Shape modification and parameter optimization method for pin roller in planetary pin roller screw

Abstract

The invention discloses a modification and parameter optimization method for a pin roller in a planetary pin roller screw, which comprises the following steps: determining an optimizable modification parameter and range according to a three-section pin roller modification method; establishing a load distribution calculation model considering roller modification; the load distribution calculation model is used for calculating the relationship between the thread tooth deformation and the load distribution state; an initial value of modification parameter optimization is determined, and the load distribution of the planetary roller screw pair in the state is calculated through model iteration; according to the optimization target, updating the modification parameters and then repeatedly calculating the load distribution so as to optimize the modification parameters; and outputting the optimized modification parameters and load distribution. The non-uniform degree of distribution of the thread load of the planetary roller screw pair is reduced after the modification design of the rollers, and is further reduced after the modification parameter optimization, and the uniform distribution of the load is beneficial to improving the bearing performance such as the rated load and the shock resistance and fatigue resistance of the planetary roller screw under the same specification.

Description

Technical Field

[0001] The present application relates to the technical field of planetary roller screw pairs, and in particular to a method for shaping and optimizing parameters of rollers in a planetary roller screw. Background Art

[0002] Planetary roller screw pair is a kind of precision transmission pair that can realize the mutual conversion between rotational motion and linear motion. It is the core transmission functional component in electromechanical servo mechanism. It has the advantages of high precision, high load-bearing capacity and long life. It is widely used in aerospace, humanoid robots, industrial robots, vehicle braking systems and other industries. In order to ensure the overall performance of electromechanical servo mechanism, it is very important to improve the performance of planetary roller screw pair. Roller is the middle part of planetary roller screw pair transmission. Roller shaping can effectively improve the uneven distribution of thread load and improve the load-bearing performance of planetary roller screw pair.

[0003] The roller shaping method of a planetary roller screw pair changes the roller thread profile shape by designing the thread grinding process, and adjusts the thread contact deformation sequence to achieve a uniform load distribution effect. The existing roller shaping methods of planetary roller screw pairs have the following problems and defects: (1) The shaping design is all for the roller thread on one side, which is not suitable for planetary roller screw pairs with bidirectional travel; (2) The shaping parameters in the shaping design are single, which is not suitable for planetary roller screw pairs with nonlinear load distribution; (3) The shaping parameters are directly determined by load distribution calculation and finite element analysis, and there is a lack of optimization method or the optimization method has a single target; (4) There is a lack of multi-objective parameter optimization method for multi-parameter shaping of planetary roller screw pairs. Summary of the invention

[0004] The present invention proposes a roller shaping and parameter optimization method for a planetary roller screw, which is suitable for multi-parameter roller shaping design and multi-objective optimization of shaping parameters of a planetary roller screw pair with bidirectional stroke, reduces the uneven load distribution of the thread teeth of the planetary roller screw pair, and improves the load-bearing performance of the planetary roller screw pair.

[0005] In a first aspect, a method for modifying the shape and optimizing the parameters of rollers in a planetary roller screw is provided, comprising:

[0006] Step 1, determining the optimizable shaping parameters and ranges according to the three-stage roller shaping method;

[0007] Step 2, establishing a load distribution calculation model considering roller modification; the load distribution calculation model is used to calculate the relationship between thread deformation and load distribution state;

[0008] Step 3, determine the initial value of the optimization of the shaping parameters, and calculate the load distribution of the planetary roller screw pair in this state through model iteration;

[0009] Step 4, according to the optimization target, update the shaping parameters and repeat step 3 to calculate the load distribution to optimize the shaping parameters;

[0010] Step 5: Output the optimized shaping parameters and load distribution.

[0011] In conjunction with the first aspect, in certain implementations of the first aspect, the optimizable shaping parameters and ranges satisfy:

[0012] Roller thread modification length l in the direction corresponding to the nut installation end 1 ;

[0013] Roller thread modification length l in the corresponding direction of the right side screw fixed end 2 ;

[0014] Maximum modification amount of the nut installation end ε 1max , occurs on the first circle of threads on the left, and the modification amount decreases linearly with the increase of thread number until it becomes the same as the unmodified thread;

[0015] Maximum modification amount ε of the screw fixed end 2max , occurs on the first circle of thread teeth on the right, and the modification amount decreases linearly with the decrease of the thread tooth number until it becomes the same as the unmodified thread.

[0016] In combination with the first aspect, in certain implementations of the first aspect, the load distribution calculation model satisfies the force balance relationship between the nut-roller side and the roller-screw side:

[0017]

[0018] Z is the number of rollers in the planetary roller screw; F is the total axial external load borne by the planetary roller screw, F NRi and F SRi The thread teeth with serial number i on the roller bear the axial load from the nut or the screw, F Si and F Ni are the axial loads borne by the thread teeth with serial number i on the nut or screw, respectively, and F NRi and F SRi is the interaction force, which is equal in magnitude, and κ is the number of thread teeth in which the roller participates in meshing;

[0019] The load distribution calculation model also satisfies the deformation coordination equilibrium equation in the closed loop:

[0020] Δl BXi +Δl TXi +Δl CXi =Δl BRi +Δl TRi +Δl CRi +ε (1或2)i

[0021] Δl represents deformation, subscripts B, T, and C represent the cumulative deformation of the shaft segment, the relative deformation of the thread teeth, and the contact deformation of the thread teeth, respectively, subscripts X=S and N represent the screw and nut, respectively, subscript R represents the roller, and subscript i represents the thread tooth number; ε 1i is the modification amount of the left thread tooth i, ε 2i is the modification amount of the left thread tooth i;

[0022] The load distribution calculation model also satisfies the stiffness-deformation relationship matrix:

[0023] [K][F]=[ε]

[0024] [K] is the stiffness matrix, [F] is the thread force matrix, and [ε] is the modification matrix.

[0025] In combination with the first aspect, in certain implementations of the first aspect, the deformation coordination balance equation in the closed loop satisfies:

[0026]

[0027] P N is the thread pitch of the nut, E N is the elastic modulus of the nut, A N E is the cross-sectional area of ​​the nut's threaded shaft segment R is the elastic modulus of the roller, A R is the cross-sectional area of ​​the roller thread shaft segment;

[0028] X=S, N represents the screw or nut, K XR (e) are the first kind complete elliptic integrals corresponding to the Hertz contact ellipse on the contact side, m Xa is the major axis coefficient of the contact ellipse; F XRi is the axial force of the roller or screw on the ith thread of the roller, ρ XR is the sum of the principal curvatures of the two thread surfaces on the contact side; E′ XR The equivalent elastic modulus of the contact surface is β X and λ X They are the corresponding parts tooth profile half angle and thread lead angle respectively;

[0029] δ TXi =δ 1i +δ 2i +δ 3i +δ 4i +δ 5Yi

[0030] The subscripts X=S, R, and N represent the screw, roller, and nut, respectively; the subscripts Y=I and E represent the internal and external threads, respectively, where the screw and roller correspond to the external thread, and the nut corresponds to the internal thread; the subscripts 1, 2, 3, 4, and 5 represent the thread deformation caused by bending, shear force, root inclination, root shear, and radial force, respectively, and the subscript i represents the thread number.

[0031] In combination with the first aspect, in some implementations of the first aspect,

[0032]

[0033] a is the thread bottom thickness, b is the thread thickness, c is the thread top thickness, h is the thread f is the thread bottom height, β is the tooth profile half angle, F a is the axial force component, μ and E are the Poisson's ratio and elastic modulus of the thread material respectively; d pI Indicates the inner diameter of the equivalent hollow cylinder of the internal thread, D pI Indicates the outer diameter of the hollow cylinder equivalent to the internal thread; d pO Indicates the diameter of the solid cylinder equivalent to the external thread.

[0034] In combination with the first aspect, in some implementations of the first aspect, D 0 Indicates the outer diameter of the nut, d N and d S Respectively represent the pitch diameter of the nut and the lead screw thread, d R Indicates the modified median diameter of the roller, h f It represents the thread bottom height and Z represents the number of rollers.

[0035] In combination with the first aspect, in some implementations of the first aspect,

[0036]

[0037] [F]=[F NR1 ,F NR2 ,…,F NRκ ,F SR1 ,F SR2 ,…,F SRκ ] T

[0038] [ε]=[ε 11 ,ε 12 ,…ε 1g1 ,0,…,0,ε 2g2 ,ε 22 ,ε 21 ] T

[0039] g1 and g2 are l1 End and l 2 Number of end profile threads.

[0040] In conjunction with the first aspect, in some implementations of the first aspect, step 3 satisfies at least one of the following:

[0041] F NRi (0) and F SRi (0) As the initial value of the iterative calculation, it satisfies:

[0042]

[0043] The termination criterion of the iterative calculation is: judging the convergence of the load distribution results after one cycle process. If the second-order moment of the results of two cycles is less than the solution accuracy, the cycle is terminated, otherwise the cycle continues.

[0044] In combination with the first aspect, in some implementations of the first aspect, the optimization goal of step 4 is to make the maximum load distribution uneven coefficient max{ζ Xi} and the maximum thread load max{F Xi}reduce,

[0045]

[0046] Where F is the axial force transmitted by the planetary roller screw pair, Z is the number of rollers, κ is the number of roller meshing threads, and i represents the thread number.

[0047] In combination with the first aspect, in some implementations of the first aspect, the kth optimization iteration of step 4 includes:

[0048] Calculate the original array A of load distribution k ;

[0049] Under the condition of meeting the constraints, select the neighborhood parameters and calculate the load distribution to update the array B k ;

[0050] According to the Metropolis criterion, k and array B k Select the best:

[0051] If it is determined that B k Better than A k , B k The original array A of load distribution for the k+1th optimization iteration k+1 , and perform the k+1th optimization iteration;

[0052] If it is determined that B k Worse than A kAccording to the Metropolis criterion, when the random number is greater than the probability, B k The original array A of load distribution for the k+1th optimization iteration k+1 , and perform the k+1th optimization iteration; when the random number is less than the probability, A k The original array A of load distribution for the k+1th optimization iteration k+1 , and perform the k+1th optimization iteration.

[0053] Compared with the prior art, the solution provided by this application includes at least the following beneficial technical effects:

[0054] The object of the modification design in the present invention is the roller thread profile in the planetary roller screw pair with a bidirectional stroke; the modification design parameters in the present invention include the maximum modification amount on the roller side of the nut, the number of single-side modification threads on the roller side of the nut, the maximum modification amount on the roller screw side, and the number of single-side modification threads on the roller screw side; the parameter optimization targets in the present invention include the maximum load distribution unevenness coefficient of the single thread and the maximum axial load size of the single thread; the axial load distribution state of the thread teeth on the roller side and the roller screw side of the planetary roller screw pair in the present invention is calculated by considering the load distribution model of the planetary roller screw pair with load-balanced modification. Compared with the existing domestic and foreign solutions, this technical solution can realize the roller modification design for the planetary roller screw pair with a bidirectional stroke and the multi-parameter multi-objective modification parameter optimization. Through the roller modification design and multi-objective modification parameter optimization, the unevenness of the load distribution of the thread teeth of the planetary roller screw pair is reduced, and the uniform distribution of the load is conducive to improving the load-bearing performance and impact and fatigue resistance of the planetary roller screw under the same specifications, such as the rated load. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] Figure 1 The present invention is a flow chart of a method for shaping and optimizing parameters of rollers in a planetary roller screw.

[0056] Figure 2 This is a flow chart of the three-stage roller shaping method.

[0057] Figure 3 Schematic diagram of thread deformation coordination closed loop.

[0058] Figure 4 Schematic diagram of shaft segment deformation.

[0059] Figure 5 Schematic diagram of thread deformation.

[0060] Figure 6 Schematic diagram of thread contact deformation.

[0061] Figure 7 Schematic diagram of the deformation coordination stiffness model of the planetary roller screw pair.

[0062] Figure 8 Flow chart for multi-objective optimization of roller structure and shaping parameters.

[0063] Fig. 9 Schematic diagram of thread force decomposition.

[0064] Fig.10 Schematic diagram of the bending strength limit of the dangerous section of the thread tooth. DETAILED DESCRIPTION

[0065] The present application is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0066] like Figure 1 As shown, the present invention provides a method for modifying the shape and optimizing the parameters of rollers in a planetary roller screw. The specific steps are as follows.

[0067] Step 1: Determine the optimizable shaping parameters and ranges based on the three-stage roller shaping method.

[0068] like Figure 2 As shown in the figure, the three-stage roller modification method is a method for optimizing the load distribution of the standard planetary roller screw pair. It changes the roller thread profile to change the contact between the roller and the nut or roller. In the planetary roller screw pair, when the roller is in meshing with the nut and the screw through the thread, the nut installation end ( Figure 2 The roller thread modification length in the corresponding direction (left side) is l 1 , the right side lead screw fixed end ( Figure 2 The roller thread modification length in the corresponding direction (right side) is l 2 , the length of the thread without modification in the middle is l 3 ; The maximum modification amount of the nut installation end is ε 1max , occurs at the first circle of threads on the left, and the modification amount decreases linearly with the increase of thread number until it becomes the same as the unmodified thread; the maximum modification amount at the fixed end of the screw is ε 2max , occurs on the first circle of threads on the right, and the modification amount decreases linearly with the decrease of thread number until it becomes the same as the unmodified thread; d R is the nominal median diameter of the roller. The optimizable shaping parameters in the current shaping method are l 1 , l 2 and ε 1max , ε 2max .

[0069] Step 2: Establish a load distribution calculation model considering roller modification. The load distribution calculation model is used to calculate the relationship between thread deformation and load distribution state.

[0070] The load distribution calculation model satisfies the force balance relationship between the nut-roller side and the roller-screw side, which is shown in Formula 1:

[0071]

[0072] Where Z is the number of rollers in the planetary roller screw. F is the axial external load (total) borne by the planetary roller screw. NRi and F SRi The thread teeth with serial number i on the roller bear the axial load from the nut or the screw, F Si and F Ni are the axial loads borne by the thread teeth with serial number i on the nut or screw, respectively, and F NRi and F SRi is the interaction force, which is equal in magnitude, and κ is the number of thread teeth in which the rollers participate in the meshing.

[0073] The load distribution calculation model can also satisfy the deformation coordination equilibrium equation in the closed loop, and the relationship is shown in Formula 2:

[0074] Δl BXi +Δl TXi +Δl CXi =Δl BRi +Δl TRi +Δl CRi +ε (1或2)i Formula 2

[0075] In the formula, Δl represents deformation, subscripts B, T, and C represent the cumulative deformation of the shaft segment, the relative deformation of the thread teeth, and the contact deformation of the thread teeth, respectively, subscripts X=S and N represent the screw and nut, respectively, subscript R represents the roller, and subscript i represents the thread tooth number. ε 1i is the modification amount of the left thread tooth i, ε 2i is the modification amount of the left thread tooth i.

[0076] The load distribution calculation model can also satisfy the stiffness-deformation relationship matrix as shown in Equation 3:

[0077] [K][F]=[ε] Formula 3

[0078] Where [K] is the stiffness matrix, [F] is the thread force matrix, and [ε] is the modification matrix.

[0079] Step 3, determine the initial value of the modification parameter optimization, and calculate the load distribution of the planetary roller screw pair under this state through the model. The iterative solution algorithm process of the load distribution of the planetary roller screw pair considering the load-balanced modification is divided into three steps: parameter input, iterative calculation, and termination judgment.

[0080] (1) Parameter input: see Figure 1Box 2, the algorithm input values ​​are the structural parameters of the planetary roller screw pair and the solution accuracy A c The structural parameters of the planetary roller screw pair include the number of heads N, pitch P, tooth profile half angle, nominal diameter of the screw, theoretical diameter of the screw, number of rollers, arc radius, thread segment length, outer diameter of the nut and other standard design structural parameters, as well as modification parameters (l 1 , l 2 and ε 1max , ε 2max ) The maximum shaping amount and shaping length of the nut installation end and the maximum shaping amount and shaping length of the screw fixed end; the solution accuracy is used in the "termination judgment step" to judge the convergence of the load distribution results after one cycle. If the second-order moment of the results of two cycles is less than the solution accuracy, the cycle is terminated, otherwise the cycle continues. The greater the solution accuracy, the more accurate the result, but the longer the iterative calculation time.

[0081] (2) Iterative calculation: During the iterative calculation process, it is necessary to consider the initial value, calculation method and output value (as input for determining the termination of the iteration)

[0082] I initial value and output value

[0083] The initial value and output value are the numerical values ​​of the axial load borne by each thread tooth. The subscript i is used as the thread tooth number of the roller, screw or nut (i = 1, 2, 3, ..., κ), κ is the number of threads in which the roller participates in meshing, and a circle of roller threads is simultaneously on the nut-roller side ( Figure 2 upper side) and roller-screw side ( Figure 2 The lower side) completes the spiral transmission, while one circle of screw or nut thread teeth only completes the spiral transmission with one circle of roller thread teeth.

[0084] Assuming that the forces on each roller are balanced, the force balance relationship on the nut-roller side and the roller-screw side is shown in equation 1:

[0085]

[0086] Where Z is the number of rollers in the planetary roller screw. F is the axial external load (total) borne by the planetary roller screw. NRi and F SRi The thread teeth with serial number i on the roller bear the axial load from the nut or the screw, F Si and F Ni are the axial loads borne by the thread teeth with serial number i on the nut or screw, respectively, and F NRi and F SRi are interaction forces of equal magnitude.

[0087] Since the force is unknown before calculation, it is necessary to assume that F NRi (0) and FSRi (0) (a total of 2κ values) are used as the initial value for iterative calculation. This method uses averaging, as shown in Formula 2 (see Figure 1 Box 3 Equation 3):

[0088]

[0089] After the n+1th iteration calculation, we get F NRi (n+1) With F SRi (n+1) , and as calculated F NRi (n+1) With F SRi (n+1) Conditional F NRi (n) With F SRi (n) As the iterative calculation output value (see Figure 1 Box 6), used to terminate the judgment (see Figure 1 Box 7).

[0090] II. Calculation Methods

[0091] The calculation method is based on the closed-loop stiffness model of single thread deformation coordination (see Figure 3 ), establish the closed-loop deformation coordination equilibrium equation (see Equation 3), and finally form the thread tooth deformation coordination closed-loop stiffness model (see Figure 7 ) and the calculation matrix (see Equation 18).

[0092] In order to first establish the relationship between thread tooth load distribution and thread tooth deformation, the thread tooth load process during the planetary roller screw transmission process is analyzed. The deformation caused by the axial force during the planetary roller screw transmission process can be decomposed into the shaft segment deformation (see formula 4, Figure 4 ), thread deformation (see formula 9, Figure 5 ), thread contact deformation (see formula 13, Figure 6 ), and is determined by the normal force (or its component force) on the thread and the shaft segment stiffness (see equation 7), the thread stiffness (see equation 11) and the contact stiffness (see equation 15).

[0093] like Figure 3 As shown, the spring between a pair of threads in contact on the nut-roller side and the roller-screw side represents the coupling of thread stiffness (see equation 11) and contact stiffness (see equation 15). The spring between the adjacent threads of the nut, roller and screw represents the shaft segment stiffness (see equation 7). Based on the single thread deformation coordination closed loop, assuming that the position of the contact point does not change during the deformation process, the deformation coordination balance equation in the closed loop is established as shown in equation 3:

[0094] Δl BXi +ΔlTXi +Δl CXi =Δl BRi +Δl TRi +Δl CRi +ε (1或2)i Formula 3

[0095] In the formula, Δl represents deformation, subscripts B, T, and C represent the cumulative deformation of the shaft segment, the relative deformation of the thread teeth, and the contact deformation of the thread teeth, respectively, subscripts X=S and N represent the screw and nut, respectively, subscript R represents the roller, and subscript i represents the thread tooth number. The following is the calculation method of each element of the equation. ε 1i is the modification amount of the left thread tooth i, ε 2i is the modification amount of the left thread tooth i.

[0096] II.1 Cumulative deformation of shaft segment Δl BXi With Δl BRi

[0097] The cumulative deformation of the shaft segment is calculated by adding the deformations of multiple continuous threaded shaft segments.

[0098] like Figure 4 As shown in Figure 4, the shaft deformation of the planetary roller screw refers to the axial tensile and compressive deformation of the nut, screw and roller shaft segments caused by the axial component when the nut-roller side and the roller-screw side are subjected to normal loads. The magnitude is shown in Formula 4:

[0099]

[0100] In the formula, δ B Indicates the deformation of the shaft segment. The subscripts X = R, S, and N represent rollers, screws, or nuts, respectively. The subscript i represents the thread number. F Xi Indicates the axial force of the corresponding threaded shaft segment, L X Indicates the length of the shaft segment, E X is the elastic modulus, A X Indicates the cross-sectional area of ​​the threaded shaft segment of a part.

[0101] where δ B and F Xi are unknown variables, which can be solved by equation 4. X 、E X , A X Calculated from the input planetary roller screw parameters. X is the length of the shaft segment corresponding to the deformation of a single thread tooth shaft segment. The screw and nut have the same pitch, and the roller has half the pitch. According to the structural characteristics of the planetary roller screw, the screw, nut and roller have the same pitch, then L X The value is shown in formula 5 (P is the pitch):

[0102]

[0103] E X is the elastic modulus, which is only relevant to the material selected for the corresponding part. R ′ Relative A R represents the effect of roller modification, A X The calculation of is shown in formula 6:

[0104]

[0105] Where D 0 Indicates the outer diameter of the nut, d N ,d R and d S Respectively represent the thread diameters of the nut, roller and screw, d R ′ Indicates the roller modified median diameter, which is the roller median diameter minus 2 times the modification amount (e.g. Figure 2 shown), h f It represents the thread bottom height and Z represents the number of rollers.

[0106] According to the calculation formula of tensile and compressive stiffness of the shaft in material mechanics, the calculation of the stiffness of the threaded shaft section of the planetary roller screw is shown in Formula 7:

[0107]

[0108] The initial position of the shaft segment before deformation is affected by the cumulative deformation of the previous shaft segment and the force deformation of the current shaft segment. Taking the condition of installation on the opposite side and the nut under tension as an example, the corresponding nut-roller side and the cumulative deformation of the roller and nut shaft segment are shown in formula 8:

[0109]

[0110] II.2 Relative deformation of thread teeth Δl TXi With Δl TRi

[0111] like Figure 5 As shown in the figure, the relative deformation of the thread teeth is calculated by the deformation of the corresponding parts thread teeth. The meshing mode of the planetary roller screw thread teeth includes the internal thread meshing on the nut-roller side and the external thread meshing on the roller-screw side. The axial deformation law caused by load bending, shearing, root tilting and root shearing is consistent for both, but the deformation caused by the radial force component is different due to the different internal and external thread structures. According to the thread connection theory, the deformation of the part thread teeth is:

[0112] δ TXi =δ 1i +δ 2i +δ 3i +δ 4i +δ 5Yi Formula 9

[0113] In the formula, subscripts X=S, R, and N represent the screw, roller, and nut, respectively. Subscripts Y=I and E represent internal and external threads, respectively, where the screw and roller correspond to external threads and the nut corresponds to internal threads. Subscripts 1, 2, 3, 4, and 5 represent thread deformation caused by bending, shear force, root tilt, root shear, and radial force, respectively, and subscript i represents the thread number.

[0114] For the thread bottom thickness a, thread thickness b, thread top thickness c, thread bottom height h f The triangular thread with a tooth half angle of β is subjected to an axial force of F. a When the Poisson's ratio and elastic modulus of the thread material are μ and E respectively. pI Indicates the inner diameter of the equivalent hollow cylinder of the internal thread, D pI Indicates the outer diameter of the hollow cylinder equivalent to the internal thread; d pO Indicates the diameter of the solid cylinder equivalent to the external thread.

[0115] The calculation formulas for each deformation are shown in formula 10:

[0116]

[0117] The total stiffness of the thread teeth is shown in formula 11:

[0118]

[0119] The deformation of any circle of thread teeth is caused by the normal force of the two adjacent thread teeth in contact. Taking the condition of nut installation on the opposite side and tension as an example, the calculation formula of the relative deformation of the thread teeth is shown in formula 12:

[0120]

[0121] II.3 Thread contact deformation Δl CNi With Δl CRi

[0122] like Figure 6 As shown in the figure, when the PRSM is loaded, because the roller has an arc-shaped tooth profile, both the nut-roller side and the roller-screw side are point contacts. From the perspective of contact deformation, the tangential friction on the contact surface can be ignored, that is, the normal elastic deformation occurs at the contact point. According to the Hertz contact theory, when the two contact surfaces are in point contact and are in the elastic deformation stage, the magnitude of the deformation is shown in Formula 13:

[0123]

[0124] In the formula, X = S, N represents the screw or nut and the corresponding contact side with the roller, K XR(e) are the first kind complete elliptic integrals corresponding to the Hertz contact ellipse on the contact side, m Xa is the major axis coefficient of the contact ellipse; F XRi is the axial force of the roller or screw on the ith thread of the roller, ρ XR is the sum of the principal curvatures of the two thread surfaces on the contact side; E ′ XR The equivalent elastic modulus of the contact surface is β X and λ X They are the corresponding part tooth profile half angle and thread lead angle respectively.

[0125] Define the unit as The contact stiffness k CX , calculated as shown in formula 14:

[0126]

[0127] Taking the thread with serial number i as an example, the relationship between contact deformation stiffness and axial force can be simplified, as shown in Equation 15:

[0128]

[0129] Taking the case of installation on opposite sides and the nut under tension as an example, the contact deformation of the thread teeth of the nut and the roller is shown in formula 16:

[0130]

[0131] II.4 Deformation Compatibility Equations

[0132] Combined with equations 3, 8, 12, and 16, taking the condition where the nut is installed on the opposite side and subjected to tension as an example, the nut-roller side deformation coordination equation is shown in equation 17:

[0133]

[0134] like Figure 7 As shown in the deformation coordination stiffness model of the planetary roller screw, the fixed end of the screw is Figure 7 On the left side of the figure, the load application end is the left end. At this time, the nut is under pressure and the screw is under tension. The total axial load F applied to the nut is equal to the support force of the mounting bearing on the screw mounting end. If the nut, roller and screw all have κ threads participating in the load, then in any correct meshing state, there are κ-1 contact points on the nut-roller side and the roller-screw side to transmit the load. That is, there is a 2(κ-1) and deformation coordination closed loop (see Figure 3 ) and 2(κ-1) deformation coordination equations (see Equation 3, Equation 17), the nut-roller side and roller-screw side force balance relationship (see Equation 1) provide two equations, and these 2κ equations form a 2κ element first-order equation system with 4κ unknowns, among which F NRi、F SRi Each κ, Δl Xi (=Δl BXi +Δl TXi +Δl CXi )2κ, the stiffness-deformation relationship matrix of the load distribution calculation process of the planetary roller screw pair with load-balanced modification installed on the opposite side is shown in Formula 18:

[0135] [K][F]=[ε] Formula 18

[0136] Where [K] is the stiffness matrix, which is BS , k BN , k BR ′ , k TS , k TN , k TR , k CS , k CN As the calculated value, it is specifically shown in Formula 19:

[0137]

[0138] [F] is the thread force matrix, as shown in formula 20:

[0139] [F]=[F NR1 ,F NR2 ,…,F NRκ ,F SR1 ,F SR2 ,…,F SRκ ] T Formula 20

[0140] [ε] is the modification matrix, as shown in formula 21:

[0141] [ε]=[ε 11 ,ε 12 ,…ε 1a ,0,…,0,ε 2b ,ε 22 ,ε 21 ] T Formula 21

[0142] In the formula, a and b are l 1 End and l 2 Number of end profile threads.

[0143] Back to the iterative calculation, combined with equation 2 and equation 18, because the forces on the thread teeth are exactly the same, the initial deformation (see Figure 1Box 3 equations 1 and 2 are also exactly the same, but due to the nonlinearity of contact deformation (see equation 14) and the cumulative deformation of the shaft segment, the contact stiffness solved by the initial value of the load distribution in equation 2 is different at this time. The deformation after the change is solved based on the load distribution (see Figure 1 Box 4), update the load distribution calculation matrix under the current stiffness (see Eq. 18, see Figure 1 Box 5), at this time, the contact deformation is known, and a new thread load distribution array can be iterated (see Figure 1 Box 6).

[0144] (3) Termination judgment: When the updated load distribution array (see Figure 1 The value of the second-order moment between box 6) and the original load distribution array is less than the solution accuracy A c When , stop the iteration and output the load distribution; otherwise, repeat the iterative calculation of step 3 (2).

[0145] Step 4: According to the optimization multi-objective function equation, the shaping parameters are optimized by simulated annealing algorithm.

[0146] like Figure 8 As shown in the figure, the numerical optimization method is the multi-objective optimization of the modification parameters of the uniformly loaded planetary roller screw pair based on the simulated annealing algorithm. The above load distribution iterative calculation is the multi-objective optimization process 2 of the modification parameters. This optimization method has the advantage of avoiding falling into local excellent results and is suitable for multi-parameter optimization. It is divided into the following five steps: (1) Determine the optimization parameters and initial values; (2) Calculate the original array A of the load distribution under the current parameters 0 ; (3) Determine the constraints; (4) Select the neighborhood parameters and calculate the load distribution to update the array B 0 ; (5) According to the Metropolis criterion, the array A k and array B k Select the best; (6) If it is determined that B k Better than A k , let A k+1 =B k Repeat step (4) to calculate B k+1 , let B k =B k+1 , repeat step (5) until the optimal solution is output. (Subscripts 0, k, k+1 represent the number of iterations) The following describes each process in detail.

[0147] (1) Determine the optimization parameters and initial values

[0148] I determine the type of optimization parameters. The optimization parameters include l 1 , l 2 and ε 1max , ε 2max The optimization goal is to make the maximum load distribution coefficient max{ζXi} and the maximum thread load max{F Xi} is reduced, where ζ i Definition

[0149] As shown in formula 22:

[0150]

[0151] Where F is the axial force transmitted by the planetary roller screw pair, Z is the number of rollers, and κ is the number of meshing threads of the rollers.

[0152] exist Figure 1 In step 2, the input screw structural parameters may include the number of rollers, the number of meshing elements, and the axial force. In this case, it can be simplified to a single target. However, for the design of planetary roller screws, the Z and κ values ​​can also be changed to perform parameter matching design for the purpose of load distribution. In addition to these two relatively direct parameters, the remaining structural parameters also affect the load distribution. In the load distribution solution (see Figure 1 ) involves.

[0153] II Determine the initial value of the parameter. Within the constraints (see step 3 of this process), considering that the axial forces in the two-way travel of the screw are in opposite directions, the load distribution directions are opposite, and the magnitudes are close, so l 1 , l 2 The initial value of is equal or approximate; when Z and κ are larger, the more roller threads are subjected to axial force at the same time, and max{F Xi} decreases but max{ζ Xi} increases, and the target weight generated according to the current design requirements is comprehensively considered. Generally, if space conditions permit, the more rollers there are, the stronger the load-bearing performance will be. According to load distribution calculations, the first few thread teeth bear most of the load. Considering weight and space limitations, the roller thread length can be moderate.

[0154] (2) Calculate the original array A of load distribution under the current parameters 0 (See Figure 1 )

[0155] (3) Determine the constraints

[0156] I Roller thread total length condition: l 1 , l 2 and l 3 The sum is the total length of the roller thread, and the maximum value is constrained by the structure and space volume.

[0157] II Yield Limit Criterion

[0158] like Fig. 9As shown in the figure, the force on the thread is decomposed. According to the Hertz contact theory, the deformation of two objects due to elastic contact is related to the contact parameters, normal load and the equivalent elastic modulus of the contact surface of the two objects. Fig. 9 Medium F Xn Indicates the normal load on the thread, F Xa represents the axial component of the normal load, F Xt represents the tangential component of the normal load, F Xr represents the radial component of the normal load. β represents the normal contact angle, i.e. the normal load F Xn The angle between the tangential force and the radial force is usually approximated by the tooth profile half angle. λ represents the angle between the resultant force of the tangential force and the axial force and the axial force. It is usually approximated by the helix angle of the corresponding part. The contact deformation of the PRSM thread tooth is shown in Equation 23:

[0159]

[0160] In the formula, K ′ =K X (e) / πm Xa is the contact parameter, which is related to the principal curvature function, E X ′ X is the equivalent elastic modulus, Q is the equivalent normal force, ∑ρ is the sum of the curvatures of the two contact surfaces, β X and λ X They are the corresponding part tooth profile half angle and thread lead angle respectively.

[0161] After determining the relationship between PRSM contact elastic deformation and material properties and load capacity, it is necessary to select a suitable yield criterion. Currently, for isotropic metal materials, the yield criteria mainly include Tresca yield criterion and Mises yield criterion. Because the Tresca yield criterion requires stress determination, and in the PRSM load distribution calculation process, the stress magnitude needs to be solved under the condition of determining the structure and working conditions, so the Tresca yield criterion is not used. According to the Mises yield criterion, the PRSM yield limit calculation is shown in Equation 24:

[0162]

[0163] In the formula, τ max is the yield strength, F nmax is the limit normal contact load, K st is the thread contact coefficient, which can be taken within the range of [0.30, 0.33] according to the eccentricity of the contact ellipse. a and b are the lengths of the major and minor semi-axes of the thread contact ellipse, respectively. Then, through F nmax The maximum axial load of PRSM under the corresponding parameters is calculated as shown in Equation 25:

[0164]

[0165] After selecting the PRSM parameters, the contact deformation during the PRSM transmission process needs to be controlled within the elastic range. Meeting this condition means that the elastic yield criterion of the PRSM thread teeth is met, that is, the maximum axial load of the thread is less than Q max , the maximum elastic yield strength is shown in Equation 26:

[0166]

[0167] III Shear Limit Criterion

[0168] like Fig.10 As shown, the bending strength limit of the dangerous section of the thread can be solved. The stress magnitude of each section is different when the PRSM is loaded. The dangerous section is the axial section. The equivalent length of the PRSM thread participating in the load is shown in formula 27:

[0169]

[0170] Therefore, according to the thread connection strength verification formula, the shear strength condition of the dangerous section of the PRSM thread tooth is shown in formula 28:

[0171]

[0172] Where, τ represents the shear stress at the tooth bottom, in MPa; f a represents the axial component of the load; C represents the root thickness; [τ] represents the allowable shear stress.

[0173] The bending strength condition of the dangerous section of the PRSM thread tooth is shown in formula 29:

[0174]

[0175] IV. Roller Space Arrangement Conditions

[0176] Limitation of the number of rollers: The number of rollers must meet the roller space arrangement conditions. In PRSM, the rollers are distributed in a planetary manner relative to the screw, and the rollers and nuts are meshed through the roller rolling gear and the inner gear ring of the nut. The nut wraps the rollers and the screw. In PRSM, there is a maximum limit on the number of rollers in space, as shown in Equation 30:

[0177]

[0178] (4) Select neighborhood parameters and calculate load distribution to update array B 0

[0179] The neighborhood parameters are first discretized, l 1 , l2 is the thread length, which affects the number of modified thread teeth and is discretized with a single pitch as the minimum division value. ε 1max , ε 2max The maximum shaping amount is discretized with the CNC indexing value of the thread processing machine tool as the minimum indexing value. The neighborhood parameter determination selection adopts semi-random selection, and the four shaping parameters change 0-1 indexing values ​​respectively and the number of parameters changing by 1 indexing value is greater than or equal to 1. Update array B 0 Same as step 2.

[0180] (5) According to the Metropolis criterion, the array A k and array B k Conduct merit selection;

[0181] The execution strategy of the simulated annealing algorithm is: start from any selected solution to search the entire search domain, then perturb the solution to generate a new solution, and judge whether to accept the new solution according to the Metropolis acceptance criterion, while controlling the temperature drop. Algorithm parameters include initial temperature, temperature decay function and Markov chain length;

[0182] ① Initial temperature: determines the probability of accepting a new solution when the optimization effect of the new solution is less than that of the old solution during the first optimization. The higher the temperature, the higher the probability of accepting a new solution.

[0183] ② Temperature decay function: determines the temperature change law after optimization, which is used to control the accuracy and calculation amount of the algorithm. The faster the temperature decays, the lower the algorithm accuracy, but the smaller the calculation amount.

[0184] ③Markov chain length: determines the termination criterion of the algorithm. The algorithm is terminated if multiple consecutive new solutions are not accepted. This numerical setting is the Markov chain length.

[0185] The specific process is as follows: first, determine the number of searches based on the current temperature, generate a random offset based on the properties of the current solution (discrete variables), and obtain a new trial point in the neighborhood of the current solution. Then take a random number in the range [0,1], and accept the new solution when the optimization effect of the new solution is greater than that of the old solution; when the optimization effect of the new solution is less than that of the old solution, give the acceptance probability corresponding to the Metropolis criterion, and when the random number is greater than the probability, accept the new solution, otherwise continue to use the old solution; if the set iteration termination condition is met, the algorithm ends and returns the current solution as the global optimal solution, otherwise continue to judge the solution offset and the optimization effect of the new trial point; reduce the temperature parameter of the current algorithm through the selected temperature attenuation function, and repeat the solution optimization.

[0186] Step 5: Output the optimized modification parameters and load distribution and compare them with the initial state to verify the effectiveness of the optimization.

[0187] The purpose of the present invention is to propose a roller shaping and parameter optimization method in a planetary roller screw, specifically a roller shaping design and shaping parameter multi-objective optimization method suitable for a planetary roller screw pair with two-way travel. The shaping parameters may include: the number of thread shaping on one side of the nut roller contact side and the maximum thread shaping amount, the number of thread shaping on the roller screw contact side and the maximum thread shaping amount. The optimization objectives may include the maximum unevenness coefficient of the load distribution of a single thread and the maximum axial load size of a single thread. After the shaping design, the unevenness of the load distribution of the thread of the planetary roller screw pair is less than that before the shaping, and after the shaping parameters are optimized, the unevenness of the load distribution of the thread is less than the initial value of the shaping parameters selected according to the load distribution and deformation of the thread without shaping.

[0188] Although the present invention is disclosed as above in the form of a preferred embodiment, it is not intended to limit the present invention. Any person skilled in the art may make possible changes and modifications without departing from the spirit and scope of the present invention. Therefore, the scope of protection of the present invention shall be based on the scope defined by the claims of the present invention.

Claims

1. A method for modifying the shape and optimizing the parameters of rollers in a planetary roller screw, characterized in that: include: Step 1, determining the optimizable shaping parameters and ranges according to the three-stage roller shaping method; Step 2, establishing a load distribution calculation model considering roller modification; the load distribution calculation model is used to calculate the relationship between thread deformation and load distribution state; Step 3, determine the initial value of the optimization of the shaping parameters, and calculate the load distribution of the planetary roller screw pair in this state through model iteration; Step 4, according to the optimization target, update the shaping parameters and repeat step 3 to calculate the load distribution to optimize the shaping parameters; Step 5: Output the optimized shaping parameters and load distribution.

2. The method according to claim 1, characterized in that: The optimizable shaping parameters and ranges meet the following requirements: The roller thread modification length l1 in the direction corresponding to the nut installation end; The roller thread modification length l2 in the corresponding direction of the right side lead screw fixed end; Maximum modification amount of the nut installation end ε 1max , occurs on the first circle of threads on the left, and the modification amount decreases linearly with the increase of thread number until it becomes the same as the unmodified thread; Maximum modification amount ε of the screw fixed end 2max , occurs in the first circle of thread teeth on the right side, and the modification amount decreases linearly with the decrease of thread tooth number until it becomes the same as the unmodified thread.

3. The method according to claim 1 or 2, characterized in that: The load distribution calculation model satisfies the force balance relationship between the nut-roller side and the roller-screw side: Z is the number of rollers in the planetary roller screw; F is the total axial external load borne by the planetary roller screw, F NRi and F SRi The thread teeth with serial number i on the roller bear the axial load from the nut or the screw, F Si and F Ni are the axial loads borne by the thread teeth with serial number i on the nut or screw, respectively, and F NRi and F SRi is the interaction force, which is equal in magnitude, and κ is the number of thread teeth in which the roller participates in meshing; The load distribution calculation model also satisfies the deformation coordination equilibrium equation in the closed loop: Δl BXi +Δl TXi +Δl CXi =Δl BRi +Δl TRi +Δl CRi +ε (1或2)i Δl represents deformation, subscripts B, T, and C represent the cumulative deformation of the shaft segment, the relative deformation of the thread teeth, and the contact deformation of the thread teeth, respectively, subscripts X=S and N represent the screw and nut, respectively, subscript R represents the roller, and subscript i represents the thread tooth number; ε 1i is the modification amount of the left thread tooth i, ε 2i is the modification amount of the left thread tooth i; The load distribution calculation model also satisfies the stiffness-deformation relationship matrix: [K][F]=[ε] [K] is the stiffness matrix, [F] is the thread force matrix, and [ε] is the modification matrix.

4. The method according to claim 3, characterized in that The deformation coordination equilibrium equation in the closed loop satisfies: P N is the thread pitch of the nut, E N is the elastic modulus of the nut, A N E is the cross-sectional area of ​​the threaded shaft section of the nut; R is the elastic modulus of the roller, A R is the cross-sectional area of ​​the roller thread shaft segment; X=S, N represents the screw or nut, K XR (e) are the first kind complete elliptic integrals corresponding to the Hertz contact ellipse on the contact side, m Xa is the major axis coefficient of the contact ellipse; F XRi is the axial force of the roller or screw on the ith thread of the roller, ρ XR is the sum of the principal curvatures of the two thread surfaces on the contact side; E′ XR The equivalent elastic modulus of the contact surface is β X and λ X They are the corresponding parts tooth profile half angle and thread lead angle respectively; d TXi =d 1i +d 2i +d 3i +d 4i +d 5Yi The subscripts X=S, R, and N represent the screw, roller, and nut, respectively; the subscripts Y=I and E represent the internal and external threads, respectively, where the screw and roller correspond to the external thread, and the nut corresponds to the internal thread; the subscripts 1, 2, 3, 4, and 5 represent the thread deformation caused by bending, shear force, root inclination, root shear, and radial force, respectively, and the subscript i represents the thread number.

5. The method according to claim 4, characterized in that a is the thread bottom thickness, b is the thread thickness, c is the thread top thickness, h is the thread f is the thread bottom height, β is the tooth profile half angle, F a is the axial force component, μ and E are the Poisson's ratio and elastic modulus of the thread material respectively; d pI Indicates the inner diameter of the equivalent hollow cylinder of the internal thread, D pI Indicates the outer diameter of the hollow cylinder equivalent to the internal thread; d pO Indicates the diameter of the solid cylinder equivalent to the external thread.

6. The method according to claim 4 or 5, characterized in that: D0 represents the outer diameter of the nut, d N and d S Respectively represent the pitch diameter of the nut and the lead screw thread, d R Indicates the modified roller median diameter, h f It represents the thread bottom height and Z represents the number of rollers.

7. The method according to any one of claims 3 to 6, characterized in that [F]=[F NR1 ,F NR2 ,…,F NRκ ,F SR1 ,F SR2 ,…,F SRκ ] T [e]=[e 11 ,he 12 ,…eh 1g1 ,0,…,0,e 2g2 ,he 22 ,he 21 ] T g1 and g2 are the number of modified thread teeth at the l1 end and the l2 end respectively.

8. The method according to any one of claims 3 to 7, characterized in that Step 3: At least one of the following is met: F NRi (0) and F SRi (0) As the initial value of the iterative calculation, it satisfies: The termination criterion of the iterative calculation is: judging the convergence of the load distribution results after one cycle process. If the second-order moment of the results of two cycles is less than the solution accuracy, the cycle is terminated, otherwise the cycle continues.

9. The method according to any one of claims 1 to 8, characterized in that The optimization goal of step 4 is to make the maximum load distribution coefficient max{ζX i } and the maximum thread load max{F Xi }reduce, Where F is the axial force transmitted by the planetary roller screw pair, Z is the number of rollers, K is the number of roller meshing threads, and i represents the thread number.

10. The method according to any one of claims 1 to 9, characterized in that The kth optimization iteration of step 4 includes: Calculate the original array A of load distribution k ; Under the condition of meeting the constraints, select the neighborhood parameters and calculate the load distribution to update the array B k ; According to the Metropolis criterion, k and array B k Select the best: If it is determined that B k Better than A k , B k The original array A of load distribution for the k+1th optimization iteration k+1 , and perform the k+1th optimization iteration; If it is determined that B k Worse than A k According to the Metropolis criterion, when the random number is greater than the probability, B k The original array A of load distribution for the k+1th optimization iteration k+1 , and perform the k+1th optimization iteration; when the random number is less than the probability, A k The original array A of load distribution for the k+1th optimization iteration k+1 , and perform the k+1th optimization iteration.

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