Friction plate spline engagement stiffness calculation method considering installation error

Abstract

The application discloses a kind of friction plate spline engagement stiffness calculation methods considering installation error, comprising the following steps: S1: obtaining installation parameter, determine the eccentric distance of inner hub installation position and theoretical position;S2: construct spline engagement position calculation model, obtain the horizontal distance of friction plate spline engagement point to base circle under the condition of considering installation error;S3: based on coordinate transformation, the angle range of variation is obtained;S4: according to the angle range, the engagement stiffness of inner hub spline and friction plate spline is calculated, and the engagement stiffness includes bending, shear and axial compression stiffness.The application considers installation error, calculates the horizontal distance of friction plate spline actual engagement point to base circle, thereby obtaining the angle variation range, and then obtains the engagement stiffness of friction plate spline through stiffness calculation model, avoids the influence of installation error on stiffness, so as to improve the accuracy and reliability of stiffness.

Description

Technical Field

[0001] This invention relates to the field of friction plate technology, and in particular to a method for calculating the spline meshing stiffness of friction plates that takes into account installation errors. Background Technology

[0002] Spline drive systems are important rotating mechanical systems widely used in automobiles, aerospace, shipbuilding, and railways. The dynamic behavior of spline systems is closely related to the vibration and noise problems caused by spline impact internal excitation, which is crucial for machine operation and spline durability. Furthermore, one of the most important internal excitations in friction plate spline drives is stiffness excitation. Therefore, accurately calculating the meshing stiffness of friction plate splines is of great significance for the dynamic system.

[0003] Existing methods do not consider deviations in installation position when calculating meshing stiffness. In actual installation, the position of the spline on the friction plate may deviate, causing errors between the calculated and actual meshing stiffness, reducing accuracy, and failing to provide accurate data support for meshing stiffness analysis. Summary of the Invention

[0004] To address the technical problem of reduced accuracy in existing technologies when calculating meshing stiffness without considering installation errors, this invention proposes a method for calculating the meshing stiffness of friction plate splines that takes installation errors into account. By considering installation errors, the meshing stiffness of friction plate splines is calculated, thereby improving accuracy.

[0005] To achieve the above objectives, the present invention provides the following technical solution:

[0006] A method for calculating the spline meshing stiffness of friction plates considering installation errors includes the following steps:

[0007] S1: Obtain installation parameters and determine the eccentricity between the inner hub installation position and the theoretical position;

[0008] S2: Construct a calculation model for the spline meshing position, and combine it with the eccentric distance to obtain the horizontal distance from the spline meshing point of the friction plate to the base circle under the condition of considering installation error;

[0009] S3: Based on coordinate transformation, obtain the range of angle change of the spline meshing point of the friction plate considering installation error, and calculate the pressure angle corresponding to the spline meshing point of the friction plate considering installation error;

[0010] S4: Calculate the meshing stiffness of the friction plate spline transmission system based on the pressure angle corresponding to the spline meshing point of the friction plate under the condition of angle variation range and considering installation error. Meshing stiffness includes bending, shear and axial compression stiffness.

[0011] Preferably, in step S1, the formula for calculating the eccentricity distance is:

[0012] d=e sin(θ) (1)

[0013] In formula (1), d represents the eccentric distance between the installation position and the theoretical position; e represents the eccentricity; and θ represents the eccentric angle.

[0014] Preferably, the eccentricity angle of the j-th spline tooth can be determined by the following formula:

[0015]

[0016] In formula (2), θ j The eccentricity angle of the j-th spline tooth is represented by θ0; the initial rotation angle is ω; the rotational angular velocity is ω; the rotation time is t; N represents the number of spline teeth; d j This represents the eccentricity distance of the j-th spline tooth.

[0017] Preferably, in step S2, the calculation model for the spline engagement position is as follows:

[0018] x P' =R b [(α P +α2)sinα P +cosα P -cosα2]+d (3)

[0019] In formula (3), x P' R represents the horizontal distance from the spline engagement point of the friction plate to the base circle, taking installation errors into account. b Indicates the base circle radius; α P α1 represents the pressure angle corresponding to the theoretical point of spline engagement of the friction plate; α2 represents the tooth half angle; d represents the eccentricity distance between the installation position and the theoretical position.

[0020] Preferably, in step S3, the formula for calculating the range of angle variation is:

[0021] α=-α2:dt:ψ,

[0022] x P =R b [(α+α2)sinα P +cosα-cosα2] (4)

[0023] In formula (4), α2 represents the tooth half-angle, dt is the step size, and α is the range of angle variation; ψ represents the central angle corresponding to the addendum circle of the friction plate spline tooth; x P This represents the horizontal distance from the spline engagement point of the friction plate to the base circle, without considering installation errors; α P This indicates the pressure angle corresponding to the spline engagement point of the friction plate without considering installation errors.

[0024] Preferably, in step S3, the formula for calculating the pressure angle corresponding to the spline engagement point of the friction plate, considering installation errors, is as follows:

[0025] x P =x' P →α' P (5)

[0026] In formula (5), x P This represents the horizontal distance from the spline engagement point of the friction plate to the base circle, without considering installation errors; x P' This represents the horizontal distance from the spline engagement point of the friction plate to the base circle, taking installation errors into account; α' P This indicates the pressure angle corresponding to the spline engagement point of the friction plate, taking into account installation errors.

[0027] Preferably, step S4 includes the following steps:

[0028] S4-1: Calculate the bending, shear, and axial compressive stiffness of the inner hub spline. The calculation formula is as follows:

[0029]

[0030] In formula (6), K b1 Indicates the bending stiffness of the inner hub spline; K S1 K represents the shear stiffness of the inner hub spline; a1 α represents the axial compressive stiffness of the inner hub spline; α2 represents the tooth half-angle; α P The pressure angle corresponding to the spline engagement point of the friction plate is not considered for installation errors; α represents the changing angle, E represents the elastic modulus, W represents the effective contact length, and ν represents Poisson's ratio.

[0031] S4-2: Calculate the bending, shear, and axial compressive stiffness of the friction plate spline. The calculation formula is as follows:

[0032]

[0033]

[0034]

[0035] In formula (7), K b2 K represents the bending stiffness of the friction plate spline; S2 K represents the shear stiffness of the friction plate spline; a2 ψ represents the axial compressive stiffness of the friction spline; ψ represents the central angle corresponding to the tip circle of the friction spline teeth; α P' This represents the pressure angle corresponding to the spline engagement point of the friction plate, considering installation errors; α2 represents the tooth half angle; α PThe pressure angle corresponding to the spline engagement point of the friction plate is not considered for installation errors; α represents the changing angle, E represents the elastic modulus, W represents the effective contact length, and v represents Poisson's ratio.

[0036] S4-3: The meshing stiffness of the friction plate spline transmission system is obtained according to formulas (6) and (7):

[0037]

[0038] In formula (8), K st K represents the meshing stiffness of the friction plate spline transmission system. bi Indicates bending stiffness; K ai Indicates axial compressive stiffness; K Si Shear stiffness; K fi Indicates matrix stiffness; K hz This indicates the Hertzian contact stiffness.

[0039] Preferably, the method further includes step S5: selecting point N at the pitch circle of the inner hub, the point where point N contacts the friction plate when moved horizontally is point N”, and the point on the pitch circle of the friction plate teeth is point N’, thus forming a right triangle ΔN”NN’, where angle N”NN’ is a right angle, and constructing a position error critical value calculation model:

[0040]

[0041] In formula (9), N”N represents the maximum installation error; c represents the tooth flank clearance; α0 represents the spline pressure angle; m represents the spline module; c * h represents the top void coefficient; c This indicates the tooth tip clearance.

[0042] In summary, by adopting the above technical solution, the present invention has at least the following beneficial effects compared with the prior art:

[0043] This invention calculates the horizontal distance from the actual meshing point of the friction plate spline to the base circle while considering installation errors, thereby obtaining the angle variation range. Then, the spline meshing stiffness of the friction plate is obtained through a stiffness calculation model, avoiding the influence of installation errors on stiffness and thus improving the accuracy and reliability of stiffness. Attached image description:

[0044] Figure 1 This is a schematic diagram of a method for calculating the spline meshing stiffness of a friction plate considering installation errors, according to an exemplary embodiment of the present invention.

[0045] Figure 2 This is a schematic diagram of the installation error of the inner hub and friction plate according to an exemplary embodiment of the present invention.

[0046] Figure 3This is a schematic diagram of a position error critical value calculation model according to an exemplary embodiment of the present invention.

[0047] Figure 4 This is a schematic diagram illustrating the principle of a spline meshing position calculation model according to an exemplary embodiment of the present invention. Detailed Implementation

[0048] The present invention will be further described in detail below with reference to embodiments and specific implementation methods. However, this should not be construed as limiting the scope of the above-described subject matter of the present invention to the following embodiments; all technologies implemented based on the content of the present invention fall within the scope of the present invention.

[0049] In the description of this invention, it should be understood that the terms "longitudinal", "lateral", "up", "down", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on this invention.

[0050] like Figure 1 As shown, this invention provides a method for calculating the spline meshing stiffness of friction plates considering installation errors, specifically including the following steps:

[0051] S1: Obtain installation parameters and determine the eccentricity between the inner hub installation position and the theoretical position.

[0052] In this embodiment, when the inner hub is mounted on the friction plate, theoretically, the centers of the two should coincide. For example... Figure 2 As shown, during installation, considering installation errors, the installation position will deviate from the theoretical position. Therefore, the obtained installation parameters include the deviation between the two centers, i.e., the eccentricity e, the initial eccentricity angle θ (the angle between the inner hub tooth centerline and the horizontal position of the center), and the radius R of the friction plate. p .

[0053] The formula for calculating the eccentricity between the installation location and the theoretical location is:

[0054] d=e sin(θ) (1)

[0055] In formula (1), d represents the eccentric distance between the installation position and the theoretical position; e represents the eccentricity; and θ represents the eccentric angle.

[0056] S2: Based on the spline tooth clearance parameters of the inner hub and friction plate, construct a calculation model for the critical value of position error and output the maximum installation error.

[0057] In this embodiment, as Figure 3As shown, a right triangle ΔN”NN’ is selected in the spline tooth backlash (N is at the pitch circle on the inner hub, and N” and N’ are on the friction plate, representing the point where N contacts the friction plate when moving horizontally and the point on the pitch circle of the friction plate tooth, respectively). Then N”N is the maximum installation error, and N’N is the tooth backlash c. The minimum value of the tooth backlash c is c. min .

[0058] The model for calculating the critical value of position error is as follows:

[0059]

[0060] In formula (2), N”N represents the maximum installation error; c represents the tooth flank clearance, which has a design standard value; α0 represents the spline pressure angle; m represents the spline module; c * This represents the headspace coefficient, typically taken as 0.25; h c This indicates the tooth tip clearance.

[0061] S3: Construct a calculation model for the spline meshing position to obtain the horizontal distance from the spline meshing point of the friction plate to the base circle of the friction plate.

[0062] like Figure 4 As shown, the spline teeth are modeled as a cantilever beam. In theory, the theoretical engagement point of the friction plate spline is point P, and the height of point P from the center O of the base circle is h. P The horizontal distance between point P and the base circle is x. P The corresponding pressure angle is α. P However, considering installation errors, the spline engagement point of the friction plate will shift (forward or backward), meaning the actual point is P', and the height of point P' from the center O of the base circle is h. P' The horizontal distance between point P' and the base circle is x. P' The corresponding pressure angle is α. P' .

[0063] In this embodiment, the calculation model for the spline engagement position is as follows:

[0064] x P' =R b [(α P +α2)sinα P +cosα P -cosα2]+d (3)

[0065] In formula (3), x P' R represents the horizontal distance from the spline engagement point of the friction plate to the base circle, taking installation errors into account. b Indicates the base circle radius; α P α1 represents the pressure angle corresponding to the theoretical point of spline engagement of the friction plate; α2 represents the tooth half angle; d represents the eccentricity distance between the installation position and the theoretical position.

[0066] In this embodiment, the positional errors of different spline teeth are not the same, so the eccentric angles will also be different. The eccentric angle of the j-th spline tooth can be determined by the following formula:

[0067]

[0068] In formula (4), θ j θj represents the eccentricity angle of the j-th spline tooth; θ0 is the initial rotation angle (the angle between the center lines of adjacent teeth at the horizontal position); ω is the rotational angular velocity; t is the rotation time; N represents the number of spline teeth; d j This represents the eccentricity distance of the j-th spline tooth.

[0069] S4: Based on the coordinate transformation, the angle variation range is obtained, and then the pressure angle corresponding to the spline meshing point of the friction plate is calculated considering the installation error.

[0070] The stiffness integral interval is from the tooth half-angle to the meshing point. Considering the position error, the meshing point changes as follows, and the corresponding angle change range (the angle between the changed meshing point and the center of the friction plate base circle) can be obtained by coordinate transformation. The algorithm is shown in the formula.

[0071] α=-α2:dt:ψ,

[0072] x P =R b [(α+α2)sinα P +cosα-cosα2] (5)

[0073] In formula (5), α2 represents the tooth half-angle, dt represents the step size, α represents the angle variation range; ψ represents the central angle corresponding to the addendum circle of the friction plate spline tooth; x P This represents the horizontal distance from the spline engagement point of the friction plate to the base circle, without considering installation errors; α P This indicates the pressure angle corresponding to the spline engagement point of the friction plate without considering installation errors.

[0074] In this embodiment, considering installation errors, the formula for calculating the pressure angle corresponding to the spline engagement point of the friction plate is as follows:

[0075] x P =x' P →α' P (6)

[0076] In formula (6), x P This represents the horizontal distance from the spline engagement point of the friction plate to the base circle, without considering installation errors; x P' This represents the horizontal distance from the spline engagement point of the friction plate to the base circle, taking installation errors into account; α' PThis indicates the pressure angle corresponding to the spline engagement point of the friction plate, taking into account installation errors.

[0077] S5: Calculate the meshing stiffness of the friction plate spline transmission system based on the pressure angle corresponding to the meshing point of the friction plate spline under the condition of angle variation range and considering installation error. Meshing stiffness includes bending, shear and axial compression stiffness.

[0078] In this embodiment, the formulas for calculating the bending, shear, and axial compressive stiffness of the inner hub spline are as follows:

[0079]

[0080] In formula (7), K b1 Indicates the bending stiffness of the inner hub spline; K S1 K represents the shear stiffness of the inner hub spline; a1 α represents the axial compressive stiffness of the inner hub spline; α2 represents the tooth half-angle; α P The pressure angle corresponding to the spline engagement point of the friction plate is not considered under the condition of installation error; α represents the angle variation range; E represents the elastic modulus; W represents the effective contact length; v represents Poisson's ratio.

[0081] In this embodiment, the formulas for calculating the bending, shear, and axial compressive stiffness of the friction plate spline are as follows:

[0082]

[0083]

[0084] In formula (8), K b2 K represents the bending stiffness of the friction plate spline; S2 K represents the shear stiffness of the friction plate spline; a2 ψ represents the axial compressive stiffness of the friction spline; ψ represents the central angle corresponding to the tip circle of the friction spline teeth; α P' This represents the pressure angle corresponding to the spline engagement point of the friction plate, considering installation errors; α2 represents the tooth half angle; α P The pressure angle corresponding to the spline engagement point of the friction plate is not considered under the condition of installation error; α represents the angle variation range; E represents the elastic modulus; W represents the effective contact length; v represents Poisson's ratio.

[0085] Then, according to formulas (7) and (8), the meshing stiffness of the friction plate spline transmission system can be obtained:

[0086]

[0087] In formula (9), K st K represents the meshing stiffness of the friction plate spline transmission system. bi Indicates bending stiffness; K aiIndicates axial compressive stiffness; K Si Shear stiffness; K fi Indicates matrix stiffness; K hz This indicates the Hertzian contact stiffness.

[0088] Those skilled in the art will understand that the above embodiments are specific examples of implementing the present invention, and in practical applications, various changes in form and detail may be made without departing from the spirit and scope of the present invention.

Claims

1. A method for calculating the spline meshing stiffness of friction plates considering installation errors, characterized in that, Specifically, the following steps are included: S1: Obtain installation parameters and determine the eccentricity between the inner hub installation position and the theoretical position; S2: Construct a calculation model for the spline meshing position, and combine it with the eccentric distance to obtain the horizontal distance from the spline meshing point of the friction plate to the base circle under the condition of considering installation error; S3: Based on coordinate transformation, obtain the range of angle change of the spline meshing point of the friction plate considering installation error, and calculate the pressure angle corresponding to the spline meshing point of the friction plate considering installation error; S4: Calculate the meshing stiffness of the friction spline transmission system based on the pressure angle corresponding to the meshing point of the friction spline under the condition of angle variation range and considering installation error. Meshing stiffness includes bending, shear and axial compression stiffness. S4 includes the following steps: S4-1: Calculate the bending, shear, and axial compressive stiffness of the inner hub spline. The calculation formula is as follows: In formula (6), represents the bending stiffness of the inner hub spline; Indicates the shear stiffness of the inner hub spline; Indicates the axial compressive stiffness of the inner hub spline; Indicates the tooth half-angle; This indicates the pressure angle corresponding to the spline engagement point of the friction plate without considering installation errors; Indicates the change in angle. Indicates the elastic modulus. Indicates the effective contact length. Indicates Poisson's ratio; S4-2: Calculate the bending, shear, and axial compressive stiffness of the friction plate spline. The calculation formula is as follows: In formula (7), This indicates the bending stiffness of the friction plate spline; this indicates the shear stiffness of the friction plate spline. This indicates the axial compressive stiffness of the friction plate spline; This indicates the central angle corresponding to the tip circle of the spline teeth on the friction plate; This represents the pressure angle corresponding to the spline engagement point of the friction plate, taking installation errors into account. Indicates the tooth half-angle; This indicates the pressure angle corresponding to the spline engagement point of the friction plate without considering installation errors; Indicates the change in angle. Indicates the elastic modulus. Indicates the effective contact length. Indicates Poisson's ratio; S4-3: The meshing stiffness of the friction plate spline transmission system is obtained according to formulas (6) and (7): In formula (8), This indicates the meshing stiffness of the friction plate spline transmission system; Indicates bending stiffness; Indicates axial compressive stiffness; Shear stiffness; Indicates the stiffness of the matrix; This indicates the Hertzian contact stiffness.

2. The method for calculating the spline meshing stiffness of friction plates considering installation errors as described in claim 1, characterized in that, In S1, the formula for calculating the eccentricity distance is: In formula (1), Indicates the eccentricity distance between the installation position and the theoretical position; Indicates the eccentricity; Indicates the eccentric angle.

3. The method for calculating the spline meshing stiffness of friction plates considering installation errors as described in claim 2, characterized in that, The eccentricity angle of the j-th spline tooth can be determined by the following formula: In formula (2), This represents the eccentricity angle of the j-th spline tooth; This is the initial turning angle; It is the rotational angular velocity; t represents the rotation time; N represents the number of spline teeth; This represents the eccentricity distance of the j-th spline tooth.

4. The method for calculating the spline meshing stiffness of friction plates considering installation errors as described in claim 1, characterized in that, In S2, the calculation model for the spline engagement position is as follows: In formula (3), This represents the horizontal distance from the spline engagement point of the friction plate to the base circle, taking installation errors into account. Indicates the base circle radius; This represents the pressure angle corresponding to the theoretical engagement point of the friction plate spline; Indicates the tooth half-angle; This indicates the eccentricity between the installation location and the theoretical location.

5. The method for calculating the spline meshing stiffness of friction plates considering installation errors as described in claim 1, characterized in that, In S3, the formula for calculating the range of angle change is: In formula (4), This represents the tooth half-angle, and dt is the step size. The range of angle variation; This represents the central angle corresponding to the tip circle of the spline tooth of the friction plate; it also represents the horizontal distance from the spline meshing point of the friction plate to the base circle without considering installation errors. This indicates the pressure angle corresponding to the spline engagement point of the friction plate without considering installation errors.

6. The method for calculating the spline meshing stiffness of friction plates considering installation errors as described in claim 1, characterized in that, In S3, considering installation errors, the formula for calculating the pressure angle corresponding to the spline engagement point of the friction plate is as follows: In formula (5), This indicates the horizontal distance from the spline engagement point of the friction plate to the base circle, without considering installation errors. This represents the horizontal distance from the spline engagement point of the friction plate to the base circle, taking installation errors into account. This indicates the pressure angle corresponding to the spline engagement point of the friction plate, taking into account installation errors.

7. The method for calculating the spline meshing stiffness of friction plates considering installation errors as described in claim 1, characterized in that, It also includes step S5: Select point N at the pitch circle of the inner hub, and move point N horizontally to the point of contact with the friction plate. The point is the point on the pitch circle of the friction plate gear teeth. Points, then form a right triangle ,horn Assuming the angle is right, construct a model for calculating the critical value of position error: In formula (9), Indicates the maximum installation error; Indicates tooth flank clearance; Indicates the spline pressure angle; m represents the spline module; Indicates the top void coefficient; This indicates the tooth tip clearance.

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