A planetary roller screw motion pair clearance design method based on roller deflection

Abstract

The present invention discloses a planetary roller screw motion pair clearance design method based on roller deflection, which belongs to the field of mechanical transmission and precision manufacturing technology. The method comprises the following steps: obtaining the clearance of each motion pair of the planetary roller screw; calculating the deflection angle of the roller around the tangential deflection and the deflection angle of the roller around the radial deflection; solving the contact position of the middle thread tooth with the screw and the nut after the roller deflection; solving the contact radius and contact deflection angle of the remaining thread teeth; solving the load distribution of the roller-screw thread pair and the roller-nut thread pair after the roller deflection; calculating the contact stress distribution of the roller-screw thread tooth and the roller-nut thread tooth after the deflection; judging whether the thread tooth contact stress meets the constraint condition. If not, iteratively optimizing the deflection angle and the clearance of each motion pair of the planetary roller screw by the interior point optimization algorithm until the constraint condition is met. The present invention solves the problem of local overload caused by improper clearance.

Description

Technical Field

[0001] The invention belongs to the technical field of mechanical transmission and precision manufacturing, and in particular relates to a planetary roller screw motion pair clearance design method based on roller deflection. Background Art

[0002] As a high-precision, high-load-bearing transmission device, planetary roller screws are widely used in high-precision equipment such as CNC machine tools, aerospace, and robotics. Their performance directly affects the positioning accuracy, load-bearing capacity, and service life of the equipment. However, in actual applications, the kinematic pair clearance of planetary roller screws can cause roller deflection, which in turn affects the load distribution of the thread teeth, leading to stress concentration and reducing the load-bearing capacity and service life of the screw. In the existing technology, the clearance optimization of planetary roller screws mostly relies on empirical design or simple mechanical analysis. There is a lack of accurate calculation and optimization of the roller deflection angle and stress distribution, making it difficult to achieve precise control of the kinematic pair clearance. Summary of the Invention

[0003] Technical issues to be solved:

[0004] In order to avoid the shortcomings of the prior art, the present invention provides a planetary roller screw kinematic pair clearance design method based on roller deflection. By solving the roller deflection angle under the clearance of each kinematic pair of the planetary roller screw, the influence of roller deflection on the load distribution of the thread is analyzed, and then the stress analysis of the thread is performed. On this basis, the clearance of each kinematic pair of the planetary roller screw is optimized with the constraint that the maximum stress of the thread does not exceed the allowable stress of the material. This application achieves the precise design and optimization of the clearance of the planetary roller screw kinematic pair by quantifying the influence of roller deflection on the load distribution and taking stress constraint as the boundary condition, thereby solving the problem of local overload caused by improper clearance.

[0005] The technical solution of the present invention is: a planetary roller screw motion pair clearance design method based on roller deflection, the specific steps are as follows:

[0006] Obtain the clearances of each kinematic pair of the planetary roller screw, including roller-screw clearance, roller-nut side clearance, roller tooth-inner gear ring clearance, and roller-cage clearance;

[0007] Based on the components of the clearance of each kinematic pair in the motion direction, the deflection angle of the roller around the tangential deflection and the deflection angle of the roller around the radial deflection are calculated respectively;

[0008] According to the deflection angle of the roller around the tangential deflection and the deflection angle of the roller around the radial deflection, the contact position between the middle thread and the screw and nut after the roller deflects is solved;

[0009] Based on the contact position of the middle thread and the screw and nut after the roller is deflected, as well as the linear geometric relationship between the middle thread and other threads, the contact radius and contact angle of the remaining threads and the screw, as well as the contact radius and contact angle of the remaining threads and the nut are calculated;

[0010] Based on the obtained contact radius and contact deflection angle, combined with the planetary roller screw thread load distribution model, the load distribution of the roller-screw thread pair and the roller-nut thread pair after roller deflection is solved;

[0011] Substituting the load distribution into the Hertz contact formula, the contact stress distribution of the roller-screw thread and the roller-nut thread after deflection is calculated;

[0012] With the constraint that the contact stress between the roller-screw thread and the roller-nut thread after deflection does not exceed the allowable stress of the material, the deflection angle of the roller around the tangential deflection, the deflection angle of the roller around the radial deflection, the roller-screw clearance, the roller-nut side clearance, the roller tooth-inner gear ring clearance, and the roller-cage clearance are iteratively optimized using the interior point optimization algorithm until the constraints are met.

[0013] A further technical solution of the present invention is that the calculation formulas for the deflection angle of the roller about the tangential deflection and the deflection angle of the roller about the radial deflection are as follows:

[0014]

[0015]

[0016]

[0017]

[0018] Where, is the deflection angle of the roller around the tangential direction, is the deflection angle of the roller around the radial direction, and are the tangential clearance and radial clearance of each kinematic pair respectively; 、 、 、 are the tangential deflection angles between the roller and the screw, nut, internal gear ring, and cage, respectively; 、 、 、 are the radial deflection angles between the roller and the screw, nut, inner gear ring, and cage, respectively; is the roller-screw or roller-nut axial clearance; The backlash between roller gear and internal gear ring or roller and cage; is the roller-screw or roller-nut radial clearance; is the top clearance between roller gear and inner gear ring; is the roller-cage side clearance, L is the roller length; S, N, r and C in the subscripts represent the screw, nut, internal gear ring and cage respectively.

[0019] A further technical solution of the present invention is that the contact position of the middle thread teeth with the lead screw and the nut after the roller is deflected is expressed as follows:

[0020] The contact position between the middle thread and the screw after the roller is deflected:

[0021]

[0022] The contact position between the middle thread and the nut after the roller is deflected:

[0023]

[0024] Where, Indicates the normal vector of the screw thread where the roller middle thread contacts the screw thread. The normal vector of the roller thread tooth where the middle thread tooth of the roller contacts the screw thread tooth; The normal vector of the nut thread tooth where the roller middle thread tooth contacts the nut thread tooth is represented by, The normal vector of the roller thread tooth where the roller middle thread tooth contacts the nut thread tooth; is the transformation matrix; The spiral surface equation representing the contact between the roller middle thread and the screw thread is: The spiral surface equation representing the contact between the roller middle thread and the screw thread is: The equation of the helical surface where the roller middle thread contacts the nut thread is: The equation of the helical surface representing the contact between the roller middle thread and the nut thread.

[0025] A further technical solution of the present invention is that the contact position is transformed by a coordinate matrix correction,

[0026]

[0027]

[0028]

[0029] In the formula, the subscript Indicates the direction of roller deflection, subscript Indicates the roller deflection around the tangential direction, the subscript Indicates the roller deflection around the radial direction; The transformation matrix representing the roller deflection around the tangential direction, Transformation matrix representing radial skew.

[0030] A further technical solution of the present invention is that the contact radius and contact angle of the remaining threads with the screw, and the contact radius and contact angle of the remaining threads with the nut are calculated as follows:

[0031]

[0032]

[0033]

[0034]

[0035] Where, is the contact radius of the roller about the tangential deflection, is the contact deflection angle of the roller about the tangential deflection, The contact radius of the roller middle thread tooth and the screw or the roller middle thread tooth and the nut when the roller is deflected about the tangential direction, The contact angle between the roller middle thread and the screw or between the roller middle thread and the nut when the roller is deflected about the tangential direction; is the contact radius of the roller around the radial deflection, is the contact deflection angle of the roller around the radial direction, The contact radius of the roller middle thread tooth and the screw or the roller middle thread tooth and the nut when the roller deflects radially. The contact angle between the roller middle thread and the screw or between the roller middle thread and the nut when the roller deflects radially; n is the number of roller thread teeth; i is the thread number; m Indicates the middle thread tooth of the roller; SR, RS, NR, and RN in the subscripts respectively represent the roller-screw contact on the screw helical surface, the roller-screw contact on the roller helical surface, the roller-nut contact on the nut helical surface, and the roller-nut contact on the roller helical surface.

[0036] A further technical solution of the present invention is that the load distribution expression of the roller-screw thread pair after the roller deflection is as follows:

[0037]

[0038] The load distribution expression of the roller-nut thread pair is as follows:

[0039]

[0040] Where, is the stiffness, and the subscripts S, R, and N represent the screw, roller, and nut respectively. B Represents the shaft segment, T Indicates thread teeth, C Indicates contact, i and j Indicates the thread number. is the roller-screw thread contact force, is the roller-nut thread contact force.

[0041] A further technical solution of the present invention is: the contact stress calculation formula of the roller-screw thread and the roller-nut thread after deflection is as follows:

[0042]

[0043] Where, is the contact stress of roller-screw thread or roller-nut thread, is the contact force between the roller and the screw thread or the roller and the nut thread, a is the semi-major axis of the contact ellipse, b is the semi-minor axis of the contact ellipse.

[0044] A further technical solution of the present invention is: the objective function of the interior point optimization algorithm is:

[0045]

[0046] The constraints are: σmax ≤[ σ ],in,[ σ ] is the allowable stress of the material.

[0047] A further technical solution of the present invention is to substitute the optimized gap parameters into dynamics simulation software, compare the theoretical load distribution with the simulation results, and verify the maximum stress error.

[0048] A planetary roller screw motion pair clearance design system based on roller deflection, comprising:

[0049] A data acquisition module is used to obtain the clearance parameters of each moving pair of the planetary roller screw;

[0050] a deflection angle calculation module connected to the data acquisition module, and calculating the deflection angle of the roller around the tangential deflection and the deflection angle around the radial deflection based on the components of the clearance of each kinematic pair in the motion direction;

[0051] a contact position determination module connected to the deflection angle calculation module, which calculates the contact position between the middle thread of the roller and the lead screw and nut based on the deflection angle of the roller around the tangential deflection and the deflection angle around the radial deflection, and corrects the geometric relationship after the roller deflection through a coordinate transformation matrix;

[0052] A load distribution analysis module, connected to the contact position determination module, calculates the contact radius and contact deflection angle of the remaining thread teeth based on the contact position and the linear recursive relationship, and establishes a load distribution model of the thread pair after roller deflection;

[0053] A stress analysis module, connected to the load distribution analysis module, calculates the contact stress distribution of the thread teeth using the Hertz contact formula and extracts the maximum contact stress value;

[0054] An optimization control module is connected to the stress analysis module, and uses an interior point optimization algorithm to iteratively adjust the clearances of each kinematic pair under the constraint that the maximum contact stress does not exceed the allowable stress of the material, and outputs the optimized clearance parameters;

[0055] The verification module is connected to the optimization control module, imports the optimized gap parameters into the dynamic simulation software, generates the thread load distribution and stress simulation results, compares the theoretical value with the simulation value, and verifies whether the error meets the requirements.

[0056] Beneficial effects

[0057] The beneficial effect of the present invention is that it optimizes the clearance parameters of each kinematic pair by accurately calculating the roller deflection angle and the contact stress distribution of the thread teeth, effectively avoiding local stress concentration. The specific advantages are analyzed as follows:

[0058] 1. This invention optimizes the clearance design of planetary roller screw kinematic pairs by precisely calculating the roller deflection angle under the clearance of the kinematic pair and combining it with stress distribution analysis of the thread. This method establishes a quantitative relationship between the roller deflection angle and the stress distribution of the thread based on mechanical analysis. Compared to traditional empirical design, this invention proposes a new approach to clearance design for planetary roller screws based on strength criteria, providing a theoretical basis and optimization direction for the strength and reliability design of planetary roller screws under high-load conditions.

[0059] 2. This invention uses an optimization algorithm to adjust the kinematic pair clearance parameters, ensuring that the maximum thread stress does not exceed the material's allowable stress, to achieve a more uniform stress distribution within the thread. This method reduces peak stress by adjusting the clearance parameters and mitigates the adverse effects of roller deflection on thread load distribution, thus avoiding the risk of fatigue failure due to stress concentration and extending the life of the screw. This technical solution provides a path for improving the long-term stable operation of planetary roller screws under high-load conditions.

[0060] 3. Based on the coupled analysis of roller deflection angle and stress distribution, this paper proposes a method for optimizing the clearance design of planetary roller screw kinematic pairs. By establishing a correlation between the roller kinematic model and the contact stress model, this method provides a theoretical basis for rationally matching the clearance between the kinematic pairs. Research results show that the optimized clearance parameters can improve the contact between the roller and the thread. This technical solution provides a new approach for vibration and noise reduction in planetary roller screws. BRIEF DESCRIPTION OF THE DRAWINGS

[0061] Figure 1 Flowchart of a planetary roller screw kinematic pair clearance design method based on roller deflection according to an embodiment of the present invention;

[0062] Figure 2 A comparison diagram of the load distribution of the thread pair after radial deflection of the roller in the embodiment of the present invention and the prior art;

[0063] Figure 3 Schematic diagram of the contact radius and contact angle between the roller and the screw, and the contact radius and contact angle between the roller and the nut after the roller is tangentially deflected in an embodiment of the present invention;

[0064] Figure 4 Schematic diagram of the contact radius and contact angle between the roller and the screw, and the contact radius and contact angle between the roller and the nut after the roller is radially deflected in an embodiment of the present invention;

[0065] Figure 5 Schematic diagram of load distribution of the roller-screw thread pair and the roller-nut thread pair after roller deflection in an embodiment of the present invention. DETAILED DESCRIPTION

[0066] The embodiments described below with reference to the accompanying drawings are exemplary and are intended to explain the present invention, but should not be construed as limiting the present invention.

[0067] In the existing technology, research on planetary roller screw clearance optimization mainly focuses on the following two methods:

[0068] Empirical design methods rely on engineering experience or test data to set clearance parameters (e.g., optimizing gear pair clearance through contact time synchronization in patent CN202410364668.8). These methods lack theoretical model support, are difficult to adapt to complex operating conditions such as high loads and high speeds, and are prone to causing localized stress overshoot.

[0069] Simplified mechanical analysis methods: Some studies optimize clearance using static load distribution models or single mechanical parameters (such as contact stiffness) (e.g., the iterative calculation of load distribution based on dynamic contact force in patent CN202210839841.6). However, these methods do not comprehensively consider the impact of roller deflection on the geometric contact relationship, leading to the following problems:

[0070] Insufficient quantification of deflection angles: The tangential and radial deflections of rollers due to clearance are not accurately modeled, making it impossible to accurately predict the thread contact position after deflection (for example, the existing technology only approximates the contact radius through linear recursion, resulting in significant error accumulation).

[0071] Lack of stress constraints: Failure to use the material allowable stress as an optimization constraint leads to a high risk of local stress concentration (e.g., the maximum stress in the conventional design in the embodiment exceeds the limit by 1 MPa, causing fatigue failure);

[0072] Furthermore, existing patents (such as CN202410364668.8) propose a synchronized design method for gear pair clearances but fail to couple this analysis with the stress distribution of threaded pairs. While CN202210839841.6 addresses dynamic load calculations, it fails to integrate clearance optimization and skew angle correction. This "isolated design" leads to mismatched clearance parameters across kinematic pairs and fails to systematically address the coupled skew-stress-wear issue.

[0073] Based on the above problems, the present invention provides a planetary roller screw motion pair clearance design method based on roller deflection, the steps are as follows:

[0074] Obtain the clearances of each kinematic pair of the planetary roller screw, including roller-screw clearance, roller-nut side clearance, roller tooth-inner gear ring clearance, and roller-cage clearance;

[0075] Based on the components of the clearance of each kinematic pair in the motion direction, the deflection angle of the roller around the tangential deflection and the deflection angle of the roller around the radial deflection are calculated respectively;

[0076] According to the deflection angle of the roller around the tangential deflection and the deflection angle of the roller around the radial deflection, the contact position between the middle thread and the screw and nut after the roller deflects is solved;

[0077] Based on the contact position of the middle thread and the screw and nut after the roller is deflected, as well as the linear geometric relationship between the middle thread and other threads, the contact radius and contact angle of the remaining threads and the screw, as well as the contact radius and contact angle of the remaining threads and the nut are calculated;

[0078] Based on the obtained contact radius and contact deflection angle, combined with the planetary roller screw thread load distribution model, the load distribution of the roller-screw thread pair and the roller-nut thread pair after roller deflection is solved;

[0079] Substituting the load distribution into the Hertz contact formula, the contact stress distribution of the roller-screw thread and the roller-nut thread after deflection is calculated;

[0080] With the constraint that the contact stress between the roller-screw thread and the roller-nut thread after deflection does not exceed the allowable stress of the material, the deflection angle of the roller around the tangential deflection, the deflection angle of the roller around the radial deflection, the roller-screw clearance, the roller-nut side clearance, the roller tooth-inner gear ring clearance, and the roller-cage clearance are iteratively optimized using the interior point optimization algorithm until the constraints are met.

[0081] The present invention provides a planetary roller screw kinematic pair clearance design system based on roller deflection, comprising:

[0082] A data acquisition module is used to obtain the clearance parameters of each moving pair of the planetary roller screw;

[0083] a deflection angle calculation module connected to the data acquisition module, and calculating the deflection angle of the roller around the tangential deflection and the deflection angle around the radial deflection based on the components of the clearance of each kinematic pair in the motion direction;

[0084] a contact position determination module connected to the deflection angle calculation module, which calculates the contact position between the middle thread of the roller and the lead screw and nut based on the deflection angle of the roller around the tangential deflection and the deflection angle around the radial deflection, and corrects the geometric relationship after the roller deflection through a coordinate transformation matrix;

[0085] A load distribution analysis module, connected to the contact position determination module, calculates the contact radius and contact deflection angle of the remaining thread teeth based on the contact position and the linear recursive relationship, and establishes a load distribution model of the thread pair after roller deflection;

[0086] A stress analysis module, connected to the load distribution analysis module, calculates the contact stress distribution of the thread teeth using the Hertz contact formula and extracts the maximum contact stress value;

[0087] An optimization control module is connected to the stress analysis module, and uses an interior point optimization algorithm to iteratively adjust the clearances of each kinematic pair under the constraint that the maximum contact stress does not exceed the allowable stress of the material, and outputs the optimized clearance parameters;

[0088] The verification module is connected to the optimization control module, imports the optimized gap parameters into the dynamic simulation software, generates the thread load distribution and stress simulation results, compares the theoretical value with the simulation value, and verifies whether the error meets the requirements.

[0089] The present invention combines deflection angle calculation with stress constraint optimization to break through the limitations of traditional empirical design; through a systematic design process and simulation verification, the efficiency and reliability of the technical solution are ensured.

[0090] The above technical solution is further described below with reference to the accompanying drawings and examples:

[0091] In one embodiment, referring to Figure 1As shown, the specific steps of the planetary roller screw motion pair clearance design method based on roller deflection in this embodiment are as follows:

[0092] Step 1: Obtain the clearance of each moving pair of the planetary roller screw, including the thread pair clearance, gear pair clearance, and cylindrical pair clearance. The thread pair clearance is the roller-screw clearance. and roller-nut side clearance , the gear pair clearance is the roller gear-inner gear clearance , the cylindrical pair clearance is the roller-cage clearance ;

[0093] Step 2: Calculate the component of the clearance in the direction of motion based on the clearance of each kinematic pair. Based on the structural principle analysis of the planetary roller screw, it is concluded that the tangential deflection and radial deflection of the roller are affected by the component of the kinematic pair in the direction of motion respectively.

[0094] Step 3: Based on the components of the clearance of each kinematic pair in the motion direction, calculate the deflection angle of the roller around the tangential deflection and the deflection angle of the roller around the radial direction ;

[0095] Step 4: Deflect the Roller Around the Tangential Deflection Angle and the deflection angle of the roller around the radial direction Substitute them into the roller-screw and roller-nut meshing equations respectively to solve the contact position between the middle thread and the screw and nut after the roller is deflected radially or tangentially;

[0096] Step 5: Based on the contact position of the middle thread with the screw and nut after the roller is deflected, and the linear geometric relationship between the middle thread and the other threads, calculate the contact radius and contact angle of the remaining threads with the screw, and calculate the contact radius and contact angle of the remaining threads with the nut;

[0097] Step 6: Based on the obtained contact radius and contact deflection angle, combined with the planetary roller screw thread load distribution model, solve the load distribution of the roller-screw thread pair and the roller-nut thread pair after roller deflection;

[0098] Step 7: Substitute the obtained load distribution of the roller-screw and roller-nut thread pairs into the Hertz contact formula to solve the contact stress distribution of the roller-screw thread and roller-nut thread after deflection;

[0099] Step 8: Take the maximum contact stress of the thread teeth in the contact stress distribution of the roller-screw thread teeth and the roller-nut thread teeth after deflection, compare it with the allowable stress of the material, and use the constraint condition that the maximum stress of the roller-screw thread teeth and the roller-nut thread teeth does not exceed the allowable stress of the material. Optimize the deflection angle and the clearance of each kinematic pair of the planetary roller screw through the interior point optimization algorithm until the constraint condition is met.

[0100] In one embodiment, based on the structural principle and kinematic principle of the planetary roller screw, when the roller deflects in the tangential direction, the roller is affected by the axial clearance between the roller and the screw, the axial clearance between the roller and the nut, the side clearance between the roller and the inner gear ring, and the side clearance between the roller and the cage. When the roller deflects in the radial direction, the roller is affected by the radial clearance between the roller and the screw, the radial clearance between the roller and the nut, the top clearance between the roller and the inner gear ring, and the side clearance between the roller and the cage. Therefore, the tangential and radial deflection angles of the roller are and The calculation formulas are shown in equations (1) to (4).

[0101] (1)

[0102] (2)

[0103] (3)

[0104] (4)

[0105] Where, is the deflection angle of the roller around the tangential direction, is the deflection angle of the roller around the radial direction, and are the tangential clearance and radial clearance of each kinematic pair respectively; 、 、 、 are the tangential deflection angles between the roller and the screw, nut, internal gear ring, and cage, respectively; 、 、 、 are the radial deflection angles between the roller and the screw, nut, inner gear ring, and cage, respectively; is the roller-screw or roller-nut axial clearance; The backlash between roller gear and internal gear ring or roller and cage; is the roller-screw or roller-nut radial clearance; is the top clearance between roller gear and inner ring gear; is the roller-cage side clearance, L is the roller length; S, N, r and C in the subscripts represent the screw, nut, internal gear ring and cage respectively.

[0106] In one embodiment, the contact position calculation formulas of the middle thread teeth, the lead screw and the nut after the roller is deflected are shown in formulas (5) to (10).

[0107] (5)

[0108] (6)

[0109] (7)

[0110] (8)

[0111] In the formula, the superscript m is the middle thread number; is the normal vector of the contact point between the screw or nut and the roller thread, is the normal vector of the contact point between the roller middle thread and the screw or nut; Indicates the direction of roller deflection, subscript Indicates the roller deflection around the tangential direction, the subscript Indicates the roller deflection around the radial direction; is the transformation matrix, The transformation matrix representing the roller deflection around the tangential direction, The transformation matrix representing the roller's radial deflection; and Represent the screw and nut respectively.

[0112] (9)

[0113] (10)

[0114] Where, is the cross-sectional abscissa of the screw or nut helical surface, is the horizontal coordinate of the cross section of the spiral surface of the roller middle thread tooth, is the cross-sectional ordinate of the screw or nut helical surface, is the ordinate of the cross section of the helical surface of the middle thread tooth of the roller.

[0115] The combined equations (5) to (8) and (9) are used to determine the contact position between the middle thread and the screw after the roller is deflected, as shown in equation (11). The combined equations (5) to (8) and (10) are used to determine the contact position between the middle thread and the nut after the roller is deflected, as shown in equation (12).

[0116] (11)

[0117] (12)

[0118] Where, Indicates the normal vector of the screw thread where the roller middle thread contacts the screw thread. The normal vector of the roller thread tooth where the middle thread tooth of the roller contacts the screw thread tooth; Indicates the normal vector of the nut thread tooth where the roller middle thread tooth contacts the nut thread tooth, The normal vector of the roller thread tooth where the roller middle thread tooth contacts the nut thread tooth; is the transformation matrix; The spiral surface equation representing the contact between the roller middle thread and the screw thread is: The spiral surface equation representing the contact between the roller thread and the screw thread is: The equation of the helical surface where the roller middle thread contacts the nut thread is: The equation of the helical surface representing the contact between the roller middle thread and the nut thread.

[0119] In one embodiment, the contact radius and contact angle between the other threads of the roller and the screw and nut are solved as shown in equations (13) to (16).

[0120] (13)

[0121] (14)

[0122] (15)

[0123] (16)

[0124] Where, is the contact radius of the roller about the tangential deflection, is the contact deflection angle of the roller about the tangential deflection, The contact radius of the roller middle thread tooth and the screw or the roller middle thread tooth and the nut when the roller is deflected about the tangential direction, The contact angle between the roller middle thread and the screw or between the roller middle thread and the nut when the roller is deflected about the tangential direction; is the contact radius of the roller around the radial deflection, is the contact deflection angle of the roller around the radial direction, The contact radius of the roller middle thread tooth and the screw or the roller middle thread tooth and the nut when the roller deflects radially. The contact angle between the roller middle thread and the screw or between the roller middle thread and the nut when the roller deflects radially; n is the number of roller thread teeth; i is the thread number; m Indicates the middle thread tooth of the roller; SR, RS, NR, and RN in the subscripts respectively represent the roller-screw contact on the screw helical surface, the roller-screw contact on the roller helical surface, the roller-nut contact on the nut helical surface, and the roller-nut contact on the roller helical surface.

[0125] Substituting the thread contact positions calculated by equations (13), (14) and (15), (16) into the planetary roller screw thread load distribution model, as shown in equations (17) and (18), the load distribution of the roller-screw thread pair and the roller-nut thread pair after the roller is deflected in the tangential and radial directions is obtained.

[0126] (17)

[0127] (18)

[0128] Where, is the stiffness, and the subscripts S, R, and N represent the screw, roller, and nut respectively. B Represents the shaft segment, T Indicates thread teeth, C Indicates contact, i and j Indicates the thread number. is the roller-screw thread contact force, is the roller-nut thread contact force.

[0129] Then substitute the load of each thread into the stress calculation formula, as shown in formula (19), to obtain the contact stress of each thread.

[0130] (19)

[0131] Where, is the contact stress of roller-screw thread or roller-nut thread, is the contact force between the roller and the screw thread or the roller and the nut thread, a and b are the semimajor and semiminor axes of the contact ellipse.

[0132] In one embodiment, the maximum contact stress of the thread The allowable stress of the material is not exceeded as a constraint. The roller deflection angle is optimized by the interior point method, and then the clearance of each kinematic pair of the planetary roller screw is solved by equation (20).

[0133] (20)

[0134] The following is a parameter table of this embodiment. The parameters of the planetary roller screw are shown in Table 1.

[0135] Table 1 Planetary roller screw parameters

[0136]

[0137] In order to verify the correctness of the load distribution model after roller deflection established in this paper, the load distribution when the deflection angle is 0 is solved according to the planetary roller screw specifications shown in Table 1. When the nut load is set to 10000N, the number of rollers is 10, the number of roller threads is 15, and the radial deflection angle is 0, the load distribution of the roller-screw thread pair and the roller-nut thread pair is solved and compared with the results of the literature [Northwestern Polytechnical University. A research method for the load characteristics of planetary roller screws based on roller deflection: 202410009466.1]. Figure 2 As shown in (a).

[0138] according to Figure 2 As shown in (a), the load distribution of the thread pair calculated in this paper has the same trend as that in the existing literature, and the results are very close. The maximum relative error of the maximum contact force of the thread teeth is only 3.2%, and the maximum relative error of the minimum load of the thread teeth is only 5.8%.

[0139] Solve for the radial deflection as The load distribution of roller-screw thread pair and roller-nut thread pair is compared with the results of existing literature. Figure 2 As shown in (b).

[0140] according to Figure 2 As shown in Figure (b), when considering roller deflection, the load distribution results of our model follow the same trend as those in existing literature, with similar maximum thread contact forces. However, the load distribution trend in our model is more linear. This is due to the use of a linear recursive relationship to calculate the contact radius and contact angle for each thread. This difference does not affect the calculated maximum thread load. Therefore, the accuracy of our model is verified.

[0141] Alternatively, the planetary roller screw parameters according to Table 1 are substituted into the dynamics simulation software, and the theoretical load distribution is compared with the simulation results to verify the maximum stress error.

[0142] Substituting the parameters in Table 1 into the planetary roller screw kinematic pair clearance calculation formulas shown in Equations (20) to (26), the clearances of each kinematic pair are obtained as shown in Table 2.

[0143] Roller-screw axial clearance Axial clearance between the upper surface of the roller and the lower surface of the screw Axial clearance between roller bottom surface and screw top surface Since the roller tooth side angle is 45°, the roller-screw axial clearance and roller-screw radial clearance Equal. Roller-screw axial clearance and roller-screw radial clearance It can be calculated by equations (20) and (21).

[0144] (20)

[0145] (twenty one)

[0146] Where, is the roller-screw axial clearance; is the roller-screw radial clearance; is the axial clearance between the upper surface of the roller and the lower surface of the screw; is the axial clearance between the lower surface of the roller and the upper surface of the screw; is the pitch of the screw and roller; Half tooth thickness; is the roller profile radius; is the tooth flank angle; The contact radius of the screw helical surface on the roller-screw contact side; is the contact radius of the roller helical surface on the roller-screw contact side, is the contact deflection angle of the screw helical surface on the roller-screw contact side, is the contact deflection angle of the roller helical surface of the roller-screw contact; is the lead; the subscripts S and R represent the screw and roller.

[0147] Roller-nut axial clearance Axial clearance between the upper surface of the roller and the lower surface of the nut Axial clearance between roller bottom surface and nut top surface Since the roller tooth side angle is 45°, the roller-nut axial clearance and roller-nut radial clearance Equal. Roller-nut axial clearance and roller-nut radial clearance It can be calculated by equations (22) and (23).

[0148] (twenty two)

[0149] (twenty three)

[0150] Where, is the roller-nut axial clearance; is the roller-nut radial clearance; is the axial clearance between the upper surface of the roller and the lower surface of the nut; is the axial clearance between the lower surface of the roller and the upper surface of the nut; is the thread pitch of the nut and roller; Half tooth thickness; is the tooth side angle; the subscripts N and R represent the nut and roller.

[0151] The calculation formulas for the circumferential side clearance and half of the top clearance on one side of the roller gear-internal gear ring are shown in Equations (24) and (25).

[0152] (twenty four)

[0153] (25)

[0154] Where, It is the circumferential backlash between the roller gear and the inner ring gear. It is half of the top clearance between roller gear and inner ring gear; is the module of the roller teeth and the internal gear ring; is the pressure angle between the roller teeth and the internal gear ring.

[0155] The calculation formula for the roller-cage half side clearance is shown in formula (26).

[0156] (26)

[0157] Where, It is half the roller-cage side clearance; is the radius of the cage hole; is the radius of the roller shaft.

[0158] Table 2 Clearances of each kinematic pair of planetary roller screws

[0159]

[0160] The clearances in Table 2 are all clearances on the contact side. Multiply the clearances of each kinematic pair in Table 2 by 2 to obtain the roller-screw axial and radial clearances, roller-nut axial and radial clearances, roller tooth-inner gear ring circumferential clearance and top clearance, and roller-cage side clearance. Then substitute into equations (1) and (2) to obtain the roller tangential deflection angle: , substitute into equations (3) and (4) to obtain the roller radial deflection angle .

[0161] Deflect the roller around the tangential and radial angles and Substituting them into equations (11) and (12), the contact radius and contact angle between the middle thread of the roller and the thread of the screw and nut are obtained as shown in Table 3.

[0162] Table 3 Contact radius and contact angle between the middle thread and the screw and nut after the roller is deflected along the tangential direction

[0163]

[0164] Table 4 Contact radius and contact angle between the middle thread and the screw and nut after the roller deflects radially

[0165]

[0166] Substitute the contact radius and contact angle of the roller middle thread teeth with the screw and nut in Table 3 and Table 4 into equations (13) to (14) and (15) to (16), and the contact radius and contact angle of the roller with the screw thread teeth and nut thread teeth after tangential and radial deflection are obtained as follows: Figure 3 and Figure 4 shown.

[0167] Substituting the calculated contact radius and contact deflection angle of each thread into the planetary roller screw thread load distribution model, the load distribution of the roller-screw thread and the roller-nut thread is obtained as follows: Figure 5 shown.

[0168] according to Figure 5 It can be seen that the contact force of the roller-screw side thread teeth is greater than the contact force of the roller-nut side thread teeth. Therefore, the maximum stress of the roller-screw side thread teeth is solved. The maximum stress of the roller-screw side thread teeth is used as a constraint to solve the maximum allowable value of the deflection angle and the maximum allowable value of the clearance.

[0169] Substituting the maximum contact forces of the roller-screw thread and the roller-nut thread into equation (19), the maximum contact stress of the roller-screw thread is obtained, as shown in Table 5.

[0170] Table 5 Maximum contact force and contact stress between roller and screw thread after roller deflection

[0171]

[0172] According to Table 5, when the radial deflection When the roller-screw thread maximum contact stress is 2101MPa, which exceeds the allowable stress of 2100MPa of GCr15, a common material for planetary roller screws. Therefore, it is necessary to optimize the roller tangential and radial deflection angles and iteratively obtain the minimum roller tangential and radial deflection angles. When the roller-screw thread maximum contact stress still does not exceed the allowable stress of GCr15 2100MPa. Therefore, the roller deflection angle can be further increased.

[0173] Finally, with the allowable stress as the constraint condition, the roller tangential deflection angle, radial deflection angle and clearance of each kinematic pair are optimized. The roller deflection angle is optimized and solved, and then the clearance caused by the clearance of each kinematic pair is made close to the maximum deflection angle. That is, the planetary roller screw deflection angle is solved by equation (27), and then the clearance of each kinematic pair is calculated by equations (1) to (4), as shown in Table 6.

[0174] (27)

[0175] Table 6 Roller deflection angle and maximum clearance of each kinematic pair

[0176]

[0177] Although the embodiments of the present invention have been shown and described above, it will be understood that the above embodiments are illustrative and are not to be construed as limitations on the present invention. A person skilled in the art may change, modify, replace and modify the above embodiments within the scope of the present invention without departing from the principles and purpose of the present invention.

Claims

1. A planetary roller screw motion pair clearance design method based on roller deflection, characterized in that The specific steps are as follows: Obtain the clearances of each kinematic pair of the planetary roller screw, including roller-screw clearance, roller-nut side clearance, roller tooth-inner gear ring clearance, and roller-cage clearance; Based on the components of the clearance of each kinematic pair in the motion direction, the deflection angle of the roller around the tangential deflection and the deflection angle of the roller around the radial deflection are calculated respectively; According to the deflection angle of the roller around the tangential deflection and the deflection angle of the roller around the radial deflection, the contact position between the middle thread and the screw and nut after the roller deflects is solved; Based on the contact position of the middle thread and the screw and nut after the roller is deflected, as well as the linear geometric relationship between the middle thread and other threads, the contact radius and contact angle of the remaining threads and the screw, as well as the contact radius and contact angle of the remaining threads and the nut are calculated; Based on the obtained contact radius and contact deflection angle, combined with the planetary roller screw thread load distribution model, the load distribution of the roller-screw thread pair and the roller-nut thread pair after roller deflection is solved; Substituting the load distribution into the Hertz contact formula, the contact stress distribution of the roller-screw thread and the roller-nut thread after deflection is calculated; With the constraint that the contact stress between the roller-screw thread and the roller-nut thread after deflection does not exceed the allowable stress of the material, the deflection angle of the roller around the tangential deflection, the deflection angle of the roller around the radial deflection, the roller-screw clearance, the roller-nut side clearance, the roller tooth-inner gear ring clearance, and the roller-cage clearance are iteratively optimized using the interior point optimization algorithm until the constraints are met.

2. The planetary roller screw kinematic pair clearance design method based on roller deflection according to claim 1, characterized in that: The calculation formulas for the deflection angle of the roller about the tangential deflection and the deflection angle of the roller about the radial deflection are as follows: Where, is the deflection angle of the roller around the tangential direction, is the deflection angle of the roller around the radial direction, and are the tangential clearance and radial clearance of each kinematic pair respectively; 、 、 、 are the tangential deflection angles between the roller and the screw, nut, internal gear ring, and cage, respectively; 、 、 、 are the radial deflection angles between the roller and the screw, nut, inner gear ring, and cage, respectively; is the roller-screw or roller-nut axial clearance; The backlash between roller gear and internal gear ring or roller and cage; is the roller-screw or roller-nut radial clearance; is the top clearance between roller gear and inner ring gear; is the roller-cage side clearance, L is the roller length; S, N, r and C in the subscripts represent the screw, nut, internal gear ring and cage respectively.

3. The planetary roller screw kinematic pair clearance design method based on roller deflection according to claim 2, characterized in that: The contact position expression of the middle thread teeth, the lead screw and the nut after the roller is deflected is as follows: The contact position between the middle thread and the screw after the roller is deflected: The contact position between the middle thread and the nut after the roller is deflected: Where, Indicates the normal vector of the screw thread where the roller middle thread contacts the screw thread. The normal vector of the roller thread tooth where the middle thread tooth of the roller contacts the screw thread tooth; The normal vector of the nut thread tooth where the roller middle thread tooth contacts the nut thread tooth is represented by, The normal vector of the roller thread tooth where the roller middle thread tooth contacts the nut thread tooth; is the transformation matrix; The spiral surface equation representing the contact between the roller middle thread and the screw thread is: The spiral surface equation representing the contact between the roller thread and the screw thread is: The equation of the helical surface where the roller middle thread contacts the nut thread is: The equation of the helical surface representing the contact between the roller middle thread and the nut thread.

4. The method for designing clearance of a planetary roller screw kinematic pair based on roller deflection according to claim 3, characterized in that: The contact position is transformed by the coordinate matrix correction, In the formula, the subscript Indicates the direction of roller deflection, subscript Indicates the roller deflection around the tangential direction, the subscript Indicates the roller deflection around the radial direction; The transformation matrix representing the roller deflection around the tangential direction, Transformation matrix representing radial skew.

5. The planetary roller screw kinematic pair clearance design method based on roller deflection according to claim 3, characterized in that: The contact radius and contact angle between the remaining thread teeth and the screw, and the contact radius and contact angle between the remaining thread teeth and the nut are calculated as follows: Where, is the contact radius of the roller about the tangential deflection, is the contact deflection angle of the roller about the tangential deflection, The contact radius of the roller middle thread tooth and the screw or the roller middle thread tooth and the nut when the roller is deflected about the tangential direction, The contact angle between the roller middle thread and the screw or between the roller middle thread and the nut when the roller is deflected about the tangential direction; is the contact radius of the roller around the radial deflection, is the contact deflection angle of the roller around the radial direction, The contact radius of the roller middle thread tooth and the screw or the roller middle thread tooth and the nut when the roller deflects radially. The contact angle between the roller middle thread and the screw or between the roller middle thread and the nut when the roller deflects radially; n is the number of roller thread teeth; i is the thread number; m Indicates the middle thread tooth of the roller; SR, RS, NR, and RN in the subscripts respectively represent the roller-screw contact on the screw helical surface, the roller-screw contact on the roller helical surface, the roller-nut contact on the nut helical surface, and the roller-nut contact on the roller helical surface.

6. The planetary roller screw kinematic pair clearance design method based on roller deflection according to claim 5, characterized in that: The load distribution expression of the roller-screw thread pair after the roller deflection is as follows: The load distribution expression of the roller-nut thread pair is as follows: Where, is the stiffness, and the subscripts S, R, and N represent the screw, roller, and nut respectively. B Represents the shaft segment, T Indicates thread teeth, C Indicates contact, i and j Indicates the thread number. is the roller-screw thread contact force, is the roller-nut thread contact force.

7. The method for designing clearance of a planetary roller screw kinematic pair based on roller deflection according to claim 6, characterized in that: The calculation formula for the contact stress between the roller-screw thread and the roller-nut thread after deflection is as follows: Where, is the contact stress of roller-screw thread or roller-nut thread, is the contact force between the roller and the screw thread or the roller and the nut thread, a is the semi-major axis of the contact ellipse, b is the semi-minor axis of the contact ellipse.

8. The planetary roller screw kinematic pair clearance design method based on roller deflection according to claim 7, characterized in that: The objective function of the interior point optimization algorithm is: The constraints are: σmax ≤[ σ ],in,[ σ ] is the allowable stress of the material.

9. The planetary roller screw kinematic pair clearance design method based on roller deflection according to claim 8, characterized in that: Substitute the optimized gap parameters into the dynamic simulation software, compare the theoretical load distribution with the simulation results, and verify the maximum stress error.

10. A planetary roller screw motion pair clearance design system based on roller deflection, used to implement the planetary roller screw motion pair clearance design method based on roller deflection according to any one of claims 1 to 9, characterized in that include: A data acquisition module is used to obtain the clearance parameters of each moving pair of the planetary roller screw; a deflection angle calculation module connected to the data acquisition module, and calculating the deflection angle of the roller around the tangential deflection and the deflection angle around the radial deflection based on the components of the clearance of each kinematic pair in the motion direction; a contact position determination module connected to the deflection angle calculation module, which calculates the contact position between the middle thread of the roller and the lead screw and nut based on the deflection angle of the roller around the tangential deflection and the deflection angle around the radial deflection, and corrects the geometric relationship after the roller deflection through a coordinate transformation matrix; A load distribution analysis module, connected to the contact position determination module, calculates the contact radius and contact deflection angle of the remaining thread teeth based on the contact position and the linear recursive relationship, and establishes a load distribution model of the thread pair after roller deflection; A stress analysis module, connected to the load distribution analysis module, calculates the contact stress distribution of the thread teeth using the Hertz contact formula and extracts the maximum contact stress value; An optimization control module is connected to the stress analysis module, and uses an interior point optimization algorithm to iteratively adjust the clearances of each kinematic pair under the constraint that the maximum contact stress does not exceed the allowable stress of the material, and outputs the optimized clearance parameters; The verification module is connected to the optimization control module, imports the optimized gap parameters into the dynamic simulation software, generates the thread load distribution and stress simulation results, compares the theoretical value with the simulation value, and verifies whether the error meets the requirements.

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