20190339139A1 (en) * 2016-12-28 2019-11-07 Ntn Corporation Load sensor and electromechanical brake system

Patent Citations (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN104565252A (en) * 2015-01-30 2015-04-29 山东大学 Dual-nut ball screw assembly with controllable pre-tightening force
CN204512340U (en) * 2015-01-30 2015-07-29 山东大学 The double nut ball screw pair that a kind of pretightening force is controlled
CN106230308A (en) * 2016-09-05 2016-12-14 山东大学 A kind of ball screw assembly, pretightning force TT&C system having from perceptive function and method
US20190339139A1 (en) * 2016-12-28 2019-11-07 Ntn Corporation Load sensor and electromechanical brake system
CN108984831A (en) * 2018-06-07 2018-12-11 武汉理工大学 A kind of double lead-screw drive system transmission chain rigidity modeling method
CN110020486A (en) * 2019-04-11 2019-07-16 西北工业大学 A kind of planetary roller screw pair contact performance calculation method considering friction

Non-Patent Citations (5)

* Cited by examiner, † Cited by third party
Title
SHANGJUN MA ET AL: "Local contact characteristics of threaded surfaces in a planetary roller screw mechanism", 《MECHANICS BASED DESIGN OF STRUCTURES AND MACHINES》 *
于珊珊: "混合陶瓷滚珠丝杠副的刚度对机床定位精度的影响", 《中国优秀硕士学位论文全文数据库电子期刊 工程科技I辑》 *
周长光: "滚珠丝杠副预紧力衰退预测及试验研究", 《中国博士学位论文全文数据库电子期刊 工程科技I辑》 *
张文杰 等: "不同安装方式下行星滚柱丝杠副载荷分布研究", 《西北工业大学学报》 *
马尚君 等: "行星滚柱丝杠副轴向弹性变形的有限元分析", 《机械传动》 *

Cited By (9)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN112597636A (en) * 2020-12-09 2021-04-02 西北工业大学 Multistage planetary roller screw motion and stress state analysis method
CN113392544A (en) * 2021-05-28 2021-09-14 东北林业大学 Method for calculating contact load of planetary threaded roller bearing based on deformation coordination theory
CN113434972A (en) * 2021-06-15 2021-09-24 汕头大学 Method for calculating axial static stiffness of planetary roller screw
CN113434972B (en) * 2021-06-15 2022-12-06 汕头大学 Method for calculating axial static stiffness of planetary roller screw
CN113297708A (en) * 2021-06-23 2021-08-24 江苏理工学院 Pre-tightening force calculation method for stack type central solenoid coil
CN113297708B (en) * 2021-06-23 2023-07-11 江苏理工学院 Pretightening force calculation method for stack type central solenoid coil
CN113609616A (en) * 2021-08-05 2021-11-05 西北工业大学 Design method for double-nut planetary roller screw pre-tightening part
CN113609616B (en) * 2021-08-05 2022-09-02 西北工业大学 Design method for double-nut planetary roller screw pre-tightening part
CN114801278A (en) * 2022-04-28 2022-07-29 南京理工大学 Intelligent press machine transmission efficiency monitoring system and method

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