Method for calculating spline engagement characteristics based on time-varying engagement position

Abstract

The application discloses a spline engagement characteristic calculation method based on time-varying engagement position, comprising: establishing a spline engagement state representation model of a spline; obtaining spline tooth side clearance and pressure angle of the spline containing parallel misalignment through the spline engagement state representation model; establishing a spline single-tooth engagement stiffness calculation model through the potential energy method and the spline tooth side clearance and pressure angle; obtaining spline tooth engagement deformation coordination conditions according to the spline single-tooth engagement stiffness calculation model; obtaining a spline engagement deformation calculation method of the spline according to the spline tooth engagement deformation coordination conditions; establishing a spline engagement force model containing parallel misalignment according to the spline engagement deformation calculation method; and obtaining spline engagement characteristics of the spline according to the spline engagement force model. The spline engagement force model containing parallel misalignment is established, so that the spline engagement characteristics can be more accurately described, and the design of a high-speed, high-reliability and low-vibration mechanical transmission system is facilitated.

Description

Technical Field

[0001] This invention relates to the field of gear design technology, and in particular to a method for calculating spline meshing characteristics based on time-varying meshing positions. Background Technology

[0002] Involute splines are widely used in various transmission systems for power transmission between the host machine and the actuator. Due to installation space limitations and the non-uniform mass of the shaft system, parallel misalignment errors are unavoidable, causing changes in the spline meshing position and affecting the spline's meshing characteristics. Existing research largely assumes that parallel misalignment does not significantly affect the spline tooth meshing position, leading to inaccurate calculations of spline meshing characteristics. As mechanical transmission mechanisms develop towards higher speeds, higher reliability, and lower vibrations, existing methods for calculating spline meshing characteristics are insufficient to provide theoretical support for spline structure design. Summary of the Invention

[0003] This invention provides a method for calculating spline meshing characteristics based on time-varying meshing positions, which solves the problem in the prior art that the assumption that parallel misalignment will not significantly affect the meshing position of spline teeth leads to inaccurate calculation of spline meshing characteristics.

[0004] On one hand, embodiments of the present invention provide a method for calculating spline meshing characteristics based on time-varying meshing positions, including:

[0005] Establish a spline meshing state characterization model;

[0006] The backlash and pressure angle of the spline teeth, including those with parallel misalignment, are obtained through the spline meshing state characterization model.

[0007] A calculation model for the meshing stiffness of a single spline tooth with parallel misalignment is established using the potential energy method, the spline tooth backlash, and the pressure angle.

[0008] The spline tooth meshing deformation compatibility condition is obtained based on the spline single-tooth meshing stiffness calculation model.

[0009] The spline meshing deformation calculation method is obtained based on the spline tooth meshing deformation compatibility condition.

[0010] A spline meshing force model containing parallel misalignment is established based on the spline meshing deformation calculation method described above.

[0011] The spline meshing characteristics are obtained based on the spline meshing force model.

[0012] In one possible implementation, the spline engagement state characterization model includes:

[0013] A spline meshing state characterization model is established based on the pitch circle, index circle, and meshing point of the standard spline.

[0014] In one possible implementation, obtaining the backlash and pressure angle of the spline teeth, including those with parallel misalignment, through the spline meshing state characterization model includes:

[0015] The displacement data of the external spline in the parallel misalignment state is obtained by moving the actual tooth position of the external spline on the spline meshing state characterization model;

[0016] Based on the displacement data of the external spline in the parallel misalignment state, the time-varying backlash change and pressure angle of the spline containing parallel misalignment are obtained;

[0017] The backlash of the spline teeth, including those with parallel misalignment, is obtained based on the time-varying backlash variation of the spline.

[0018] In one possible implementation, establishing a calculation model for the meshing stiffness of a single spline tooth containing parallel misalignment using the potential energy method, the spline tooth backlash, and the pressure angle includes:

[0019] Calculate the single-tooth bending stiffness, shear stiffness, and axial compressive stiffness of the external and internal splines of the spline;

[0020] Based on the single-tooth bending stiffness, shear stiffness, axial compressive stiffness, and the establishment of the calculation model for the meshing stiffness of the single-tooth spline containing parallel misalignment.

[0021] In one possible implementation, establishing a calculation model for the meshing stiffness of a single spline tooth containing parallel misalignment using the potential energy method, the spline tooth backlash, and the pressure angle includes:

[0022] Calculate the single-tooth bending stiffness, shear stiffness, and axial compressive stiffness of the external and internal splines of the spline;

[0023] Based on the single-tooth bending stiffness, shear stiffness, axial compressive stiffness, and the establishment of the calculation model for the meshing stiffness of the single-tooth spline containing parallel misalignment.

[0024] In one possible implementation, the step of obtaining the spline tooth meshing deformation compatibility condition based on the spline single-tooth meshing stiffness calculation model includes:

[0025] The spline front and back meshing deformations are calculated using a single-tooth meshing stiffness calculation model under the parallel misalignment state of the spline.

[0026] In one possible implementation, the method for calculating the spline meshing deformation based on the spline tooth meshing deformation compatibility condition includes:

[0027] The spline meshing force of the spline is calculated using the spline meshing deformation calculation method.

[0028] A method for calculating the spline meshing deformation by using the spline meshing force.

[0029] The spline meshing characteristic calculation method based on time-varying meshing position in this invention has the following advantages:

[0030] Establishing a spline meshing force model that includes parallel misalignment can more accurately describe spline meshing characteristics, which is of great significance for the design of high-speed, high-reliability, and low-vibration mechanical transmission systems. Attached Figure Description

[0031] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0032] Figure 1 A flowchart illustrating the method for calculating spline meshing characteristics based on time-varying meshing positions provided in this application embodiment;

[0033] Figure 2 A schematic diagram of spline meshing with parallel misalignment, illustrating the spline meshing characteristic calculation method based on time-varying meshing position provided in this application embodiment;

[0034] Figure 3 A schematic diagram of a single-tooth spline meshing state with parallel misalignment, provided for the spline meshing characteristic calculation method based on time-varying meshing position in the embodiments of this application.

[0035] Figure 4 A schematic diagram of the external spline meshing state of the spline meshing characteristic calculation method based on time-varying meshing position provided in the embodiments of this application;

[0036] Figure 5 A schematic diagram of the internal spline meshing state of the spline meshing characteristic calculation method based on time-varying meshing position provided in the embodiments of this application;

[0037] Figure 6 A schematic diagram of the coordinate transformation of K1' and K2' in the spline meshing characteristic calculation method based on time-varying meshing position provided in the embodiments of this application;

[0038] Figure 7 A schematic diagram of an external spline cantilever beam model for calculating spline meshing characteristics based on time-varying meshing position, as provided in the embodiments of this application;

[0039] Figure 8 A schematic diagram of an internal spline cantilever beam model for the spline meshing characteristic calculation method based on time-varying meshing position provided in the embodiments of this application;

[0040] Figure 9 A geometrical schematic diagram of the external spline root circle for the spline meshing characteristic calculation method based on time-varying meshing position provided in the embodiments of this application;

[0041] Figure 10 A geometrical schematic diagram of the internal spline root circle for the spline meshing characteristic calculation method based on time-varying meshing position provided in the embodiments of this application;

[0042] Figure 11 A comparison of spline meshing forces considering and not considering the time-varying meshing position when the parallel misalignment is 50 μm, according to the spline meshing characteristic calculation method based on time-varying meshing position provided in the embodiments of this application. Detailed Implementation

[0043] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0044] Figure 1 This is a flowchart illustrating the method for calculating spline meshing characteristics based on time-varying meshing positions according to an embodiment of the present invention. The embodiment of the present invention provides a method for calculating spline meshing characteristics based on time-varying meshing positions, including:

[0045] Establish a spline meshing state characterization model;

[0046] The backlash and pressure angle of the spline teeth, including those with parallel misalignment, are obtained through the spline meshing state characterization model.

[0047] A calculation model for the meshing stiffness of a single spline tooth with parallel misalignment is established using the potential energy method, the spline tooth backlash, and the pressure angle.

[0048] The spline tooth meshing deformation compatibility condition is obtained based on the spline single-tooth meshing stiffness calculation model.

[0049] The spline meshing deformation calculation method is obtained based on the spline tooth meshing deformation compatibility condition.

[0050] A spline meshing force model containing parallel misalignment is established based on the spline meshing deformation calculation method described above.

[0051] The spline meshing characteristics are obtained based on the spline meshing force model.

[0052] The spline engagement state characterization model includes:

[0053] A spline meshing state characterization model is established based on the pitch circle, index circle, and meshing point of the standard spline.

[0054] The backlash and pressure angle of the spline teeth, including those with parallel misalignment, obtained through the spline meshing state characterization model include:

[0055] The displacement data of the external spline in the parallel misalignment state is obtained by moving the actual tooth position of the external spline on the spline meshing state characterization model;

[0056] Based on the displacement data of the external spline in the parallel misalignment state, the time-varying backlash change and pressure angle of the spline containing parallel misalignment are obtained;

[0057] The backlash of the spline teeth, including those with parallel misalignment, is obtained based on the time-varying backlash variation of the spline.

[0058] A calculation model for the meshing stiffness of a single spline tooth containing parallel misalignment is established using the potential energy method, the spline tooth backlash, and the pressure angle, including:

[0059] Calculate the single-tooth bending stiffness, shear stiffness, and axial compressive stiffness of the external and internal splines of the spline;

[0060] Based on the single-tooth bending stiffness, shear stiffness, axial compressive stiffness, and the establishment of the calculation model for the meshing stiffness of the single-tooth spline containing parallel misalignment.

[0061] The spline tooth meshing deformation compatibility conditions obtained from the spline single-tooth meshing stiffness calculation model include:

[0062] The spline front and back meshing deformations are calculated using a single-tooth meshing stiffness calculation model under the parallel misalignment state of the spline.

[0063] The method for calculating the spline meshing deformation based on the spline meshing deformation compatibility condition includes:

[0064] The spline meshing force of the spline is calculated using the spline meshing deformation calculation method.

[0065] A method for calculating the spline meshing deformation by using the spline meshing force.

[0066] For example, firstly, a spline meshing state characterization model is established to obtain the backlash and pressure angle of spline teeth with parallel misalignment; then, based on the potential energy method, a calculation model for the meshing stiffness of a single spline tooth with parallel misalignment is established according to the magnitude of the spline tooth pressure angle; finally, based on the spline tooth meshing deformation compatibility condition, a calculation method for spline meshing deformation is proposed, and a spline meshing force model with parallel misalignment is established. The overall calculation process is as follows: Figure 1 As shown.

[0067] First, a spline meshing state characterization model is established, including the single-tooth meshing state of splines with parallel misalignment, such as... Figure 3 As shown. For a normal spline, the pitch circle and the index circle coincide, and the meshing point is K1 (K2) (K1 is located on the external spline tooth, and K2 is located on the internal spline tooth). When there is a parallel misalignment error in the spline, assuming the internal spline is fixed, the actual tooth position of the external spline moves along the tooth profile symmetry line. At this point, the external spline engagement point becomes K. 1' The internal spline engagement point becomes K. 2' Assume that the distance K2 moves along the line of symmetry of the tooth profile is 0.5. Then the pitch circle radius of any tooth in a spline containing parallel misalignment is:

[0068] (1)

[0069] In the formula, and The pitch circle radius and number of teeth of the spline; Internal spline engagement point The perpendicular distance to the symmetry line of the external spline tooth shape is calculated according to formula (8); The equivalent misalignment of any tooth in a spline is calculated using the following formula:

[0070] (2)

[0071] In the formula, and For inner / outer spline edges x and y Displacement in direction; E mis and For parallel misalignment and phase angle; Let be the position angle of any tooth, and its calculation formula is:

[0072] (3)

[0073] In the formula, j For the tooth mark; θ e This represents the angular displacement of the external spline.

[0074] A schematic diagram of the external spline engagement state is shown below. Figure 4 As shown in the figure, there are two coordinate systems: one is the global coordinate system (…). X G , Y G The other is a local coordinate system used to determine the coordinates of the external spline meshing line. X Le , Y Le In the local coordinate system ( X Le , Y Le In ), K 1' Coordinates can be represented as:

[0075] (4)

[0076] In the formula, r b It is the base circle radius; It is the external spline in K 1' The pressure angle of a point is expressed as:

[0077] (5)

[0078] A schematic diagram of the internal spline engagement state is shown below. Figure 5 As shown in the figure, the local coordinate system ( X Li , Y Li This is used to determine the coordinates of the involute of the external spline. In the local coordinate system ( X Li , Y Li In the diagram, the coordinates of K2' can be represented as:

[0079] (6)

[0080] In the formula, It is the internal spline K 2' The pressure angle of a point is expressed as:

[0081] (7)

[0082] based on Figure 5 The geometric relationship in the diagram is as follows: The perpendicular distance from the meshing point K2' of the internal spline tooth to the line of symmetry of the external spline tooth profile is:

[0083] (8)

[0084] In the formula, K2' is the angle between the line of engagement at the meshing point and the tooth thickness direction; α2 represents the half-tooth angle. Their calculation formula is:

[0085] (9)

[0086] (10)

[0087] In the above formula This is the pressure angle at the spline pitch circle. When the external spline rotates a certain angle to mesh with the internal spline, K1' and K2' coincide. By solving for the rotation angle, the time-varying backlash of the spline, including parallel misalignment, can be calculated. This angle can be calculated based on the coordinates of K1' and K2' in the global coordinate system, such as... Figure 6 As shown. The coordinates of K1' in the global coordinate system are:

[0088] (11)

[0089] The coordinates of K2' in the global coordinate system are:

[0090] (12)

[0091] Therefore, the rotation angle is:

[0092] (13)

[0093] The change in spline backlash caused by parallel misalignment is:

[0094] (14)

[0095] The time-varying backlash of the spline teeth is:

[0096] (15)

[0097] In the formula, b s0 This is the initial side clearance.

[0098] Secondly, the spline single-tooth meshing stiffness model containing parallel misalignment is constructed as follows:

[0099] Considering the influence of time-varying spline meshing position caused by parallel misalignment, the equivalent cantilever beam model of internal and external splines is as follows: Figure 7 , 8 As shown in Figures 9 and 10, the bending stiffness, shear stiffness, and axial compressive stiffness of its single tooth are:

[0100] (16)

[0101] (17)

[0102] (18)

[0103] (19)

[0104] (20)

[0105] (twenty one)

[0106] In the formula, K be / i , K se / i and K ae / i These are the bending stiffness, shear stiffness, and axial compressive stiffness of a single tooth in an external / internal spline. E , G and v These are Young's modulus, shear modulus, and Poisson's ratio, respectively. β The distance from the starting point of the involute tooth profile on the root fillet x The angle between the radius of the root circle at point 1 and the perpendicular line to the line of symmetry of the tooth profile passing through the center of the root fillet; β 0 is the angle between the radius of the root fillet at the starting point of the involute tooth profile of the external spline and the perpendicular line to the line of symmetry of the tooth profile passing through the center of the root fillet. β 1 is the angle between the radius of the root fillet at the end of the external spline tooth root fillet and the perpendicular line to the line of symmetry of the tooth profile passing through the center of the root fillet; β i0 It is the angle between the radius of the root fillet at the starting point of the involute tooth profile of the internal spline and the perpendicular line to the line of symmetry of the tooth profile passing through the center of the root fillet. β i1 It is the angle between the radius of the root fillet at the end of the internal spline and the perpendicular line to the line of symmetry of the tooth profile passing through the center of the root fillet; γ 1'、 d 1'、 h e '、 d i 'and h i The angle between the perpendicular line of the meshing line at point K2 and the line of symmetry of the tooth profile, the distance from the intersection of the external spline root circle and the involute tooth profile to the meshing point along the line of symmetry of the tooth profile, the perpendicular distance from the meshing point of the external spline to the line of symmetry of the tooth profile, the distance from the intersection of the internal spline root circle and the involute tooth profile to the meshing point along the line of symmetry of the tooth profile, and the perpendicular distance from the meshing point of the internal spline to the line of symmetry of the tooth profile are expressed as follows:

[0107] (twenty two)

[0108] (twenty three)

[0109] (twenty four)

[0110] (25)

[0111] (26)

[0112] The meshing stiffness of a single spline tooth is:

[0113] (27)

[0114] In the formula, K fe , K fi and K h These are the external spline matrix stiffness, internal spline matrix stiffness, and Hertzian contact stiffness.

[0115] Finally, the meshing force model for a single tooth of a spline containing parallel misalignment is constructed as follows:

[0116] Considering the time-varying meshing position of the spline caused by parallel misalignment, the meshing deformation on the front side of the spline is as follows:

[0117] (28)

[0118] The dorsal meshing deformation is as follows:

[0119] (29)

[0120] The spline meshing force can be expressed as:

[0121] (30)

[0122] In the formula, F sj f / b The meshing force is between the front and back sides; C sj For meshing damping.

[0123] Comparison of spline meshing forces considering and not considering time-varying meshing positions when the parallel misalignment is 50 μm. Figure 11 As shown, the results indicate that when the parallel misalignment is 50 μm, the peak-to-peak values ​​of the spline meshing force considering the time-varying meshing position and not considering it are 1035.06 N and 275.49 N, respectively, with a difference of 759.57 N. The results demonstrate that neglecting the time-varying spline meshing position leads to a significant error in the spline meshing force, highlighting the importance of considering this factor.

[0124] Although preferred embodiments of the invention have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including both the preferred embodiments and all changes and modifications falling within the scope of the invention.

[0125] Obviously, those skilled in the art can make various modifications and variations to this invention without departing from its spirit and scope. Therefore, if these modifications and variations fall within the scope of the claims of this invention and their equivalents, this invention also intends to include these modifications and variations.

Claims

1. A method for calculating spline meshing characteristics based on time-varying meshing positions, characterized in that, include: Establish a spline meshing state characterization model; The backlash and pressure angle of the spline teeth, including those with parallel misalignment, are obtained through the spline meshing state characterization model. A calculation model for the meshing stiffness of a single spline tooth with parallel misalignment is established using the potential energy method, the spline tooth backlash, and the pressure angle. The spline tooth meshing deformation compatibility condition is obtained based on the spline single-tooth meshing stiffness calculation model. The spline meshing deformation calculation method is obtained based on the spline tooth meshing deformation compatibility condition. A spline meshing force model containing parallel misalignment is established based on the spline meshing deformation calculation method described above. Considering the time-varying meshing position of the spline caused by parallel misalignment, the meshing deformation on the front side of the spline is as follows: The dorsal meshing deformation is as follows: The spline meshing force can be expressed as: In the formula, F sj f / b The meshing force is between the front and back sides; C sj For meshing damping, x e and x i For external splines and internal splines in x Displacement in the axial direction; y e and y i For external splines and internal splines in y Displacement in the axial direction; θ e and θ i For the angular displacement of the external and internal splines; E mis and φ mis For parallel misalignment and misalignment phase; φ sj For the spline number j The position angle of each tooth; r b and b s For the base circle radius and tooth flank clearance of the spline; α 0 ' and α 0 '' The pressure angles of the external and internal splines after the change of the engagement point; The spline meshing characteristics are obtained based on the spline meshing force model.

2. The method for calculating spline meshing characteristics based on time-varying meshing position according to claim 1, characterized in that, The spline engagement state characterization model includes: A spline meshing state characterization model is established based on the pitch circle, index circle, and meshing point of the standard spline.

3. The method for calculating spline meshing characteristics based on time-varying meshing position according to claim 1, characterized in that, The backlash and pressure angle of the spline teeth, including those with parallel misalignment, obtained through the spline meshing state characterization model include: The displacement data of the external spline in the parallel misalignment state is obtained by moving the actual tooth position of the external spline on the spline meshing state characterization model; Based on the displacement data of the external spline in the parallel misalignment state, the time-varying backlash change and pressure angle of the spline containing parallel misalignment are obtained; The backlash of the spline teeth, including those with parallel misalignment, is obtained based on the time-varying backlash variation of the spline.

4. The method for calculating spline meshing characteristics based on time-varying meshing position according to claim 1, characterized in that, A calculation model for the meshing stiffness of a single spline tooth containing parallel misalignment is established using the potential energy method, the spline tooth backlash, and the pressure angle, including: Calculate the single-tooth bending stiffness, shear stiffness, and axial compressive stiffness of the external and internal splines of the spline; Based on the bending stiffness, shear stiffness, axial compressive stiffness of the single tooth, and the backlash and pressure angle of the spline tooth, a calculation model for the meshing stiffness of the spline single tooth with parallel misalignment is established.

5. The method for calculating spline meshing characteristics based on time-varying meshing position according to claim 1, characterized in that, The spline tooth meshing deformation compatibility conditions obtained from the spline single-tooth meshing stiffness calculation model include: The spline front and back meshing deformations are calculated using a single-tooth meshing stiffness calculation model under the parallel misalignment state of the spline.

6. The method for calculating spline meshing characteristics based on time-varying meshing position according to claim 1, characterized in that, The method for calculating the spline meshing deformation based on the spline meshing deformation compatibility condition includes: The spline meshing force of the spline is calculated using the spline meshing deformation calculation method. A method for calculating the spline meshing deformation by means of the spline meshing force.

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