CN112597636B - Multistage planetary roller screw motion and stress state analysis method - Google Patents
Multistage planetary roller screw motion and stress state analysis method Download PDFInfo
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- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
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- F16H25/18—Gearings comprising primarily only cams, cam-followers and screw-and-nut mechanisms for conveying or interconverting oscillating or reciprocating motions
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Abstract
The invention discloses a method for analyzing the motion and stress states of a multi-stage planetary roller screw, which relates to the technical field of screw transmission dynamics and comprises the following steps: according to the motion and stress characteristics of the multistage planetary roller screw, the generalized force corresponding to the rotational freedom of the screw and the retainer at each stage is deduced, and a Lagrange equation of the mechanism is established; and (3) considering the friction force between each stage of screw rod and each roller and the friction force between each stage of screw rod, supplementing and establishing a rotating motion equation of each stage of screw rod and an axial movement motion equation of each stage of screw rod, each roller and each nut, and completing simultaneous solution of each motion equation to obtain the motion and stress states of the multistage planetary roller screw rod. The invention realizes the analysis of the motion and stress states of all parts of the multi-stage planetary roller screw under different use working conditions, and provides a basis for the structural design and performance optimization of the mechanism.
Description
Technical Field
The invention relates to the technical field of screw drive dynamics, in particular to a method for analyzing the motion and stress state of a multi-stage planetary roller screw.
Background
The multi-stage planetary roller screw is a transmission mechanism which couples a plurality of sets of planetary roller screws to realize conversion from rotary motion to long-stroke linear drive. At present, single-stage planetary roller screws are mostly used as research objects by researchers, and the researches mainly focus on the research directions of meshing characteristics, load distribution and rigidity calculation, lubricating friction and motion characteristics, transmission precision and the like. And compared with a single-stage planetary roller screw, the multi-stage planetary roller screw has more complex motion and stress states. Firstly, in a multi-stage planetary roller screw, the motion and stress of each part in each stage are different and mutually influenced. Secondly, the multi-stage planetary roller screw contains more parts. Finally, friction and structural parameters at the connection of the planetary roller screws of all levels have great influence on the movement and stress of the planetary roller screws of all levels.
However, no analysis method related to the motion and stress of the multistage planetary roller screw exists in the prior art. And the analysis of the motion and stress under different working conditions is the basis of the structural design and performance optimization of the multistage planetary roller screw and is also the basis of the drive, control and motor design of the electromechanical servo system of the multistage planetary roller screw.
Therefore, in order to avoid the complicated analysis process, it is necessary to establish a more efficient analysis method. Aiming at the problems in the prior art, the application provides a method for analyzing the motion and stress states of a multi-stage planetary roller screw, which is used for analyzing the motion and stress states of all parts in the mechanism under different use working conditions. The method is convenient for strength and rigidity check, friction and wear analysis and structural design of the multi-stage planetary roller screw.
Disclosure of Invention
The invention aims to provide a method for analyzing the motion and stress states of a multi-stage planetary roller screw, which is used for analyzing the motion and stress states of all parts in a mechanism under different use conditions. The method is convenient for strength and rigidity check, friction and wear analysis and structural design of the multi-stage planetary roller screw.
The invention provides a method for analyzing the motion and stress state of a multistage planetary roller screw, which comprises the following steps:
step 1: collecting motion data of the multistage planetary roller screw, analyzing stress characteristics of the multistage planetary roller screw, and acquiring total kinetic energy of the multistage planetary roller screw in the operation process;
step 2: establishing a Lagrange model of the multistage planetary roller screw to obtain generalized force corresponding to the rotational freedom degrees of the screw and the retainer at each stage;
and step 3: performing stress analysis on the motion of the screw rod, the roller and the nut, additionally establishing a motion equation according to a Newton second law, and combining a Lagrange model with the motion equation to establish a dynamic model of the multistage planetary roller screw rod;
and 4, step 4: and analyzing the motion and stress states of the multistage planetary roller screw based on a dynamic model.
Further, the calculation mode of the total kinetic energy in the operation process of the multistage planetary roller screw in the step 1 is as follows:
in the formula:
-the rotation speed of the screw,
Rotational speed n of the kth cage T Overall number of stages of multi-stage planetary roller screws, N Rk The number of k-th stage rollers, J Sk And J Pk Moment of inertia, m, of the k-th screw and the cage Sk 、m Pk 、m Nk And m Pk Quality of screw, roller, nut and cage of the kth stage, L Si Lead of i-th stage screw, n Sk The number of thread heads of the kth-stage screw rod, r Sk And r Rk -nominal radius of the k-th order screw and roller.
Further, in the lagrangian model in step 2, the generalized force calculation method corresponding to the rotational degrees of freedom of the lead screw and the retainer is as follows:
the axial movement speed of the kth stage nut can be expressed as:
the drive torque of the k-th stage screw and roller can be expressed as:
in the formula: f. of Srxk 、f Sryk And f Srzk ——f Srk Component of x-, y-and z-, mu SR Coefficient of friction between screw and roller, F Srk -the contact force between the k-th stage screw and the roller,
-the sliding speed between the k-th stage screw and the roller;
in the formula: r is Srk 、
r Rsk And
-the engagement radius and the engagement declination angle, L, of the k-th stage screw and the roller Sk -lead of kth stage lead screw;
the k-th order rotation matrix may be expressed as:
in the formula: theta Pk -angle of rotation of the kth stage cage;
the speed of movement of the k-th stage screw contact point can be expressed as:
the friction between the kth stage screw and the kth-1 stage screw can be expressed as:
in the formula: mu.s SS -the kth-stage filamentCoefficient of friction between the bar and the (k-1) th lead screw, r SSk -equivalent radius, M, of the connection of the kth screw and the kth-1 screw Sk -drive torque of the kth stage screw;
the axial movement speed of the k-th stage screw can be expressed as:
in the formula:
-speed of movement of the k-1 th stage nut;
in the lagrangian model in the step 2, the generalized force corresponding to the rotational degree of freedom of the screw is expressed as:
in the formula:
n th T The external force applied to the secondary nut,
N th T Axial moving speed M of step nut S1 Drive torque f of the 1 st stage screw Srk -friction between the k-th lead screw and the roller,
-speed of movement of k-th stage screw contact point, H Pk The kth order rotation matrix, f Sk The friction force between the kth-level screw rod and the kth-1-level screw rod,
-axial displacement speed of the kth stage screw;
according to the lagrange method, the generalized force corresponding to the kth stage cage rotational degree of freedom can be expressed as:
in the formula:
-speed of the k-th stage roller contact point;
the lagrangian equation for a multistage planetary roller screw can be expressed as:
using kinetic energy T total The lagrange equation may be further expressed as:
in the formula: g S Generalized force, G, corresponding to the degree of freedom of rotation of the screw Pk Generalized forces corresponding to the rotational freedom of the kth cage,
-the rotational acceleration of the screw,
-rotational acceleration of the kth stage cage.
Further, in the step 3, the process of performing stress analysis on the motion of the screw, the roller and the nut and additionally establishing a motion equation is as follows:
the kinetic equation for the kth stage screw rotation is:
in the formula: j. the design is a square Sk Moment of inertia, M, of the k-th stage screw Sk And M S(k+1) -drive torque of the k-th and k + 1-th leadscrews;
the dynamic equation corresponding to the axial movement of the screw in the kth stage (k >1) is as follows:
in the formula: m is a unit of Sk The mass of the kth-stage screw rod,
-axial movement acceleration of the kth lead screw, F N(k-1) Load of the k-1 st nut, f Sk And f S(k+1) Friction force f experienced at the connection of the k-th and k + 1-th lead screws Srzk -axial component of friction force of screw and roller of the kth stage, F Srzk -the axial component of the k-th stage screw-to-roller contact force;
in the formula: f Srk -contact force, β, of screw and roller of the k-th stage Sk -flank angle of the kth stage screw;
the kinetic equation for the axial movement of the kth stage roller and nut is:
in the formula: m is a unit of Rk Mass of the kth roller, m Nk The mass of the kth-stage nut,
-axial movement acceleration of the kth nut, F Nk -load of the kth stage nut.
Further, step 4 is based on a dynamic model, and the method for analyzing the motion and stress state of the multistage planetary roller screw comprises the following steps:
the Lagrange equation and the complementary equation of motion are jointly contained (4 n) T -1) nonlinear equations with (4 n) T -1) unknowns, when the rotation speed of the screw and the load of the nut are known, solving by directly using a nonlinear equation solving function fsolve provided by Matlab software, and analyzing and obtaining the motion and stress states of the screw, the roller, the nut and the retainer at each stage by applying a multi-stage planetary roller screw Lagrange equation, a screw rotation motion equation and a screw, roller and nut axial movement motion equation.
Compared with the prior art, the invention has the following remarkable advantages:
the method for analyzing the motion and stress state of the multi-stage planetary roller screw does not need to repeatedly consider motion equations of the retainers of all stages, moving motion equations of the rollers of all stages along the tangential direction and the radial direction and rotating motion equations of the rollers of all stages, greatly simplifies a dynamic model and improves the solving efficiency. The motion and stress state calculation of each part of the multistage planetary roller screw under different use conditions can be completed under the condition of avoiding solving a large number of nonlinear equations, and a basis is provided for strength and rigidity check, friction and wear analysis and structural design of the mechanism.
Drawings
FIG. 1 is a flow chart of a method for analyzing rigid motion and stress states of a multi-stage planetary roller screw according to an embodiment of the present invention;
FIG. 2 is a structural composition and motion analysis diagram of a multi-stage planetary roller screw provided by an embodiment of the invention;
FIG. 3 is a force analysis diagram of a kth-stage planetary roller screw according to an embodiment of the present invention;
fig. 4 is a diagram illustrating a calculation result of the motion and stress states of the two-stage planetary roller screw according to the embodiment of the present invention.
Detailed Description
The technical solutions of the embodiments of the present invention are clearly and completely described below with reference to the drawings in the present invention, and it is obvious that the described embodiments are some embodiments of the present invention, but not all embodiments. All other embodiments, which can be obtained by a person skilled in the art without any inventive step based on the embodiments of the present invention, shall fall within the scope of protection of the present invention.
Referring to fig. 1-4, the invention provides a method for analyzing the motion and stress state of a multistage planetary roller screw, which comprises the following steps:
step 1: collecting motion data of the multistage planetary roller screw, analyzing stress characteristics of the multistage planetary roller screw, and acquiring total kinetic energy of the multistage planetary roller screw in the operation process;
and 2, step: establishing a Lagrange model of the multistage planetary roller screw to obtain generalized force corresponding to the rotational freedom degrees of the screw and the retainer at each stage;
and step 3: performing stress analysis on the motion of the screw rod, the roller and the nut, additionally establishing a motion equation according to a Newton second law, and combining a Lagrange model with the motion equation to establish a dynamic model of the multistage planetary roller screw rod;
and 4, step 4: and analyzing the motion and stress states of the multistage planetary roller screw based on a dynamic model.
Example 1
As shown in fig. 2, the multi-stage planetary roller screw mainly comprises a screw, a nut, rollers, a retainer and an inner gear ring. Symbol k denotes a k-th planetary roller screw, where k is 1,2, …, n T ，n T Representing the total number of stages of the multi-stage planetary roller screw. In FIG. 1, n T 2. Since the screw # (k-1) and the screw # k are connected by the sliding spline, the screws of the respective stages have the same rotational speed.
In the formula:
-the rotational speed of the kth stage screw;
as shown in fig. 2, the nut # (k-1) and the screw # k are connected through a thrust bearing, so that both have the same axial moving speed;
in the formula:
and
-axial displacement speed of the kth stage screw and the kth-1 stage nut;
if the screw, the nut and the roller are all right-handed threads, the axial moving speed of the k-th nut can be expressed as:
in the formula: l is Si -lead of the i-th stage lead screw (i ═ 1,2, …, k);
the autorotation speed of the kth-stage roller and the rotating speed of the retainer have the following relations:
in the formula:
and
-the rotation speed of the kth roller and the rotation speed of the cage, n Sk -number of screw heads of kth stage.
The calculation mode of the total kinetic energy in the operation process of the multistage planetary roller screw in the step 1 is as follows:
in the formula:
-the rotation speed of the screw,
Rotational speed n of the kth cage T Overall number of stages of multi-stage planetary roller screws, N Rk The number of the k-th stage rollers, J Sk And J Pk The moment of inertia of the k-th spindle and cage (k ═ 1,2, …, n T )、m Sk 、m Rk 、m Nk And m Pk Quality, L, of the kth screw, roller, nut and cage Si -lead (i ═ 1,2, …, k) of i-th stage lead screw, n Sk The number of thread heads of the kth-stage screw rod, r Sk And r Rk -nominal radius of the k-th order screw and roller.
Example 2
The force analysis of the kth stage planetary roller screw is shown in fig. 3. In FIG. 3, M Sk And f Sk Respectively the driving torque and the friction force acting on the k-th stage screw connection. F Nk Is the kth stage nut load, f SRk Is the friction between the k-th stage screw and the roller. o Pk -x Pk y Pk z Pk O-XYZ is a global coordinate system for a local coordinate system fixed on the kth-stage retainer. Theta Pk Is the angle of rotation of the kth cage. The force analysis shows that the friction force at the k-th stage screw rod connection part is as follows:
in the formula: mu.s SS -coefficient of friction, r, between the kth and the kth-1 stage screw SSk -the equivalent radius of the connection of the kth stage screw and the kth-1 stage screw;
according to the coulomb friction model, the friction force between the k-th stage screw and the roller can be expressed as:
in the formula: f. of Srxk 、f Sryk And f Srzk ——f Srk Component of x-, y-and z-, mu SR Coefficient of friction between screw and roller, F Srk -the contact force between the k-th stage screw and the roller,
-the sliding speed between the k-th stage screw and the roller;
in the formula: r is Srk 、
r Rsk And
-the engagement radius and the engagement declination angle, L, of the k-th stage screw and the roller Sk -lead of the kth stage lead screw;
local coordinate system o of the k-th order Pk -x Pk y Pk z Pk The rotation matrix transformed to the global coordinate system O-XYZ is:
in the formula: theta Pk -angle of rotation of the kth stage cage;
in the lagrangian model in the step 2, the generalized force corresponding to the rotational freedom of the screw is expressed as:
in the formula:
n th T The external force applied to the secondary nut,
N th T Axial moving speed M of step nut S1 -drive torque of the 1 st stage screw, f Srk -friction between the k-th lead screw and the roller,
-speed of movement of k-th stage screw contact point, H Pk -the kth order rotation matrix, f Sk Friction between the kth screw and the kth-1 screw (k)>1)、
-axial displacement speed of the kth stage screw;
the generalized force corresponding to the rotational degree of freedom of the kth stage cage can be expressed as:
in the formula:
-the speed of the k-th stage roller contact point.
By utilizing the kinetic energy and the generalized force expression of the multistage planetary roller screw, the lagrangian equation of the multistage planetary roller screw can be expressed as follows:
using kinetic energy T total The lagrange equation may be further expressed as:
in the formula: g S -generalized force, G, corresponding to the degree of freedom of rotation of the screw Pk -generalized forces corresponding to the rotational degrees of freedom of the kth stage cage,
-the rotational acceleration of the screw,
-rotational acceleration of the kth stage cage.
Example 3
Lagrange's equation of multi-stage planetary roller screw is contained (n) T +1) nonlinear equations. Due to the contact force F between the k-th order screw and the roller in the Lagrange's equation SRk And k (k)>1) Drive torque M of a stepped spindle Sk Unknown, so additional equations of motion need to be supplemented to complete the equation solution. The step 4 is based on a dynamic model, and the steps of analyzing the motion and stress state of the multistage planetary roller screw are as follows:
the kinetic equation for the kth stage screw rotation is:
in the formula: j is a unit of Sk Moment of inertia, M, of the k-th stage screw Sk And M S(k+1) -drive torque of the k-th and k + 1-th leadscrews;
the dynamic equation corresponding to the axial movement of the screw in the kth stage (k >1) is as follows:
in the formula: m is Sk The mass of the kth-stage screw rod,
-axial movement acceleration of the kth lead screw, F N(k-1) Load of the k-1 st nut, f Sk And f S(k+1) Friction force f experienced at the connection of the k-th and k + 1-th lead screws Srzk -axial component of friction force of screw and roller of the kth stage, F Srzk -the axial component of the k-th stage screw-to-roller contact force;
in the formula: f Srk -the k-th stage screw-roller contact force, β Sk -flank angle of the kth stage screw;
the kinetic equation for the axial movement of the kth stage roller and nut is:
in the formula: m is Rk Mass of the kth roller, m Nk -the mass of the kth nut,
-axial movement acceleration of the kth nut, F Nk -load of the kth stage nut.
Co-packaging of Lagrange's equations and complementary equations of motionContaining (4 n) T -1) nonlinear equations with (4 n) T -1) unknowns, when the rotation speed of the screw and the load of the nut are known, solving by directly using a nonlinear equation solving function fsolve provided by Matlab software, and analyzing and obtaining the motion and stress states of the screw, the roller, the nut and the retainer at each stage by applying a multi-stage planetary roller screw Lagrange equation, a screw rotation motion equation and a screw, roller and nut axial movement motion equation.
Example 4
The analysis method established by the invention is illustrated by taking a double-stage planetary roller screw as an example. The mechanical parameters of the double-stage planetary roller screw are shown in table 1, and the mass parameters are shown in tables 2 and 3. And calculating the motion and stress state of the mechanism when the rotating speed of the screw rod is step input 955r/min and the external load of the nut is FN2 to 5000N all the time. Taking u from friction coefficient of screw and roller at each stage SR 0.1, the coefficient of friction at the screw connection is u SS ＝0.2。
Calculated zeta ratio of k-th-stage retainer to rotating speed of lead screw PSk (k 1 or 2) drive torque M of the k-th stage screw Sk Axial component F of the contact force between the screw and the roller of the k-th order Srzk And the friction force f at the joint of the transmission efficiency eta and the 2 nd-stage screw rod S2 As shown in fig. 4(a) - (d), respectively. Wherein, the ratio of the retainer to the rotating speed of the screw is ζ PSk And the transmission efficiency η is a dimensionless quantity, and is calculated by the following formulas, respectively.
Under the working condition of step input, the 1 st-stage retainer and the rotating speed of the screw rod reach a steady-state value earlier. The drive torque of the stage 1 spindle is significantly higher than that of the stage 2 spindle, although the nominal radius of the stage 1 spindle is smaller. The axial component of the contact force between the stage 1 screw and the rollers increases first and then decreases to 818N. The axial component of the contact force between the stage 2 screw and the rollers gradually increases to 794N. The initial efficiency of the double-stage planetary roller screw is less than 0.45, gradually increases along with simulation time, and reaches 0.80 in a steady state. The change of the friction force at the connection part of the 2 nd-stage screw rod is the same as the change trend of the driving torque of the 2 nd-stage screw rod, and is reduced from 300N to 150N.
TABLE 1 structural parameters of a two-stage planetary roller screw
TABLE 2 quality parameters of the 1 st planetary roller screw
TABLE 3 quality parameters of 2 nd stage planetary roller screws
The above disclosure is only for a few specific embodiments of the present invention, however, the present invention is not limited to the above embodiments, and any variations that can be made by those skilled in the art are intended to fall within the scope of the present invention.
Claims (5)
1. A method for analyzing the motion and stress states of a multistage planetary roller screw is characterized by comprising the following steps of:
step 1: collecting motion data of the multistage planetary roller screw, analyzing stress characteristics of the multistage planetary roller screw, and acquiring total kinetic energy of the multistage planetary roller screw in the operation process;
and 2, step: establishing a Lagrange model of the multistage planetary roller screw to obtain generalized force corresponding to the rotational freedom degrees of the screw and the retainer at each stage;
and step 3: performing stress analysis on the motion of the screw rod, the roller and the nut, additionally establishing a motion equation according to a Newton second law, and combining a Lagrange model with the motion equation to establish a dynamic model of the multistage planetary roller screw rod;
and 4, step 4: and analyzing the motion and stress states of the multistage planetary roller screw based on a dynamic model.
2. The method for analyzing the motion and stress state of the multistage planetary roller screw according to claim 1, wherein the calculation mode of the total kinetic energy of the multistage planetary roller screw in the step 1 in the operation process is as follows:
in the formula:
-the rotation speed of the screw,
Rotational speed n of the kth cage T Overall number of stages of multi-stage planetary roller screws, N Rk The number of k-th stage rollers, J Sk And J Pk Moment of inertia of the kth screw and cage, m Sk 、m Rk 、m Nk And m Pk Quality of screw, roller, nut and cage of the kth stage, L Si Lead of i-th stage screw, n Sk The number of thread heads of the kth-stage screw rod, r Sk And r Rk -nominal radius of the k-th order screw and roller.
3. The method for analyzing the motion and stress state of the multistage planetary roller screw according to claim 1, wherein the Lagrangian model in the step 2 has the following generalized force calculation modes corresponding to the rotational degrees of freedom of each stage of the screw and the retainer:
the axial movement speed of the kth stage nut can be expressed as:
the drive torque of the k-th stage screw and roller can be expressed as:
in the formula: f. of Srxk 、f Sryk And f Srzk ——f Srk Component of x-, y-and z-, mu SR Coefficient of friction between screw and roller, F Srk -the contact force between the k-th stage screw and the roller,
-the sliding speed between the k-th stage screw and the roller;
in the formula: r is Srk 、
r Rsk And
-the engagement radius and the engagement declination angle, L, of the k-th stage screw and the roller Sk -lead of the kth stage lead screw;
the k-th order rotation matrix may be expressed as:
in the formula: theta Pk -the rotation angle of the kth cage;
the speed of movement of the k-th stage screw contact point can be expressed as:
the friction between the kth stage screw and the kth-1 stage screw can be expressed as:
in the formula: mu.s SS -coefficient of friction, r, between the kth and the kth-1 stage screw SSk -equivalent radius, M, of the connection of the kth screw and the kth-1 screw Sk -drive torque of the kth stage screw;
the axial movement speed of the k-th stage screw can be expressed as:
in the formula:
-speed of movement of the k-1 th nut;
in the lagrangian model in the step 2, the generalized force corresponding to the rotational freedom of the screw is expressed as:
in the formula:
n th T The external force born by the secondary nut,
N th T Axial moving speed M of step nut S1 Drive torque f of the 1 st stage screw Srk -friction between the k-th lead screw and the roller,
-speed of movement of k-th stage screw contact point, H Pk The kth order rotation matrix, f Sk The friction force between the kth-level screw rod and the kth-1-level screw rod,
-axial displacement speed of the kth stage screw;
according to the lagrange method, the generalized force corresponding to the kth stage cage rotational degree of freedom can be expressed as:
in the formula:
-speed of the k-th stage roller contact point;
the lagrangian equation for a multistage planetary roller screw can be expressed as:
using kinetic energy T total The lagrange equation may be further expressed as:
in the formula: g S -generalized force, G, corresponding to the degree of freedom of rotation of the screw Pk -generalized forces corresponding to the rotational degrees of freedom of the kth stage cage,
-the rotational acceleration of the screw,
-rotational acceleration of the kth stage cage.
4. The method for analyzing the motion and stress state of the multistage planetary roller screw according to claim 1, wherein the process of analyzing the stress of the motion of the screw, the roller and the nut and additionally establishing a motion equation in the step 3 is as follows:
the kinetic equation corresponding to the kth stage screw rotation is:
in the formula: j. the design is a square Sk Moment of inertia, M, of the k-th stage screw Sk And M S(K+1) -drive torque of the k-th and k + 1-th leadscrews;
the kinetic equation corresponding to the axial movement of the screw in the kth stage (k >1) is as follows:
in the formula: m is Sk The mass of the kth-stage screw rod,
-axial movement acceleration of the kth lead screw, F N(k-1) Load of the k-1 st nut, f Sk And f S(k+1) Friction force f experienced at the connection of the k-th and k + 1-th lead screws Srzk The kthAxial component of friction force between stage screw and roller, F Srzk -the axial component of the k-th stage screw-to-roller contact force;
in the formula: f Srk -contact force, β, of screw and roller of the k-th stage Sk -flank angle of the kth stage screw;
the kinetic equation for the axial movement of the kth stage roller and nut is:
in the formula: m is a unit of Rk Mass of the kth roller, m Nk The mass of the kth-stage nut,
-axial movement acceleration of the kth nut, F Nk -load of the kth stage nut.
5. The method for analyzing the motion and stress state of the multistage planetary roller screw according to claim 1, wherein the step 4 is based on a dynamic model, and the method for analyzing the motion and stress state of the multistage planetary roller screw is as follows:
the Lagrange equation and the complementary equation of motion are jointly contained (4 n) T -1) nonlinear equations with (4 n) T -1) unknowns; when the rotating speed of the screw rod and the load of the nut are known, a nonlinear equation solving function fsolve provided by Matlab software is directly used for solving, and the motion and stress states of the screw rods, the rollers, the nuts and the retainer at all levels are obtained through analysis by applying a multi-level planetary roller screw Lagrange equation, a screw rod rotating motion equation and a screw rod, roller and nut axial movement motion equation.
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