Planetary roller screw bearing characteristic analysis method considering roller deflection and pitch error

Abstract

The invention discloses a planetary roller screw bearing characteristic analysis method considering roller deflection and pitch errors, and belongs to the field of planetary roller screws. The method comprises the following steps: firstly, establishing a roller deflection model according to a gear pair backlash, and calculating a meshing clearance caused by deflection; meanwhile, a screw pitch error model of the lead screw, the nut and the roller is established according to the number of thread heads. And further, the error amount is used as an initial geometric deviation to be embedded into a planetary roller screw basic mechanical model based on a deformation coordination and force balance principle, a nonlinear load distribution equation set reflecting the error coupling influence is constructed, and solving is carried out through an iterative algorithm. Finally, the rule of the influence of the roller deflection angle and the pitch error on the thread load distribution uniformity and the maximum bearing capacity is revealed through parameterized analysis. According to the method, a theoretical basis closer to the actual working condition is provided for precision design, tolerance distribution and performance optimization of the planetary roller screw.

Description

Technical Field

[0001] This invention belongs to the field of planetary roller screws, and specifically relates to a method for analyzing the load-bearing characteristics of planetary roller screws that takes into account roller skew and pitch error. Background Technology

[0002] The multi-point contact and multi-pair meshing structure of planetary roller screws endows them with excellent characteristics such as high load capacity, high transmission accuracy, and impact resistance. However, it also inevitably brings problems such as uncontrollable machining errors and roller skew affecting load capacity. Pitch error causes fluctuations in the load distribution of planetary roller screws, affecting their load-bearing capacity; at the same time, roller skew also affects the contact state and meshing position of the thread teeth, resulting in severe load unevenness. Therefore, establishing a planetary roller screw load-bearing model that comprehensively considers the effects of thread machining errors and roller skew is of significant theoretical and practical value for guiding the production and processing of planetary roller screws and improving their load-bearing capacity.

[0003] Roller skew and pitch error are both important factors affecting the load distribution of planetary roller screw threads. The current understanding of the impact of roller skew and pitch error on load distribution is as follows: On the one hand, pitch error originates from precision deviations during thread machining, which can cause a shift in the theoretical meshing position between the thread teeth, thereby altering the load distribution among them. Studies have shown that even minute pitch errors can trigger significant fluctuations in load distribution, and may even lead to disengagement of some thread teeth, severely reducing the actual load-bearing capacity and fatigue life of the leadscrew.

[0004] On the other hand, roller misalignment is usually caused by factors such as installation clearance, uneven force distribution, or gear backlash, resulting in the roller axis tilting relative to its theoretical position. This misalignment alters the contact area and contact state of the threads between the roller and the lead screw / nut, causing localized stress concentration and exacerbating the unevenness of load distribution, which in turn negatively impacts transmission accuracy, load-bearing capacity, and reliability.

[0005] In actual operating conditions, roller skew and pitch error often coexist and couple with each other, jointly affecting contact clearance, meshing stiffness, and load transmission path. Models that only consider a single factor cannot accurately reflect the load distribution characteristics under complex error coupling, resulting in theoretical limitations in design optimization, accuracy allocation, and life prediction, thus restricting further improvement of planetary roller screw performance and application reliability.

[0006] Therefore, there is an urgent need for a load-bearing characteristic analysis method that can simultaneously consider the coupling effect of roller skew and pitch error, so as to more realistically reflect the load distribution law under actual error conditions and provide a theoretical basis for the precision design, manufacturing process optimization and performance improvement of planetary roller screws. Summary of the Invention

[0007] The technical problem to be solved: To overcome the shortcomings of existing technologies, this invention provides a method for analyzing the load-bearing characteristics of planetary roller screws that considers roller skew and pitch error. This method integrates the roller skew model and the pitch error model, and analyzes the load distribution characteristics of the planetary roller screw thread under their coupled effect. This comprehensive analysis method aims to more realistically and comprehensively assess the impact of errors, providing an effective theoretical tool and optimization basis for the design and manufacturing of high-precision, high-reliability planetary roller screws.

[0008] The technical solution of this invention is: a method for analyzing the load-bearing characteristics of a planetary roller screw considering roller skew and pitch error, comprising the following steps: Step 1: Establish a roller skew model, correlate the roller skew angle with the gear pair backlash, and obtain the skew components of the rollers in mutually perpendicular planes. Step 2: Based on the roller skew model, establish a planetary roller screw meshing model that considers roller skew, and solve for the meshing clearance of each meshing thread tooth between the roller and the screw, and between the roller and the nut. Step 3: Establish a pitch error model. Based on the number of threads of the planetary roller screw, define the pitch error of each helix of the screw and nut and the rollers respectively, and express the actual pitch as the sum of the theoretical pitch and the corresponding error. Step 4: Based on the principles of deformation coordination and force balance, construct a basic mechanical model of the load distribution of the planetary roller screw thread teeth; this basic mechanical model includes calculating the axial stiffness of the thread tooth body, the stiffness of the component shaft segment, and the Hertzian contact stiffness of the thread contact pair, and establishing the system's force balance equation and deformation coordination equation including the thread tooth clearance. Step 5: The meshing clearance obtained in Step 2 and the pitch error obtained in Step 3 are used as initial clearance variables and introduced into the deformation coordination equation in Step 4 to establish a comprehensive load distribution model that considers the coupling effect of roller misalignment and pitch error. The coupling effect is achieved by simultaneously introducing the meshing clearance change caused by misalignment and the axial clearance change caused by pitch error into the deformation coordination equation. Step 6: Based on the load distribution model, solve the nonlinear contact equations through iterative calculation to obtain the thread tooth load distribution results; Step 7: Change the pitch error and roller skew parameters, and analyze the influence of their individual and coupled effects on the uniformity of thread load distribution and the maximum load.

[0009] A further technical solution of the present invention is: in step 1, establishing the roller skew model specifically involves: Based on the geometric relationship between the two end gears and the tooth surfaces on both sides of the internal gear ring when the roller is tilted, the roller deflection angle is established.m gear pair backlash d RNg Relationship:

[0010] in, l T This refers to the length of the roller thread segment. l G The length of the roller gear segment. m The roller skew angle. d RNg This refers to the backlash of the gear pair. This further decomposes the roller skew into the surrounding... x shaft and y The two perpendicular planes of the axis correspond to the skew angles. f and ψ They are respectively:

[0011]

[0012] in, f For roller winding x The angle of axis deflection, P For roller winding y The angle of axis deflection, α This is the pressure angle of the gear pair. A further technical solution of the present invention is: in step 2, establishing a meshing model considering roller skew includes: Establish the parametric equations for the helical surfaces of the lead screw, nut, and roller respectively; Constructing the roller skew matrix H R Transform the surface points in the roller coordinate system to the global coordinate system; Based on the conditions that the position vectors of the lead screw and roller, and the nut and roller coincide at the meshing point and that their normal vectors are collinear, a set of meshing equations is established. Solving the system of equations yields the meshing clearance vectors for each meshing pair of roller and lead screw, and roller and nut.

[0013] A further technical solution of the present invention is: the meshing equation set is as follows:

[0014] in, , For the first lead screw k S The position vector and external normal vector of each thread engagement point in the lead screw coordinate system; , Roller No. kRS The position vector and outward normal vector of each thread engagement point in the roller coordinate system; Let be a unit vector along the z-axis, and ; For the roller k RS The clearance between each thread tooth and the corresponding lead screw thread tooth; ζ is a constant.

[0015] A further technical solution of the present invention is: In step 3, establishing the pitch error model specifically involves: For the number of heads is m The planetary roller screw has a set screw and nut respectively with m There are 1 different pitch error, and the roller has 1 pitch error; The actual pitches of the lead screw, nut, and roller are expressed as follows:

[0016]

[0017]

[0018] in, P N 、P S 、P R These are the theoretical pitches for the nut, lead screw, and roller, respectively. , , These represent the pitch errors of different helical lines of nuts and leadscrews, and rollers, respectively. A The number representing the spiral. A =1, 2, 3, 4, 5.

[0019] A further technical solution of the present invention is: in step 4, constructing the basic mechanical model of the load distribution of the planetary roller screw thread teeth specifically includes: calculating the axial stiffness of the thread teeth of the screw, nut, and rollers under axial force. k xT Calculate the deformation stiffness of the lead screw, nut, and roller shaft section. k SB , k NB 、k RB Based on Hertzian contact theory, the axial contact stiffness of the planetary roller screw threads is calculated. k xRCEstablish the system's force balance equation, where the sum of the axial forces on all meshing thread teeth is equal to the external axial load; establish the basic deformation coordination equation without considering errors and skewness, where for each closed loop formed by adjacent thread teeth, the cumulative axial deformation on the nut side is equal to the cumulative axial deformation on the roller side.

[0020] A further technical solution of the present invention is as follows: the calculation formulas for the axial stiffness, deformation stiffness, and contact stiffness are as follows: Axial stiffness of the threaded teeth of lead screws, nuts, and rollers under axial force k xT The calculation formula is:

[0021] in, d 1 and d 2 represents the deformation caused by bending and the deformation caused by shear force; d 3 represents the deformation caused by root tilting; d 4 represents the deformation caused by root shearing; d 5 represents the deformation caused by the radial component of the force; d xT This represents the axial deformation of the thread teeth in a lead screw, roller, or nut. k xT Represents the axial stiffness of the thread teeth of a lead screw, roller, or nut; F a This represents the axial force acting on the thread teeth; Deformation stiffness of lead screw, nut, and roller shaft section k SB , k NB 、k RB The calculation formula is:

[0022]

[0023]

[0024] in, k SB The stiffness of the lead screw shaft section; k NB The stiffness of the nut's shaft section; k NB The stiffness of the nut's shaft section; A S The cross-sectional area of ​​the lead screw thread shaft section; A N This represents the cross-sectional area of ​​the threaded shaft section of the nut. A RThis represents the cross-sectional area of ​​the roller thread shaft section; E S The elastic modulus of the lead screw material; E N The elastic modulus of the nut material; E R The elastic modulus of the roller material; , 、 For PRSM lead screws, rollers, and nuts; Axial contact stiffness of planetary roller screw threads k xRC The calculation formula is:

[0025] in, k xRC For the axial contact stiffness of the thread teeth; x Use the subscript to select the index. S or N , respectively referring to lead screw or nut; d xRC-a The axial component of the thread tooth contact deformation is given in mm. d xRC-n The normal contact deformation of the thread teeth is expressed in mm.

[0026] A further technical solution of the present invention is: in step 5, constructing the comprehensive load distribution model specifically includes: The meshing clearance vector obtained in step 2, and the pitch clearance calculated from the pitch error in step 3, are combined as an additional clearance term and introduced into the deformation compatibility equation in step 4, forming the following deformation compatibility equation that considers the coupling of error and skew:

[0027] Where, ∑Δ l Ni For the first i The sum of the axial deformation of the nut within each pitch closed loop; ∑Δ l Ri For the first i The sum of the axial deformation of the rollers within each pitch closed loop; Δ P Ni For the nut i The pitch error of each thread tooth; Δ P Ri For the roller i Pitch error of each thread tooth; For the roller nut side i Axial engagement clearance of each thread tooth; For the roller nut sidei +1 thread tooth axial engagement clearance; Calculate the shaft stiffness of the lead screw, nut, and roller, as well as the axial contact stiffness of the thread teeth; combine the deformation compatibility equations of all thread teeth with the system force balance equations to form a matrix-form comprehensive load distribution model.

[0028] A further technical solution of the present invention is: step 6, iterative calculation includes: Assuming the initial thread tooth load is uniformly distributed, calculate the corresponding Hertzian contact stiffness. Substituting the contact stiffness into the load distribution model, a new load distribution is obtained by solving the problem. The contact stiffness of each meshing pair is recalculated based on the new load, and the model is updated. Repeat the iterative process until the difference between the load vectors of two adjacent iterations satisfies the preset convergence condition.

[0029] A further technical solution of the present invention is: in step 7, analyzing the influencing patterns includes: Different pitch error ranges and roller skew angles are set respectively; Compare the load distribution curves considering only skewness, only error, and the coupling effect of the two; The study evaluates the variation trend of maximum thread tooth load and load distribution uniformity, summarizes the enhancement or weakening effect of coupling on load-bearing characteristics, and provides a basis for precision design and error control.

[0030] Beneficial effects The beneficial effects of this invention are as follows: By establishing an integrated mathematical model, this invention, for the first time, couples the changes in meshing state caused by roller skew and the axial position deviation caused by pitch error within a unified mechanical framework for analysis. This more realistically reflects the complex working conditions of planetary roller screws in actual machining and assembly, where multiple errors coexist, significantly improving the completeness and accuracy of the theoretical analysis of load-bearing characteristics. Specific advantages are analyzed below: 1. Based on the relationship between the roller skew angle and the gear pair backlash, this invention establishes a roller skew angle model, which can be used to design the roller skew angle.

[0031] 2. This invention considers the influence of roller skew and pitch error on the load distribution of planetary roller screws and establishes a load-bearing model. This model can be used to calculate the thread load distribution law and its uniformity when there is a certain pitch error and roller skew.

[0032] 3. The load distribution model established in this invention provides a certain foundation for the optimized design of parameters such as pitch error and gear backlash of planetary roller screws in terms of load-bearing capacity. Attached Figure Description

[0033] Figure 1 To consider the meshing method of gear pairs with roller misalignment; Figure 2 This is a schematic diagram showing the misalignment of the roller axis; Figure 3 This is a roller skew coordinate system; Figure 4 For planetary roller screw components and thread tooth coordinate system; Figure 5 For the tooth profile coordinate system of the lead screw, roller, and nut; Figure 6 This is a schematic diagram of thread tooth deformation; Figure 7 The thread tooth meshing clearance is designed to account for roller misalignment and pitch error; Figure 8 The process for solving the load distribution of planetary roller screws; Figure 9 A thread load distribution curve that takes into account roller misalignment and pitch error. Detailed Implementation

[0034] The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain the invention, and should not be construed as limiting the invention.

[0035] On the one hand, the influence of pitch error on load distribution is considered: Zhang Wenjie. Calculation Model and Method for Thread Load Distribution of Planetary Roller Screw Pair [D]. Northwestern Polytechnical University, 2017. A thread load distribution model considering pitch error was established, the influence law of pitch error on load distribution was analyzed, and it was concluded that pitch error will cause fluctuations in the thread load distribution of planetary roller screw, and even cause thread disengagement. The rationality of the relevant conclusions was verified by comparing experiments with theory.

[0036] On the other hand, the influence of roller skew on load distribution is considered: Fu Xiaojun, Xu Ye, Liu Geng, et al. Calculation method of load distribution of planetary roller screw considering roller skew [J]. Journal of Mechanical Engineering, 2024, 60(13): 247-256. A load distribution model of planetary roller screw considering roller skew was established, and the influence law of roller skew on the thread meshing state and load distribution of planetary roller screw was analyzed. Through example calculation, it was found that when the skew angle around a certain direction is greater than 1′, the thread teeth will have obvious disengagement phenomenon, and the maximum thread teeth are subjected to force about 3 times that of the ideal state.

[0037] Based on the problems existing in the prior art, this invention proposes a method for analyzing the load-bearing characteristics of planetary roller screws considering roller skew and pitch error. The specific steps include: Step 1: Establish a roller skew model, correlate the roller skew angle with the gear pair backlash, and obtain the skew components of the rollers in mutually perpendicular planes. Step 2: Based on the roller skew model, establish a planetary roller screw meshing model that considers roller skew, and solve for the meshing clearance of each meshing thread tooth between the roller and the screw, and between the roller and the nut. Step 3: Establish a pitch error model. Based on the number of threads of the planetary roller screw, define the pitch error of each helix of the screw and nut and the rollers respectively, and express the actual pitch as the sum of the theoretical pitch and the corresponding error. Step 4: Based on the principles of deformation coordination and force balance, construct a basic mechanical model of the load distribution of the planetary roller screw thread teeth; this basic mechanical model includes calculating the axial stiffness of the thread tooth body, the stiffness of the component shaft segment, and the Hertzian contact stiffness of the thread contact pair, and establishing the system's force balance equation and deformation coordination equation including the thread tooth clearance. Step 5: The meshing clearance obtained in Step 2 and the pitch error obtained in Step 3 are used as initial clearance variables and introduced into the deformation coordination equation in Step 4 to establish a comprehensive load distribution model that considers the coupling effect of roller misalignment and pitch error. The coupling effect is achieved by simultaneously introducing the meshing clearance change caused by misalignment and the axial clearance change caused by pitch error into the deformation coordination equation. Step 6: Based on the load distribution model, solve the nonlinear contact equations through iterative calculation to obtain the thread tooth load distribution results; Step 7: Change the pitch error and roller skew parameters, and analyze the influence of their individual and coupled effects on the uniformity of thread load distribution and the maximum load.

[0038] The above technical solution will be further explained below with reference to the accompanying drawings: In one embodiment, a method for analyzing the load-bearing characteristics of a planetary roller screw considering roller skew and pitch error includes the following steps: S1 establishes a roller skew model with tooth backlash as a constraint. The meshing mode of the gears at both ends of the roller after skew is as follows: Figure 1 As shown in the diagram, gear pair 1 is the gear at the left end of the roller, and gear pair 2 is the gear at the right end of the roller. The roller axis is misaligned as follows: Figure 2 As shown, its skew angle m tooth flank clearance d The size relationship of RNg is as follows:

[0039] in, l T The length of the roller thread section is in mm; l G The length of the roller gear segment is in mm; mThe roller skew angle; d RNg The backlash of the gear pair is measured in mm.

[0040] S2 decomposes the roller skewness into horizontal and vertical directions, and the skewness coordinate system is as follows. From the figure, we can obtain the roller skewness around the horizontal and vertical directions. x Axis (vertical direction) and y The skew angles of the axis (horizontal direction) are as follows:

[0041]

[0042] in, f The skew angle of the roller about the x-axis; ψ The deflection angle of the roller about the y-axis; α The pressure angle of the gear pair.

[0043] S3 Coordinate System for Lead Screws, Nuts, and Rollers o i x i y i z i like Figure 4 As shown, i = S , R , N The figures represent the lead screw, roller, and nut, respectively. The coordinate system of the parts in the diagram... o i x i y i z i of z i The axes are aligned with the axes of the corresponding parts. Simultaneously, a corresponding thread tooth coordinate system is established on the helix of each part. o , i u i v i w i The spiral passes through the origin of the coordinate system. o , i The tooth profile coordinate system of lead screws, nuts, and rollers is as follows: Figure 5 As shown, where β i0 , a i , bi , c i These represent the tooth flank angle, tooth crest height, tooth root height, and half tooth thickness of the corresponding parts, respectively. C i1 , C i2 These represent the upper and lower contour lines of the tooth profile, respectively. Let the lead screw and nut be... j The curved surfaces on the threaded rod in their respective part coordinate systems o S x S y S z S , o N x N y N z N The equations on are respectively , The helical surface of the roller in the coordinate system o R x R y R z R The equation above is Then, from the parametric representation method of helical surfaces, we can obtain:

[0044]

[0045]

[0046] Where: the "+" in the symbol "±" corresponds to the upper helical surface. C i1 "—" corresponds to the lower spiral surface C i2 ; u i , i i Represents the coordinates of the helical surface; L i Represents the lead of the helix; S4 uses the surface equation to represent the roller skewness from the roller coordinate system to the global coordinate system through coordinate transformation, resulting in:

[0047]

[0048]

[0049] in, H R This is the roller skew matrix; r R Let be the position vector of a point on the roller surface in the global coordinate system; This is the position vector of a point on the roller surface in the roller coordinate system; P R This is the position vector of the origin in the rolling coordinate system in the global coordinate system; P Rr This is the position vector of the roller skew around the point in the global coordinate system.

[0050] S5 According to the surface coordinate equation, the lead screw... k S The position vector and outward normal vector of each thread engagement point in the lead screw coordinate system; the first roller... k RS The position vectors and outward normal vectors of each thread engagement point in the roller coordinate system are as follows:

[0051]

[0052]

[0053]

[0054] Among them, the first is the lead screw. k S The helix angle at the meshing point of the thread teeth; for the first... k RS The helix angle at the meshing point of the thread teeth; for the first... k RS The tooth flank angle at the engagement point of each thread tooth; L S For the lead screw; L R For roller lead; k S , k RS This refers to the thread number of the lead screw or roller.

[0055] When the leadscrew and rollers mesh, the position vectors and normal directions of the threaded surfaces of the leadscrew and rollers at the meshing point coincide, thus yielding the following system of equations:

[0056] in, Let be the unit vector along the z-axis, and ; For the roller k RS The clearance between each thread tooth and the corresponding lead screw thread tooth; ζ is a constant.

[0057] Solving the system of equations in S6 yields five independent variables, namely the lead screw's meshing radius. Meshing angle ; Roller engagement radius Meshing angle meshing clearance Assume the rollers and lead screw have a total of n For threaded teeth involved in meshing, the interaction between the roller and the screw is represented in vector form. n For the engagement radius and engagement clearance of the thread teeth, we get:

[0058]

[0059]

[0060] Similarly, the rollers and nuts... n For the meshing radius and meshing clearance of the intermeshing threads:

[0061]

[0062]

[0063] Based on the relationship between pitch error and geometric parameters, S8 shows the actual pitch considering the error:

[0064] in, P x Theoretical pitch, mm; Actual pitch, mm; Δ P x The pitch error is in mm. x This represents a lead screw, roller, or nut.

[0065] The S9 planetary roller screw and nut each contain five helical lines (taking a 5-start planetary roller screw as an example). The roller thread is a single-start thread, containing only one helical line. Based on actual measurement results, assuming that the pitch error of the thread teeth on each helical line is consistent, the screw and nut each have 5 different pitch errors, while the roller has only 1 pitch error. Therefore, the pitch error and actual pitch of the screw, roller, and nut can be expressed as:

[0066]

[0067]

[0068] in, , , These represent the pitch errors of different helical lines of the nut, lead screw, and roller, respectively. A The number representing the spiral. A =1, 2, 3, 4, 5.

[0069] There are four deformation modes of the S10 thread under load. Based on the different deformation modes of the thread teeth under load, we can know the total axial deformation of the thread teeth and the corresponding axial stiffness of the thread teeth under axial load of the planetary roller screw:

[0070]

[0071] in, d 1 and d 2 represents the deformation caused by bending and the deformation caused by shear force; d 3 represents the deformation caused by root tilting; d 4 represents the deformation caused by root shearing; d 5 represents the deformation caused by the radial component of the force; d xT This represents the axial deformation of the thread teeth in a lead screw, roller, or nut. k xT Represents the axial stiffness of the thread teeth of a lead screw, roller, or nut; F a This represents the axial force exerted on the thread teeth.

[0072] Based on the axial deformation characteristics of the planetary roller screw, S11 calculates the deformation stiffness of the shaft segments of the screw, nut, and rollers as follows:

[0073]

[0074]

[0075] in, k SB The stiffness of the lead screw shaft section; k NB The stiffness of the nut's shaft section; k NB The stiffness of the nut's shaft section; AS The cross-sectional area of ​​the lead screw thread shaft section; A N This represents the cross-sectional area of ​​the threaded shaft section of the nut. A R This represents the cross-sectional area of ​​the roller thread shaft section; E S The elastic modulus of the lead screw material; E N The elastic modulus of the nut material; E R The elastic modulus of the roller material; , 、 This refers to the actual pitch of the PRSM lead screw, roller, and nut.

[0076] Using Hertz's contact formula, the normal contact deformation of the thread teeth can be obtained as follows:

[0077] in, d The normal contact deformation of the thread teeth is expressed in mm. d* To and ∑r Relevant contact parameters; ∑r Let be the sum of the curvatures of the two contact surfaces.

[0078] Therefore, the axial contact stiffness of the planetary roller screw thread teeth is:

[0079] in, k xRC For the axial contact stiffness of the thread teeth; x Use the subscript to select the index. S or N , respectively referring to lead screw or nut; d xRC-a The axial component of the thread tooth contact deformation is given in mm. d xRC-n The normal contact deformation of the thread teeth is expressed in mm.

[0080] S13 Considering roller skewness and pitch error, the closed-loop clearance of the planetary roller screw thread is as follows: Figure 7 As shown in the figure g Xi The axial clearance of the thread teeth caused by pitch error is expressed as follows:

[0081] Where, Δ P xi Indicates the first lead screw or nut i The pitch error of each thread tooth, ΔP R This indicates the pitch error of the roller.

[0082] Based on the deformation coordination relationship of the closed-loop thread, the planetary roller screw roller nut side needs to consider roller skew and pitch error. i Deformation compatibility formula within a closed loop of a thread:

[0083] Where, ∑Δ l Ni For the first i The sum of the axial deformation of the nut within each pitch closed loop; ∑Δ l Ri For the first i The sum of the axial deformation of the rollers within each pitch closed loop; Δ P Ni For the nut i The pitch error of each thread tooth; Δ P Ri For the roller i Pitch error of each thread tooth; For the roller nut side i Axial engagement clearance of each thread tooth; For the roller nut side i +1 threaded tooth axial engagement clearance.

[0084] In step S14, the sum of the axial deformation of the nut and the sum of the axial deformation of the roller in S13 can be expressed as:

[0085]

[0086] in, F NRi and F NRi+1 The roller nut side is respectively i and i +1 Axial force on the thread teeth; F SRi and F SRi+1 They are respectively the first roller screw side i and i +1 Axial force on the thread teeth According to the principle of force balance, the sum of the axial forces on the threads of both the roller screw contact side and the roller nut contact side is equal to the external load. F applied ,Right now:

[0087] Written in vector form:

[0088] in, F applied for n The sum of the axial forces acting on each thread tooth.

[0089] S16 expresses the deformation compatibility relationships of all threaded closed rings in vector form and combines them with the equations in S15 to obtain the planetary roller screw load distribution matrix equations considering roller skew and pitch error:

[0090] Where K is the load distribution stiffness matrix; l is the row vector. m is a row vector f is a column vector .

[0091] S17 Because the Hertzian contact variation in the thread tooth load distribution calculation model is nonlinear—that is, the Hertzian contact stiffness of the thread tooth is not a constant but a variable related to the magnitude of the load on the thread tooth—the matrix equation in the load distribution model is a nonlinear equation, requiring iterative calculation. The calculation process is as follows: Figure 8 As shown. First, assuming a uniform distribution of PRSM thread tooth load, the corresponding contact stiffness is calculated. At this point, the Hertzian contact stiffness of each pair of meshing threads is the same. This contact stiffness is substituted into the thread tooth load distribution model to obtain the corresponding load distribution and the contact stiffness of each pair of threads under this contact force. This is then substituted into the model to obtain a new matrix, which is solved again. This process is repeated until the thread tooth load converges. The convergence criterion for the thread tooth load is set to 10. -6 That is, |f(k)-f(k-1)|<10 -6 When the iteration result meets this condition, it is determined that the iteration result has reached the convergence criterion, and the result of the kth iteration is taken as the calculation result of the PRSM thread load distribution.

[0092] S18 Substitute the planetary roller screw parameters from the table below into the above model and conduct four sets of tests: considering only skew (gear pair backlash 0.01mm), considering only pitch error (error range [-0.001, 0.001]), and considering both error and coupling effects (two sets of tests). Calculate the load distribution for each set of tests and express the results as a curve, such as... Figure 9 As shown.

[0093] Table 1

[0094] As shown in the figure, the load distribution results obtained when considering both error and skew are different from those considering only skew or only error. The load distribution uniformity of test group 1 is better than both of these cases, while the load distribution uniformity of test group 2 is worse. The maximum thread load considering only skew is 27731 N, and the maximum thread load considering only error is 323.11 N. Considering both factors, the maximum thread load of test group 1 is 267.40 N, and the maximum thread load of test group 2 is 364.62 N. This phenomenon occurs because both skew and pitch error affect the thread clearance. Skew worsens the load distribution uniformity, while thread error can either improve or worsen it, with a degree of randomness. Therefore, when both factors worsen the load distribution, the following result occurs. Figure 9 The situation of experimental group 2.

[0095] Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art can make changes, modifications, substitutions and variations to the above embodiments within the scope of the present invention without departing from the principles and spirit of the present invention.

Claims

1. A method for analyzing the load-bearing characteristics of planetary roller screws considering roller skew and pitch error, characterized in that, Includes the following steps: Step 1: Establish a roller skew model, correlate the roller skew angle with the gear pair backlash, and obtain the skew components of the rollers in mutually perpendicular planes. Step 2: Based on the roller skew model, establish a planetary roller screw meshing model that considers roller skew, and solve for the meshing clearance of each meshing thread tooth between the roller and the screw, and between the roller and the nut. Step 3: Establish a pitch error model. Based on the number of threads of the planetary roller screw, define the pitch error of each helix of the screw and nut and the rollers respectively, and express the actual pitch as the sum of the theoretical pitch and the corresponding error. Step 4: Based on the principles of deformation coordination and force balance, construct a basic mechanical model of the load distribution of the planetary roller screw thread teeth; this basic mechanical model includes calculating the axial stiffness of the thread tooth body, the stiffness of the component shaft segment, and the Hertzian contact stiffness of the thread contact pair, and establishing the system's force balance equation and deformation coordination equation including the thread tooth clearance. Step 5: The meshing clearance obtained in Step 2 and the pitch error obtained in Step 3 are used as initial clearance variables and introduced into the deformation coordination equation in Step 4 to establish a comprehensive load distribution model that considers the coupling effect of roller misalignment and pitch error. The coupling effect is achieved by simultaneously introducing the meshing clearance change caused by misalignment and the axial clearance change caused by pitch error into the deformation coordination equation. Step 6: Based on the load distribution model, solve the nonlinear contact equations through iterative calculation to obtain the thread tooth load distribution results; Step 7: Change the pitch error and roller skew parameters, and analyze the influence of their individual and coupled effects on the uniformity of thread load distribution and the maximum load.

2. The method for analyzing the load-bearing characteristics of a planetary roller screw considering roller skew and pitch error according to claim 1, characterized in that: In step 1, establishing the roller skew model specifically involves: Based on the geometric relationship between the two end gears and the tooth surfaces on both sides of the internal gear ring when the roller is tilted, the roller deflection angle is established. μ gear pair backlash δ RNg Relationship: in, l T This refers to the length of the roller thread segment. l G The length of the roller gear segment. μ The roller skew angle. δ RNg This refers to the backlash of the gear pair. This further decomposes the roller skew into the surrounding... x shaft and y The two perpendicular planes of the axis correspond to the skew angles. φ and ψ They are respectively: in, φ For roller winding x The angle of axis deflection, Ψ For roller winding y The angle of axis deflection, α This is the pressure angle of the gear pair.

3. The method for analyzing the load-bearing characteristics of a planetary roller screw considering roller skew and pitch error according to claim 2, characterized in that: In step 2, establishing the meshing model that considers roller skew includes: Establish the parametric equations for the helical surfaces of the lead screw, nut, and roller respectively; Constructing the roller skew matrix H R Transform the surface points in the roller coordinate system to the global coordinate system; Based on the conditions that the position vectors of the lead screw and roller, and the nut and roller coincide at the meshing point and that their normal vectors are collinear, a set of meshing equations is established. Solving the system of equations yields the meshing clearance vectors for each meshing pair of roller and lead screw, and roller and nut.

4. The method for analyzing the load-bearing characteristics of a planetary roller screw considering roller skew and pitch error according to claim 3, characterized in that: The meshing equations are as follows: in, , For the first lead screw k S The position vector and external normal vector of each thread engagement point in the lead screw coordinate system; , Roller No. k RS The position vector and outward normal vector of each thread engagement point in the roller coordinate system; Let be a unit vector along the z-axis, and ; For the roller k RS The clearance between each thread tooth and the corresponding lead screw thread tooth; ζ is a constant.

5. The method for analyzing the load-bearing characteristics of a planetary roller screw considering roller skew and pitch error according to claim 3, characterized in that: In step 3, establishing the pitch error model specifically involves: For the number of heads is m The planetary roller screw has a set screw and nut respectively with m There are 1 different pitch error, and the roller has 1 pitch error; The actual pitches of the lead screw, nut, and roller are expressed as follows: in, P N 、P S 、P R These are the theoretical pitches for the nut, lead screw, and roller, respectively. , , These represent the pitch errors of different helical lines of nuts and leadscrews, and rollers, respectively. A The number representing the spiral. A =1, 2, 3, 4, 5.

6. The method for analyzing the load-bearing characteristics of a planetary roller screw considering roller skew and pitch error according to claim 5, characterized in that: In step 4, constructing the basic mechanical model of the load distribution of the planetary roller screw thread teeth specifically includes: calculating the axial stiffness of the thread teeth of the screw, nut, and rollers under axial force. k xT Calculate the deformation stiffness of the lead screw, nut, and roller shaft section. k SB , k NB 、k RB Based on Hertzian contact theory, the axial contact stiffness of the planetary roller screw threads is calculated. k xRC Establish the system's force balance equation, where the sum of the axial forces on all meshing thread teeth is equal to the external axial load; establish the basic deformation coordination equation without considering errors and skewness, where for each closed loop formed by adjacent thread teeth, the cumulative axial deformation on the nut side is equal to the cumulative axial deformation on the roller side.

7. The method for analyzing the load-bearing characteristics of a planetary roller screw considering roller skew and pitch error according to claim 6, characterized in that: The formulas for calculating axial stiffness, deformation stiffness, and contact stiffness are as follows: Axial stiffness of the threaded teeth of lead screws, nuts, and rollers under axial force k xT The calculation formula is: in, δ 1 and δ 2 represents the deformation caused by bending and the deformation caused by shear force; δ 3 represents the deformation caused by root tilting; δ 4 represents the deformation caused by root shearing; δ 5 represents the deformation caused by the radial component of the force; δ xT This represents the axial deformation of the thread teeth in a lead screw, roller, or nut. k xT Represents the axial stiffness of the thread teeth of a lead screw, roller, or nut; F a This represents the axial force acting on the thread teeth; Deformation stiffness of lead screw, nut, and roller shaft section k SB , k NB 、k RB The calculation formula is: in, k SB The stiffness of the lead screw shaft section; k NB The stiffness of the nut's shaft section; k NB The stiffness of the nut's shaft section; A S The cross-sectional area of ​​the lead screw thread shaft section; A N This represents the cross-sectional area of ​​the threaded shaft section of the nut. A R This represents the cross-sectional area of ​​the roller thread shaft section; E S The elastic modulus of the lead screw material; E N The elastic modulus of the nut material; E R The elastic modulus of the roller material; , 、 For PRSM lead screws, rollers, and nuts; Axial contact stiffness of planetary roller screw threads k xRC The calculation formula is: in, k xRC This refers to the axial contact stiffness of the thread teeth. x Use the subscript to select the index. S or N , respectively referring to lead screw or nut; δ xRC-a The axial component of the thread tooth contact deformation is given in mm. δ xRC-n The normal contact deformation of the thread teeth is expressed in mm.

8. The method for analyzing the load-bearing characteristics of a planetary roller screw considering roller skew and pitch error according to claim 6, characterized in that: Step 5, in which the comprehensive load distribution model is constructed, specifically includes: The meshing clearance vector obtained in step 2, and the pitch clearance calculated from the pitch error in step 3, are combined as an additional clearance term and introduced into the deformation compatibility equation in step 4, forming the following deformation compatibility equation that considers the coupling of error and skew: Where, ∑Δ l Ni For the first i The sum of the axial deformation of the nut within each pitch closed loop; ∑Δ l Ri For the first i The sum of the axial deformation of the rollers within each pitch closed loop; Δ P Ni For the nut i The pitch error of each thread tooth; Δ P Ri For the roller i Pitch error of each thread tooth; For the roller nut side i Axial engagement clearance of each thread tooth; For the roller nut side i +1 thread tooth axial engagement clearance; Calculate the shaft stiffness of the lead screw, nut, and roller, as well as the axial contact stiffness of the thread teeth; combine the deformation compatibility equations of all thread teeth with the system force balance equations to form a matrix-form comprehensive load distribution model.

9. The method for analyzing the load-bearing characteristics of a planetary roller screw considering roller skew and pitch error according to claim 8, characterized in that: Step 6, iterative calculation, includes: Assuming the initial thread tooth load is uniformly distributed, calculate the corresponding Hertzian contact stiffness. Substituting the contact stiffness into the load distribution model, a new load distribution is obtained by solving the problem. The contact stiffness of each meshing pair is recalculated based on the new load, and the model is updated. Repeat the iterative process until the difference between the load vectors of two adjacent iterations satisfies the preset convergence condition.

10. The method for analyzing the load-bearing characteristics of a planetary roller screw considering roller skew and pitch error according to claim 9, characterized in that: In step 7, the analysis of the influencing patterns includes: Different pitch error ranges and roller skew angles are set respectively; Compare the load distribution curves considering only skewness, only error, and the coupling effect of the two; The study evaluates the variation trend of maximum thread tooth load and load distribution uniformity, summarizes the enhancement or weakening effect of coupling on load-bearing characteristics, and provides a basis for precision design and error control.

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