Method for calculating dynamic load distribution of planetary roller screw thread

Abstract

The application discloses a kind of planetary roller screw thread tooth dynamic load distribution calculation method, mainly solve the load distribution of planetary roller screw under the action of inertial force in actual work.Its implementation steps are: according to the meshing principle of planetary roller screw helical surface, the static contact force of roller, screw and nut at contact point is obtained, then the roller is taken as the research object, and the inertia force generated by screw rotation and the contact force on the side of screw and nut are analyzed in the axial and radial directions of roller, the dynamic contact force of roller, screw and nut after force analysis is taken as external load, and substituted into thread load distribution model, the dynamic load distribution of planetary roller screw thread tooth can be obtained.The application fills the blank of the theoretical model of planetary roller screw thread tooth dynamic load distribution, and can directly solve the load distribution of planetary roller screw under different screw speeds and different loads, as well as the influence of screw speed and load on load distribution.

Description

Technical Field

[0001] This invention belongs to the field of planetary roller screw transmission, specifically involving a method for calculating the dynamic load distribution of planetary roller screw threads, laying the foundation for studying the load-sharing design of planetary roller screws and improving transmission efficiency. Background Technology

[0002] Planetary roller screws are mechanical devices that convert rotary motion into linear motion. They are characterized by high load-bearing capacity, high precision, high speed, and long service life. Based on these advantages, planetary roller screws are widely used in aerospace, precision machine tools, food packaging, energy and chemical industries, metallurgical processing, and special equipment. The calculation method for the dynamic load distribution of planetary roller screw threads is of great significance for studying the load distribution, transmission efficiency, and engineering applications of planetary roller screws.

[0003] In recent years, theoretical research on the load distribution of planetary roller screw threads has yielded certain results. Based on Hertzian elastic contact theory, Yang Jiajun considered the rollers as a whole, taking into account Hertzian deformation between the rollers and screw threads, axial deformation caused by contact between the screw, nut, and rollers, and thread deformation between the screw and nut. He established an axial static stiffness model for planetary roller screws and obtained the load distribution curve of the planetary roller screw threads through recursive calculation. Jones et al. considered the stiffness of the screw thread shaft section, thread stiffness, and thread contact stiffness, and established a theoretical model of the axial stiffness of planetary roller screws based on the direct stiffness method. This provides an effective theoretical method for calculating the axial stiffness of planetary roller screws, and this method can also be used to solve for the load distribution of the threads. Jan et al. equivalently treated the meshing area of ​​the planetary roller screw's rollers, screw, and nut threads as rectangular elements bearing shear stress. Considering thread contact deformation and the deformation of the threaded shaft segments of the screw, rollers, and nut, they established a calculation model for the thread load distribution and a finite element verification model. They compared the numerical solution with the finite element solution, but the agreement was poor. This model did not consider the deformation of the threaded teeth after the planetary roller screw was loaded, therefore it is only suitable for analysis and calculation in the preliminary design process. Abevi et al., based on the assumption of uniform load distribution between rollers and that the material is in an elastic stage, used beam, rod, and nonlinear spring elements to replace different elements of the planetary roller screw and their interactions. Considering four boundary conditions and different positions of the nut relative to the screw, they established a planetary roller screw load distribution model and studied it using a reverse-parameter planetary roller screw. Their results agreed well with those obtained from the finite element model. To improve the load distribution of planetary roller screws, Ma Shangjun et al. established a calculation model for the load distribution of roller screws considering errors, based on the deformation coordination relationship between the two contact sides of the rollers, under the action of axial tension on the screw and axial pressure on the nut. They studied the influence of manufacturing errors on the load distribution of the screw threads. The study showed that under the same error distribution, the smaller the load, the greater the fluctuation in the load distribution of the roller screw threads; negative errors are more conducive to reducing the load ratio of the first three screw threads. Their research helps guide the reasonable control of errors during the machining process of planetary roller screws. Zhang Wenjie established a load distribution model for planetary roller screws under different installation methods and analyzed the influence of various thread parameters on the load distribution.

[0004] In summary, there is currently no research method that can calculate the dynamic load distribution of planetary roller screw threads. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention aims to provide a method for calculating the dynamic load distribution of planetary roller screw threads. Based on the calculation of contact force at the contact point of the helical surface of the planetary roller screw, the roller force balance equation, and the solution of load distribution, the dynamic load distribution of the planetary roller screw threads is obtained, laying the foundation for studying the load-sharing design of planetary roller screws and improving transmission accuracy.

[0006] To achieve the above objectives, the present invention adopts the following technical solution:

[0007] 1. A method for calculating the dynamic load distribution of planetary roller screw threads, characterized by comprising the following steps:

[0008] S1: Solve for the static contact forces between the roller and the lead screw, and between the roller and the nut. and

[0009] The static contact force at the contact point between the roller and the screw is calculated based on the principle of helical surface meshing of the planetary roller screw. and the static contact force at the contact point between the roller and the nut

[0010] S2: Iteratively solve for the dynamic contact force F between the roller and the lead screw, and between the roller and the nut. SR and F NR :

[0011] Taking the roller as the research object, a force analysis is performed on it, and the initial value of the contact angle α is set. SR0 and α NR0 The inertial force F generated by the rotation of the lead screw c Solve the force balance equations for the contact forces between the ball screw and nut on both the axial and radial sides of the rollers, and determine the dynamic contact force F of the planetary roller ball screw considering inertial forces. SR and F NR ;

[0012] S3: Solve for the actual contact angle α SR and α NR :

[0013] The dynamic contact force F obtained from S2 SR and F NR Substituting into Hertzian contact theory, the contact deformation δ is obtained. SRC and δ NRC Then the actual contact angle α is obtained. SR and α NR ;

[0014] S4: Verify the actual contact angle α SR and α NR Correctness:

[0015] The actual contact angle α SR and α NR With the initial contact angle α SR0 and α NR0 If the difference is less than the set minimum value ε, then the dynamic contact force F is output. SR and F NR If the difference is greater than the set minimum value, then the initial contact angle value α is reset. SR0and α NR0 until the difference is less than the set minimum value;

[0016] S5: Output dynamic contact force F SR and F NR Actual contact angle α SR and α NR and contact deformation δ SRC and δ NRC ;

[0017] S6: Solve for the dynamic load distribution of the thread on the side of the roller and lead screw, and the roller and nut:

[0018] The dynamic contact force F obtained in S4 SR and F NR Substituting the external load into the planetary roller screw load distribution model, the thread dynamic load distribution between the roller and the screw, and between the roller and the nut, is obtained.

[0019] 2. The method for calculating the dynamic load distribution of planetary roller screw threads according to claim 1, characterized in that the static contact force at the contact point between the roller and the screw in step S1... The calculation formula is:

[0020]

[0021]

[0022] λ is the amplitude of the contact force. SR and β SR These are the helix angle and tooth flank angle at the contact point between the lead screw and the roller, respectively; φ SR F is the engagement angle of the roller on the lead screw side. Nz n is the load on the nut. roller This represents the number of rollers.

[0023] tanλ SR =L R / (2πr SR (3)

[0024]

[0025] u TR =-r TR ·sinβ R (5)

[0026] Among them, L R The lead of the roller; r SR r is the engagement radius of the roller on the leadscrew side. R r is the nominal radius of the roller; TRThe radius of the roller's tooth profile; u TR The center of the roller tooth profile is at u R v R w R u in the plane R Coordinate value, β R This refers to the flank angle of the roller tooth.

[0027] Static contact force at the contact point between the roller and the nut as described in S1 The calculation formula is:

[0028]

[0029] Due to the meshing angle φ between the nut and the roller NR =0, the helix angle λ at the contact point between the nut and the roller NR Tooth lateral angle β NR Equal to the helix angle λ of the roller R And tooth lateral angle β R ,therefore

[0030]

[0031]

[0032] tanλ R =L R / (2πr R (9)

[0033]

[0034] 3. The method for calculating the dynamic load distribution of planetary roller screw threads according to claim 1, characterized in that the inertial force F generated by the rotation of the screw in S2... c As shown in Equation 11, the equation for the balance of axial and radial forces of the roller is shown in Equation 12:

[0035]

[0036]

[0037] m is the mass of the roller, d0 is the diameter of the roller's revolution, and α SR α is the actual contact angle between the roller and the lead screw. NR ω is the actual contact angle between the roller and the nut. P F is the angular velocity of the roller's revolution. c For inertial force, F SR and F NR This refers to the dynamic contact force between the roller and the lead screw, and between the roller and the nut.

[0038] 4. The method for calculating the dynamic load distribution of planetary roller screw threads according to claim 1, characterized in that the contact deformation δ in S3... SRC and δ NRC The calculation formulas are as follows:

[0039]

[0040]

[0041] Where, δ SRC and δ NRC δ is the deformation caused by the contact between the roller and the lead screw or nut. * Here, ∑ρ represents the contact parameters related to the curvature of the two contact surfaces, μ is Poisson's ratio, and E is the elastic modulus.

[0042] The actual contact angle α between the roller and the lead screw and nut sides SR and α NR The calculation formulas are as follows:

[0043]

[0044]

[0045] α SR0 Let α be the initial value of the contact angle between the roller and the lead screw. NR0 Let r be the initial value of the contact angle between the roller and the nut. S Let r be the nominal radius of the leadscrew. N The nominal radius of the nut.

[0046] 5. The method for calculating the dynamic load distribution of planetary roller screw threads according to claim 1, characterized in that the planetary roller screw load distribution model in S6 is:

[0047] Based on the structural characteristics and load-bearing principle of planetary roller screws, they are discretized into three structural elements: threaded shaft segment, thread teeth, and thread tooth contact point.

[0048] Stiffness k of threaded shaft section XB This refers to the tensile and compressive stiffness of the matrix of two adjacent load-bearing threaded parts in a lead screw, roller, or nut. This stiffness can be solved using the formula for the tensile and compressive stiffness of shafts in mechanics of materials. In a planetary roller screw, the shaft stiffness of the lead screw and nut is:

[0049]

[0050] Where, k XB E X and A X These represent the shaft stiffness, elastic modulus, and cross-sectional area of ​​the lead screw or nut, respectively; P is the pitch of the lead screw, roller, or nut.

[0051] The cross-sectional area A of the lead screw shaft segment S The cross-sectional area A of the shaft segment of the nut N They are respectively:

[0052]

[0053]

[0054] Where, d S and d N These are the thread pitch diameters of the lead screw and nut, respectively; h f n is the thread root height of the lead screw and nut; roller D0 represents the number of rollers; D0 represents the outer diameter of the nut.

[0055] Since the rollers mesh with both the lead screw and the nut, the stiffness of its shaft section is equal to the stiffness within half the screw pitch. Therefore, the stiffness k of the roller shaft section is... RB for:

[0056]

[0057] The cross-sectional area A of the roller shaft segment R for:

[0058]

[0059] Based on the force analysis of the thread teeth, the axial component F of the normal contact load between the lead screw or nut and the roller is known. XRa and radial component F XRr They are respectively:

[0060] F XRa =F XR ·sinα XR (twenty two)

[0061] F XRr =F XR ·cosα XR (twenty three)

[0062] Where, α XR F is the actual contact angle between the roller and the lead screw or nut. XR This refers to the dynamic contact force between the roller and the lead screw or nut.

[0063] When a planetary roller screw is subjected to a load, the roller threads mesh with the screw and nut threads respectively and bear the load. After being subjected to force, the threads will deform along the screw axis. The axial deformation of the threads includes deformation δ1 caused by bending, deformation δ2 caused by shear force, deformation δ3 caused by root inclination, deformation δ4 caused by root shear, and deformation δ5 caused by radial component force. The calculation methods for each deformation of the threads will not be elaborated in this article.

[0064] The total axial deformation of the planetary roller screw thread teeth under axial load is:

[0065] δ XT =δ1+δ2+δ3+δ4+δ5 (24)

[0066] The corresponding thread stiffness k XT for:

[0067]

[0068] Thread tooth contact stiffness k XRC This refers to the dynamic contact force F between the roller and the normal direction of the screw or nut thread. SR and F NR With contact deformation δ SRC and δ NRC The ratio of .

[0069] Assuming that the axial load of the planetary roller screw is uniformly distributed among the threads involved in the meshing, according to Hertzian contact theory, the deformation of the contact area between the roller and the screw or nut side thread under normal contact load can be obtained by equations 13 and 14.

[0070] The axial component δ of the deformation of the planetary roller screw roller in contact with the screw or nut XRC-axial It can be represented as:

[0071] δ XRC-axial =δ XRC ·cosα XR ·cosλ XR (26)

[0072] The corresponding axial contact stiffness k XRC for:

[0073]

[0074] Substituting the shaft stiffness model, thread tooth stiffness model, and contact stiffness model into the thread tooth closed-loop model yields the thread tooth deformation compatibility relationship.

[0075] Taking the roller-nut contact side as an example, the total deformation of the nut within the i-th threaded closed loop can be obtained as ∑l Ni Let Δl be the total deformation of the nut shaft segment within the i-th threaded closed loop. NBi The total deformation of the nut thread teeth Δl NTi The total deformation of the nut thread teeth at contact Δl RNCi The total thread deformation Δl of the inner nut in the (i+1)th threaded closed loop NTi+1 The sum, that is:

[0076] ∑l Ni =ΔlNBi +Δl NTi +Δl NTi+1 +Δl RNCi (28)

[0077] The total deformation of the inner rollers in the i-th threaded closed loop ∑l Ri Let Δl be the total deformation of the inner roller shaft segment of the i-th threaded closed loop. RBi The total deformation of the roller thread teeth Δl RTi The total deformation Δl of the inner roller shaft segment of the (i+1)th threaded closed loop RBi+1 Total thread deformation Δl RTi+1 and the total deformation of the thread teeth Δl RNCi+1 The sum, that is:

[0078] ∑l Ri =Δl RBi +Δl RBi+1 +Δl RTi +Δl RTi+1 +Δl RNCi+1 (29)

[0079] According to the deformation compatibility relationship, we have:

[0080] P N +∑l Ni =P R +∑l Ri (30)

[0081] Since the nut pitch is equal to the roller pitch, i.e. P N =P R Then we have:

[0082] ∑l Ni =∑l Ri (31)

[0083] Substituting the shaft stiffness, thread stiffness, and contact stiffness into the above formula yields the dynamic load distribution model for the roller and lead screw side threads:

[0084]

[0085] Similarly, the dynamic load distribution model of the thread teeth on the roller and nut sides is as follows:

[0086]

[0087] The sum of the loads on each thread tooth is the overall contact force between the roller and the lead screw or nut, as shown in Equation 34:

[0088]

[0089] The beneficial effects of this invention are as follows:

[0090] 1. Similar to threaded connections, planetary roller screws suffer from uneven load distribution between the thread teeth. This leads to increased transmission noise, accelerated wear, and reduced service life. The calculation method for dynamic load distribution on planetary roller screw threads can solve for the load distribution under different screw speeds or loads. This lays the theoretical foundation for improving the uneven load distribution of planetary roller screw threads, further enhancing their high load-bearing capacity, and increasing their fatigue life.

[0091] 2. The planetary roller screw has a complex thread structure, and current research often uses simplified models for force analysis, resulting in low calculation accuracy. This invention solves for the contact force at the contact points between the roller, screw, and nut based on the helical surface equation of the planetary roller screw. By performing force analysis at the accurate contact positions on the helical surface, the accuracy of contact force, shaft stiffness, thread stiffness, and contact stiffness in the load distribution model can be improved.

[0092] 3. In actual machining, planetary roller screws inevitably experience machining errors. The calculation method in this invention can not only solve for the dynamic load distribution of the thread teeth under error-free conditions, but also analyze the influence of machining errors on the dynamic load distribution of the thread teeth. Therefore, this invention can provide theoretical guidance for the dynamic load distribution of planetary roller screws in practical operation. Attached Figure Description

[0093] Figure 1 This is a flowchart of the present invention;

[0094] Figure 2 This is a schematic diagram of the contact force between the roller and the lead screw at the contact point;

[0095] Figure 3 This is a schematic diagram of the contact force between the roller and the nut at the contact point;

[0096] Figure 4 A schematic diagram illustrating the geometric relationship between the deformation coordination of the roller, lead screw, and nut;

[0097] Figure 5 Schematic diagram of the calculation model for the load distribution of planetary roller screw threads.

[0098] Figure 6 A schematic diagram of the calculation results for the dynamic load distribution of the planetary roller screw thread.

[0099] Figure 7 The effect of lead screw speed on the contact angle of the lead screw and nut sides

[0100] Figure 8 The effect of lead screw speed on the contact force on the lead screw and nut sides.

[0101] Figure 9The effect of lead screw speed on the contact deformation of the lead screw and nut sides.

[0102] Figure 10 The effect of lead screw speed on the load distribution on the lead screw side.

[0103] Figure 11 The effect of lead screw speed on load distribution on the nut side

[0104] Figure 12 The effect of load on the contact angle of the lead screw and nut sides

[0105] Figure 13 The effect of load on the contact force on the lead screw and nut sides

[0106] Figure 14 The effect of load on the contact deformation of the lead screw and nut sides

[0107] Figure 15 The effect of load on the load distribution on the leadscrew side

[0108] Figure 16 The effect of load on the load distribution on the leadscrew side Detailed Implementation

[0109] The present invention will be further described below with reference to the accompanying drawings. It should be noted that this embodiment is based on the present technical solution and provides detailed implementation methods and specific operation processes, but the protection scope of the present invention is not limited to this embodiment.

[0110] 1. For example Figure 1 As shown, the method for calculating the dynamic load distribution of planetary roller screw threads includes the following steps:

[0111] S1: Solve for the static contact forces between the roller and the lead screw, and between the roller and the nut. and

[0112] The static contact force at the contact point between the roller and the screw is calculated based on the principle of helical surface meshing of the planetary roller screw. and the static contact force at the contact point between the roller and the nut

[0113] Static contact force at the contact point between the roller and the lead screw The calculation formula is:

[0114]

[0115]

[0116] λ is the amplitude of the contact force. SR and β SRThese are the helix angle and tooth flank angle at the contact point between the lead screw and the roller, respectively; φ SR F is the engagement angle of the roller on the lead screw side. Nz n is the load on the nut. roller This represents the number of rollers.

[0117] tanλ SR =L R / (2πr SR (3)

[0118]

[0119] u TR =-r TR ·sinβ R (5)

[0120] Among them, L R The lead of the roller; r SR r is the engagement radius of the roller on the leadscrew side. R r is the nominal radius of the roller; TR The radius of the roller's tooth profile; u TR The center of the roller tooth profile is at u R v R w R u in the plane R Coordinate value, β R This refers to the flank angle of the roller tooth.

[0121] Static contact force at the contact point between the roller and the nut The calculation formula is:

[0122]

[0123] Due to the meshing angle φ between the nut and the roller NR =0, the helix angle λ at the contact point between the nut and the roller NR Tooth lateral angle β NR Equal to the helix angle λ of the roller R And tooth lateral angle β R ,therefore

[0124]

[0125]

[0126] tanλ R =L R / (2πr R (9)

[0127]

[0128] The structural parameters of the thread teeth are shown in Table 1:

[0129] Table 1

[0130]

[0131] The meshing radius r between the roller and the lead screw is obtained based on the principle of helical surface meshing. SR According to Table 1, the roller lead L R Substituting it into Equation 3, we obtain tanλ. SR Given the radius r of the roller tooth profile. TR According to Table 1, the roller tooth flank angle β R Substituting it into equation 5, we get u TR r SR L R r TR and u TR Substituting into Equation 4, we obtain tanβ SR Substituting Equations 3 and 4 into Equation 2, we set the load size F. Nz Number of rollers n roller The static contact force between the roller and the lead screw can then be calculated.

[0132] Similarly, the nominal radius r of the roller... R and roller lead L R Substituting into Equation 9, we obtain tanλ. R . will u TR and r TR Substituting into Equation 10, we obtain tanβ R Substituting Equations 9 and 10 into Equation 8, we set the load size F. Nz Number of rollers n roller The static contact force between the roller and the nut can then be calculated.

[0133] In this example, the load is set to 5000N and the number of rollers is 20. The static contact force between the roller and the lead screw is calculated to be 714.46N, and the static contact force between the roller and the nut is calculated to be 708.23N.

[0134] S2: Iteratively solve for the dynamic contact force F between the roller and the lead screw, and between the roller and the nut. SR and F NR :

[0135] Taking the roller as the research object, a force analysis is performed on it, and the initial value of the contact angle α is set. SR0 and α NR0 The inertial force F generated by the rotation of the lead screw c Solve the force balance equations for the contact forces between the ball screw and nut on both the axial and radial sides of the rollers, and determine the dynamic contact force F of the planetary roller ball screw considering inertial forces.SR and F NR .

[0136] The inertial force F generated by the rotation of the lead screw c As shown in Equation 11, the equation for the balance of axial and radial forces of the roller is shown in Equation 12:

[0137]

[0138]

[0139] m is the mass of the roller, d0 is the diameter of the roller's revolution, and α SR α is the actual contact angle between the roller and the lead screw. NR ω is the actual contact angle between the roller and the nut. P F is the angular velocity of the roller's revolution. c For inertial force, F SR and F NR This refers to the dynamic contact force between the roller and the lead screw, and between the roller and the nut.

[0140] By measuring the roller mass m and setting the lead screw speed, the roller's angular velocity ω can be calculated. P The revolution diameter d0 of the roller can be obtained from the mean diameter of the roller and the lead screw. Then, m and ω... P Substituting d0 into Equation 11, the inertial force F can be obtained. c In this example, m = 0.032 kg, ω P = 30 rad / s.

[0141] Set the initial contact angle α between the roller and the lead screw and nut respectively. SR0 and α NR0 Substituting this into Equation 12, we can obtain the dynamic contact force F between the roller and the lead screw and nut. SR and F NR .

[0142] S3: Solve for the actual contact angle α SR and α NR :

[0143] The dynamic contact force F obtained from S2 SR and F NR Substituting into Hertzian contact theory, the contact deformation δ is obtained. SRC and δ NRC Then the actual contact angle α is obtained. SR and α NR .

[0144] Contact deformation δ between the roller and the lead screw and nut sides SRC and δ NRC The calculation formulas are as follows:

[0145]

[0146]

[0147] Where, δ SRC and δ NRC δ is the deformation caused by the contact between the roller and the lead screw or nut. * Here, ∑ρ represents the contact parameters related to the curvature and sum of the two contact surfaces, μ is Poisson's ratio, and E is the elastic modulus. In this example, E = 212 × 10⁻⁶. 3 MPa, μ = 0.29.

[0148] The relevant contact parameters δ between the roller, lead screw, and nut were obtained by referring to the table. * ∑ρ, μ, and E, representing the dynamic contact force F between the roller and the lead screw and nut sides obtained in S2. SR and F NR Substituting these values ​​into equations 13 and 14 respectively, the contact deformation δ between the roller and the lead screw and nut can be obtained. SRC and δ NRC .

[0149] The actual contact angle α between the roller and the lead screw and nut sides SR and α NR The calculation formulas are as follows:

[0150]

[0151]

[0152] α SR0 Let α be the initial value of the contact angle between the roller and the lead screw. NR0 Let r be the initial value of the contact angle between the roller and the nut. S Let r be the nominal radius of the leadscrew. N The nominal radius of the nut.

[0153] The initial value α of the contact angle between the roller and the lead screw and nut side set in S2 is... SR0 and α NR0 and the contact deformation δ obtained in S3 SRC and δ NRC Substituting these values ​​into equations 15 and 16 respectively, we can obtain the actual contact angle α between the roller and the lead screw and nut sides. SR and α NR .

[0154] S4: Verify the actual contact angle α SR and α NR Correctness:

[0155] The difference between the actual contact angle and the initial contact angle value is calculated. If the difference is less than the set minimum value, the dynamic contact force, contact angle, and contact deformation are output. If the difference is greater than the set minimum value, the initial contact angle value is reset, and S2, S3, and S4 are repeated.

[0156] S5: Output dynamic contact force F SR and F NR Actual contact angle α SR and α NR and contact deformation δ SRC and δ NRC .

[0157] S6: Solve for the dynamic load distribution of the thread on the side of the roller and lead screw, and the roller and nut:

[0158] The dynamic contact force F obtained in S4 SR and F NR Substituting the external load into the planetary roller screw load distribution model, the thread dynamic load distribution between the roller and the screw, and between the roller and the nut, is obtained.

[0159] Based on the structural characteristics and load-bearing principle of planetary roller screws, they are discretized into three structural elements: threaded shaft segment, thread teeth, and thread tooth contact point.

[0160] Stiffness k of threaded shaft section XB This refers to the tensile and compressive stiffness of the matrix of two adjacent load-bearing threaded parts in a lead screw, roller, or nut. This stiffness can be solved using the formula for the tensile and compressive stiffness of shafts in mechanics of materials. In a planetary roller screw, the shaft stiffness of the lead screw and nut is:

[0161]

[0162] Where, k XB E X and A X These represent the shaft stiffness, elastic modulus, and cross-sectional area of ​​the lead screw or nut, respectively; P is the pitch of the lead screw, roller, or nut.

[0163] The cross-sectional area A of the lead screw shaft segment S The cross-sectional area A of the shaft segment of the nut N They are respectively:

[0164]

[0165]

[0166] Where, d S and d N These are the thread pitch diameters of the lead screw and nut, respectively; h f n is the thread root height of the lead screw and nut; rollerD0 represents the number of rollers; D0 represents the outer diameter of the nut.

[0167] The thread pitch diameter d of the lead screw and nut S and d N Thread root height h f Number of rollers n roller Substituting the outer diameter D0 of the screw and nut into equations 18 and 19 respectively, the cross-sectional areas A of the shaft segments of the screw and nut are obtained. S and A N . A S and A N The elastic modulus E of the lead screw and nut S and E N Substituting the pitch P into Equation 17, the stiffness k of the screw and nut shaft sections can be obtained. SB and k NB .

[0168] Since the rollers mesh with both the lead screw and the nut, the stiffness of its shaft section is equal to the stiffness within half the screw pitch. Therefore, the stiffness k of the roller shaft section is... RB for:

[0169]

[0170] The cross-sectional area A of the roller shaft segment R for:

[0171]

[0172] The thread pitch diameter d of the roller R and thread root height h f Substituting into Equation 21, the cross-sectional area A of the roller shaft segment is obtained. R The cross-sectional area A of the roller shaft segment. R Roller elastic modulus E R Substituting the pitch P into Equation 20, the stiffness k of the roller shaft section can be obtained. RB .

[0173] Based on the force analysis of the thread teeth, the axial component F of the normal contact load between the lead screw or nut and the roller is known. XRa and radial component F XRr They are respectively:

[0174] F XRa =F XR ·sinα XR (twenty two)

[0175] F XRr =F XR ·cosα XR (twenty three)

[0176] Where, α XRF is the actual contact angle between the roller and the lead screw or nut. XR This refers to the dynamic contact force between the roller and the lead screw or nut.

[0177] The obtained dynamic contact force F between the roller and the lead screw and nut sides is... SR and F NR and actual contact angle α SR and α NR Substituting these values ​​into equations 22 and 23 respectively, the axial and radial components F of the forces on the roller and lead screw or nut sides can be obtained. XRa and F XRr .

[0178] When a planetary roller screw is subjected to a load, the roller threads mesh with the screw and nut threads respectively and bear the load. After being subjected to force, the threads will deform along the screw axis. The axial deformation of the threads includes deformation δ1 caused by bending, deformation δ2 caused by shear force, deformation δ3 caused by root inclination, deformation δ4 caused by root shear, and deformation δ5 caused by radial component force. The calculation methods for each deformation of the threads will not be elaborated in this article.

[0179] The total axial deformation of the planetary roller screw thread teeth under axial load is:

[0180] δ XT =δ1+δ2+δ3+δ4+δ5 (24)

[0181] The corresponding thread stiffness k XT for:

[0182]

[0183] Thread tooth contact stiffness k XRC This refers to the dynamic contact force F between the roller and the normal direction of the screw or nut thread. SR and F NR With contact deformation δ SRC and δ NRC The ratio of .

[0184] F obtained from equations 22 and 23 XRa and F XRr Substituting Equation 24 into Equation 25, the thread stiffness k of the lead screw, roller, or nut can be obtained. XT .

[0185] The axial component δ of the deformation of the planetary roller screw roller in contact with the screw or nut XRC-axial It can be represented as:

[0186] δ XRC-axial =δ XRC ·cosα XR ·cosλ XR (26)

[0187] The corresponding axial contact stiffness k XRC for:

[0188]

[0189] The contact deformation δ obtained from equations 13 and 14 SRC and δ NRC Actual contact angle α SR and α NR and helix angle λ SR and λ NR Substituting into Equation 26, the axial component δ of the contact deformation is obtained. XRC-axial The axial component δ of the contact deformation XRC-axial The dynamic contact force F between the roller and the lead screw or nut SR and F NR Substituting into Equation 27, the axial contact stiffness k of the lead screw, roller, or nut can be obtained. XRC .

[0190] Substituting the shaft stiffness model, thread tooth stiffness model, and contact stiffness model into the thread tooth closed-loop model yields the thread tooth deformation compatibility relationship.

[0191] Taking the roller-nut contact side as an example, the total deformation of the nut within the i-th threaded closed loop can be obtained as ∑l Ni Let Δl be the total deformation of the nut shaft segment within the i-th threaded closed loop. NBi The total deformation of the nut thread teeth Δl NTi The total deformation of the nut thread teeth at contact Δl RNCi The total thread deformation Δl of the inner nut in the (i+1)th threaded closed loop NTi+1 The sum, that is:

[0192] ∑l Ni =Δl NBi +Δl NTi +Δl NTi+1 +Δl RNCi (28)

[0193] The total deformation of the inner rollers in the i-th threaded closed loop ∑l Ri Let Δl be the total deformation of the inner roller shaft segment of the i-th threaded closed loop. RBi The total deformation of the roller thread teeth Δl RTi The total deformation Δl of the inner roller shaft segment of the (i+1)th threaded closed loop RBi+1 Total thread deformation Δl RTi+1 and the total deformation of the thread teeth Δl RNCi+1 The sum, that is:

[0194] ∑l Ri =Δl RBi +ΔlRBi+1 +Δl RTi +Δl RTi+1 +Δl RNCi+1 (29)

[0195] According to the deformation compatibility relationship, we have:

[0196] P N +∑l Ni =P R +Σl Ri (30)

[0197] Since the nut pitch is equal to the roller pitch, i.e. P N =P R Then we have:

[0198] Σl Ni =Σl Ri (31)

[0199] Substituting the shaft stiffness, thread stiffness, and contact stiffness into the above formula yields the dynamic load distribution model for the roller and lead screw side threads:

[0200]

[0201] Similarly, the dynamic load distribution model of the thread teeth on the roller and nut sides is as follows:

[0202]

[0203] The sum of the loads on each thread tooth is the overall contact force between the roller and the lead screw or nut, as shown in Equation 34:

[0204]

[0205] In this example, unassigned parameters can be obtained by looking up a table or by using already assigned parameters. The final calculated dynamic load distribution on the roller, lead screw, and nut sides is as follows: Figure 6 As shown.

[0206] The inventive points of this invention can be further illustrated by calculation results:

[0207] The calculation method for dynamic load distribution of planetary roller screw threads can analyze the influence of screw speed on the contact angle, contact force, contact deformation and load distribution of the screw and nut sides when the load is constant; and the influence of load on the contact angle, contact force, contact deformation and load distribution of the screw and nut sides when the screw speed is constant.

[0208] With a constant load, as the screw speed increases, the contact angle on the screw side increases, while the contact angle on the nut side decreases. Figure 7 As shown; the contact force on the leadscrew side decreases, while the contact force on the nut side increases, as... Figure 8As shown; the contact deformation on the lead screw side decreases, while the contact deformation on the nut side increases, as... Figure 9 As shown; the load distribution on the lead screw side shows a decreasing trend, such as Figure 10 As shown; the load distribution on the nut side shows an increasing trend, such as Figure 11 As shown.

[0209] The lead screw speed is constant. As the load increases, the contact angle on the lead screw side decreases, while the contact angle on the nut side increases. Figure 12 As shown; the contact forces on both the leadscrew and nut sides increase, with the increase in contact force on the leadscrew side being greater, such as... Figure 13 As shown; the contact deformation on both the lead screw and nut sides increases, and the increase in contact deformation on the lead screw side is greater, such as... Figure 14 As shown; the load distribution on the lead screw side shows a decreasing trend, such as Figure 15 As shown; the load distribution on the nut side shows an increasing trend, such as Figure 16 As shown.

[0210] For those skilled in the art, various corresponding changes and modifications can be made based on the above technical solutions and concepts, and all such changes and modifications should be included within the protection scope of the claims of this invention.

Claims

1. A method for calculating the dynamic load distribution of the thread of a planetary roller screw, characterized in that, Includes the following steps: S1: Solve for the static contact forces between the roller and the lead screw, and between the roller and the nut. and : The static contact force at the contact point between the roller and the screw is calculated based on the principle of helical surface meshing of the planetary roller screw. and the static contact force at the contact point between the roller and the nut ; S2: Iteratively solve the dynamic contact forces between the roller and the lead screw, and between the roller and the nut. and : Taking the roller as the research object, we conduct a force analysis on it and set an initial value for the contact angle. and The inertial force generated by the rotation of the lead screw Solve the dynamic contact force of the planetary roller screw considering inertial forces by deriving the force balance equations for the contact forces with the lead screw and nut sides in the axial and radial directions of the rollers. and ; S3: Solve for the actual contact angle and : The dynamic contact force obtained from S2 and Substituting into Hertzian contact theory, the contact deformation is obtained. and Then the actual contact angle is obtained. and ; S4: Verify the actual contact angle and Correctness: Actual contact angle and With initial contact angle and Calculate the difference; if the difference is less than the set minimum value... Then the dynamic contact force is output. and If the difference is greater than the set minimum value, then the initial contact angle value is reset. and until the difference is less than the set minimum value; S5: Output dynamic contact force and Actual contact angle and and contact deformation and ; S6: Solving for the dynamic load distribution of the side threads of the rollers and leadscrew, and the rollers and nut: The planetary roller leadscrew load distribution model in S6 is as follows: Based on the structural characteristics and load-bearing principle of planetary roller screws, they are discretized into three structural elements: threaded shaft segment, thread teeth, and thread tooth contact point. Stiffness of threaded shaft section This refers to the tensile and compressive stiffness of the matrix of two adjacent load-bearing threaded parts in a lead screw, roller, or nut. This stiffness can be solved using the formula for the tensile and compressive stiffness of shafts in mechanics of materials. In a planetary roller lead screw, the shaft stiffness of the lead screw and nut is: (17) in, , and These are the shaft stiffness, elastic modulus, and cross-sectional area of ​​the lead screw or nut, respectively. The pitch of the lead screw, roller, or nut; Cross-sectional area of ​​the lead screw shaft Cross-sectional area of ​​the shaft segment of the nut They are respectively: (18) (19) in, and These are the mean diameters of the threads of the lead screw and nut, respectively. The thread root height of the lead screw and nut; The number of rollers; The outer diameter of the nut; Since the rollers mesh with both the lead screw and the nut, the stiffness of the shaft section is the stiffness within half a screw pitch. Therefore, the stiffness of the roller shaft section is... for: (20) cross-sectional area of ​​roller shaft segment for: (21) Based on the force analysis of the thread teeth, the axial component of the normal contact load between the lead screw or nut and the roller can be determined. and radial component They are respectively: (22) (23) in, This is the actual contact angle between the roller and the lead screw or nut. This refers to the dynamic contact force between the roller and the lead screw or nut. When a planetary roller screw is subjected to a load, the roller threads mesh with the screw and nut threads respectively and bear the load. After being stressed, the threads will deform along the screw axis. The axial deformation of the threads includes deformation caused by bending. Deformation caused by shear force Deformation caused by root tilting Deformation caused by root shearing and deformation caused by radial component force The calculation methods for various deformations of the thread teeth will not be elaborated in this article; The total axial deformation of the planetary roller screw thread teeth under axial load is: (24) Corresponding thread stiffness for: (25) Thread tooth contact stiffness This refers to the dynamic contact force in the normal direction between the roller and the screw or nut thread. and Contact deformation and The ratio; Assuming the axial load of the planetary roller screw is uniformly distributed among the meshing thread teeth, according to Hertzian contact theory, the deformation of the contact area between the roller and the thread teeth on the screw or nut side under normal contact load can be obtained from... and Seek; The axial component of the deformation of the planetary roller screw roller in contact with the screw or nut. It can be represented as: (26) Corresponding axial contact stiffness for: (27) Substituting the shaft stiffness model, thread tooth stiffness model, and contact stiffness model into the thread tooth closed-loop model yields the thread tooth deformation compatibility relationship. Taking the contact side between the roller and the nut as an example, we can obtain the first... i The total deformation of the nut within each threaded closed loop For the first i The total deformation of the nut shaft segment within the closed thread loop Total deformation of nut thread teeth Total deformation of nut thread teeth Passing the exam i +1 Total thread tooth deformation of the inner nut in the closed-loop threaded section The sum, that is: (28) No. i The total deformation of the inner rollers of the threaded closed ring For the first i The total deformation of the inner roller shaft section of the threaded closed loop Total deformation of roller thread teeth , No. i +1 Total deformation of the inner roller shaft segment of the threaded closed loop Total thread deformation and the total deformation of the thread teeth The sum, that is: (29) According to the deformation compatibility relationship, we have: (30) Since the pitch of the nut is equal to the pitch of the roller, that is... Then we have: (31) Substituting the shaft stiffness, thread stiffness, and contact stiffness into the above formula yields the dynamic load distribution model for the roller and lead screw side threads: (32) Similarly, the dynamic load distribution model of the thread teeth on the roller and nut sides is as follows: (33) The sum of the loads on each thread tooth is the overall contact force between the roller and the lead screw or nut, as shown in Equation 34: (34) The dynamic contact force obtained in S4 and Substituting the external load into the planetary roller screw load distribution model, the thread dynamic load distribution between the roller and the screw, and between the roller and the nut, is obtained.

2. The method for calculating the dynamic load distribution of planetary roller screw threads according to claim 1, characterized in that, The static contact force at the contact point between the roller and the lead screw mentioned in S1 The calculation formula is: (1) (2) The magnitude of the contact force; and These are the helix angle and the tooth flank angle at the contact point between the lead screw and the roller, respectively. The engagement angle of the roller on the lead screw side; For the load on the nut, The number of rollers; (3) (4) (5) in, For the lead of the roller; The engagement radius of the roller on the lead screw side; The nominal radius of the roller; The radius of the tooth profile of the roller; The center of the roller tooth profile is at in the plane Coordinate values For roller tooth flank angle; Static contact force at the contact point between the roller and the nut as described in S1 The calculation formula is: (6) Due to the meshing angle between the nut and the roller The helix angle at the contact point between the nut and the roller Tooth flank angle Equal to the helix angle of the roller and tooth lateral angle ,therefore (7) (8) (9) (10) 3. The method for calculating the dynamic load distribution of planetary roller screw threads according to claim 1, characterized in that, The inertial force generated by the rotation of the lead screw in S2 As shown in Equation 11, the equation for the balance of axial and radial forces of the roller is shown in Equation 12: (11) (12) For the mass of the roller, The diameter of the roller's revolution. This is the actual contact angle between the roller and the lead screw. This is the actual contact angle between the roller and the nut. The angular velocity of the roller's revolution. It is an inertial force. and This refers to the dynamic contact force between the roller and the lead screw, and between the roller and the nut.

4. The method for calculating the dynamic load distribution of planetary roller screw threads according to claim 1, characterized in that, Contact deformation in S3 and The calculation formulas are as follows: (13) (14) in, and Deformation occurs due to the contact between the roller and the lead screw or nut. To and Relevant contact parameters, For the curvature and function of two contacts, Poisson's ratio, It is the elastic modulus; Actual contact angle between roller and lead screw and nut side and The calculation formulas are as follows: (15) (16) This is the initial value of the contact angle between the roller and the lead screw. This is the initial value of the contact angle between the roller and the nut. Let be the nominal radius of the leadscrew. The nominal radius of the nut.

Images